# WAI Extension: Receipt Ledger

> Status: Draft. Registers the record `wai.delivery.ledger`: invoice lines a customer can
> recompute from the signed records WAI already defines. A seller and a buyer both sign a
> **tariff**, `WLT1`: one currency, and one price for each unit those records state, the
> units of a room session ([live-metering](live-metering.md) §4.4), the acknowledged bytes of
> each object class ([settlement](settlement.md) §3.3), the packages, entries and stored bytes
> of a package receipt ([packaging](packaging.md) §9), the counted impressions of a
> `wai.video.ssai` receipt of the break form ([live-ads](live-ads.md) §8,
> [ad-presentation](ad-presentation.md) §9.2) and the presentations of ads another party
> stitched ([stitched-presentation](stitched-presentation.md) §7.4); and the **scope** it
> covers, the rooms, the delivering parties, the packagers, and the ad deciders and stitchers
> whose records are billed under it. The
> ledger verifies each **source** by the extension that defines it, and the seller signs an
> **invoice**, `WLI1`, for a period: the records it was computed from, one line per source,
> unit and price, each line citing the records it came from, and the joules those records
> state, per scope and per acquisition class with their largest declared uncertainty, never
> summed across classes or scopes. Invoices under one tariff form a chain, and no record is
> billed in two of them. A verifier given the tariff, the invoice, the invoice before it and
> the sources recomputes every line and refuses an invoice that does not recompute. Beside the
> invoice, the ledger states two **reports**: the ad decisions reconciled against the players'
> presentation claims (for a stitched stream, stitched-presentation §7.5's own statement), and
> the delivery of each party under the one tariff with the bytes two parties were acknowledged
> for twice. A tariff of version 2 also prices **media jobs** (§4.5): a job is billed from
> its route record ([route-record](route-record.md)), its hops' OER/2 receipts and WAI's
> receipt of its output, in the units those receipts state. A tariff of version 3 prices a
> job by its capability **and its operation** (§4.6), since an encode and a decode spend
> different energy, and bills a job's **work** once, its route record and its hops' receipts,
> its output's receipt being the evidence a re-run may cite again (§6.9). A tariff of version 4
> also bills what the rest of the work spends (§4.7): a room's bytes out, which a room-session
> receipt of version 2 states (live-metering §4.4), at a price per 10^9 bytes; a package's work
> once per run that made it, by the work units it states, its receipt the product each run
> cites; a package's storage by byte-days for each period it is held; and its invoices state
> every hop's energy, the hops not billed in a scope of their own (§6.6). A tariff of version 6
> also prices a job **per endpoint**, and by the **usage** a third party's hop record states
> ([route-record](route-record.md) §6.2), and bills an upscale and a tone mapping by the subpixels
> their records state, each re-derived from what it read (§4.9). A tariff of version 7 also
> prices a **transmission** on a shared bearer (§4.10): the octets and pass time a publisher's
> schedule plans on a `multicast` or `unidirectional` instance it declared
> ([carousel](carousel.md) §5.4, [bearer-receipts](bearer-receipts.md) §4), at a price for each
> bearer class, unit and ceiling of the passes' rate, from a source that is a group with its
> declarations and its standing schedules or a node's own instance of one; an **aggregated
> impression** (§4.11), the count of an aggregate receipt ([impression-aggregates](impression-aggregates.md)),
> in a unit of its own; and an object an **agent consumed** (§4.12), from its consumption claims
> ([ai-usage](ai-usage.md) §6). A tariff of version 8 also prices **storage held over time**
> (§4.13), such as a stream's recent window or a clip cut from it, by byte-days, from a holder's
> **storage record** of a stored set over an interval, `WLH1`, whose byte-seconds the verifier
> recomputes from the holder's signed **snapshots** of what the set listed, `WLS1`, and refuses
> when they do not support it. A tariff of version 9 may **follow** another (§4.14): signed by
> both parties as every tariff is, it names the tariff whose chain it continues, so a scope or a
> price changed when a party's key is made or retired keeps the chain, the storage of what it
> holds and what it has billed once. Whatever the version,
> a job's output receipt is of an object its served hop states it delivered, where its route
> record states it (§5.1), and a route record's routing figures are never charges. No new transport, no payment
> and no tax: an invoice is the recomputable figures a payment rests on. The reference implementation is the
> `receipt_ledger` module of `wai-rs` (feature `receipt_ledger`) and the service
> `wai/wai-ledger`; the corpus is [`live-conformance/ledger/`](../live-conformance/ledger/),
> and its second implementation is `live-conformance/receipt_ledger_verify.py`.
> Keywords **MUST**, **MUST NOT**, **SHOULD**, **MAY** are RFC 2119/8174.
>
> Texts read for this revision: the WAI texts this one cites; ISO 4217 (the alphabetic
> currency code); RFC 8032; RFC 8259; FIPS 180-4.

## 1. Scope

In scope: how one tariff prices rooms, packages, HTTP and relayed delivery, ads, and in version 7
transmissions on shared bearers, aggregated impressions and what agents consume together, and in
version 8 storage held over time (§3); the tariff, its two signatures and its scope, and in version
9 a tariff that follows another, its chain continuing that tariff's (§4); the
snapshot and the storage record a holder signs (§4.13); the sources a ledger is given and what
each contributes (§5); the invoice, its records, lines, citations and energy, its signature and
its chain (§6); verification (§7); the two reports (§8); and the reference service (§9).

Out of scope: a transport; payment, a payment rail, tax and any contact with a party outside the
records; how a seller chooses its prices; how a party measures its energy, which
[energy-measurement](energy-measurement.md) governs; and the records themselves, which their own
extensions define, verify and leave as they are. The live-metering tariff and the settlement
statement's tariff keep their meaning: this extension reads them, and changes neither.

Relationship to the core spec: `wai.delivery.ledger` is a **record** ([SPEC](../SPEC.md) §5):
a signed record a WAI tool emits and verifies. It names no payload format and is not
dispatchable.

## 2. Terms

- **Seller**, **buyer**: Ed25519 keys (RFC 8032). The seller operates the ledger and signs its
  invoices; the buyer is the customer billed.
- **Holder** (version 8): an Ed25519 key that keeps objects for the buyer over time and signs what
  it kept (§4.13).
- **Time**: microseconds since 1970-01-01T00:00:00Z, the unit of a room's `t0` (live-rooms §3.1).
  A **period** is a span of time from its `start` (included) to its `end` (excluded).
- **Minor unit**: a currency's smallest unit (ISO 4217); an **amount** is an integer of
  millionths of one, as settlement §7.3's amounts are.
- **Source**: one record a ledger bills from, with what its own verifier is given (§5).
- **Record identity**: the 32 bytes a record of a kind is named by (§5.2).
- *u64*, *u32*, *u16*, *u8*: little-endian unsigned integers of that many bits. A **digest** is
  SHA-256 (FIPS 180-4), 32 bytes; **zero** of a key or digest field is 32 zero bytes.
- **Class**, **tag**, **unmetered marker**: an acquisition class of energy-measurement §2.7, its
  tag byte (2 `ModelBased`, 3 `Estimator`, 4 `OnChipCounter`, 5 `CalibratedInstrument`), and a
  figure of 0 with no class.

## 3. One tariff across rooms, packages and HTTP delivery

The records a deployment bills from state their units in their own terms. A room-session receipt
states microseconds and events (live-metering §4.4), and may state a `tariff` of its own, which
prices the session's grants against their funds ceilings (§4.6 there). A settlement statement
states acknowledged bytes by object class, whatever carried them: a relay over MOQT, or a cache
over HTTP whose deliveries were acknowledged as settlement §9.1 maps them; it may state a tariff
too, which prices its own lines (§7.3 there). A package receipt states entries and bytes
(packaging §9) and no tariff. An ad decision's receipt states impressions (live-ads §8.2) and
no tariff of the seller's; so does a stream another party stitched, whose stitcher signs a
pod-input record, `WSI1`, of the ads it chose and whose players sign a claim, `WSC1`, of each ad
presented (stitched-presentation §4, §5).

A tariff of this extension prices every one of those units in one currency, so one invoice bills
a buyer's rooms, deliveries, packages and ads together. Three rules keep every figure in it
consistent with what the records say:

1. **A record that states a tariff states this one.** A room-session receipt of a source either
   states no tariff (currency zero) or the tariff's currency and its room prices, in
   live-metering §4.1's order: the thirteen, and the price of bytes out, which a receipt of
   version 1 and a tariff of versions 1 to 3 do not state and read as 0; a settlement statement either states no tariff or the tariff's
   currency and its four delivery prices, in settlement §7.1's order. A record under another
   tariff is refused `tariff_conflict` (§7.2 step 5): the funds its grants were held to, or the
   amount its party stated, were computed at other prices, and an invoice at these prices would
   contradict it.
2. **One rounding, the same everywhere.** Every amount is a quantity times a price, divided by
   the unit's divisor and rounded down once per invoice line (§6.4), as settlement §7.3 rounds a
   statement's line. A statement's own amount rounds once per payer; the invoice rounds once per
   party and class, so the two can differ by less than one millionth of a minor unit per payer
   line, and the delivery report (§8.2) states both.
3. **Units are never converted.** A room is billed in its own units (in version 4, its bytes
   out too), a delivery in bytes, a package in packages, entries and stored bytes (in version
   4, in byte-days held), an ad in impressions, a job in jobs or in the subpixels its output's
   receipt states (§4.5), and in version 4 in the work units of the packages it made, and in version
   7 a transmission in the octets and the pass time its schedule states (§4.10), an aggregate
   receipt in its count (§4.11) and an agent's consumption in objects (§4.12), and in version 8 a
   holder's storage in the byte-seconds its records state, in whole byte-days (§4.13). No line turns one unit
   into another, and no line is priced from joules: the energy of an invoice is stated beside
   its lines (§6.6), per class, and is not an amount.

So the tariff is the one place prices live: a room receipt's funds verdicts, a statement's
amount and an invoice's lines all follow from it, and a buyer who holds the tariff and the
records recomputes all three.

## 4. The tariff

### 4.1 Layout

| field | size | meaning |
|---|---|---|
| `magic` | 4 | `WLT1` (ASCII) |
| `version` | 1 | 1; 2 for a tariff that prices jobs (§4.5); 3 for one that prices them per operation and bills their work (§4.6, §6.9); 4 for one that also prices bytes out, a package's work and its storage by byte-time (§4.7); 5 for one that holds a decode to its frames (§4.8); 6 for one that also prices a job per endpoint and by a third party's usage, and bills an upscale and a tone mapping (§4.9); 7 for one that also prices a transmission per bearer class, unit and ceiling (§4.10), an aggregated impression (§4.11) and a consumed object (§4.12); 8 for one that also prices storage held over time (§4.13); 9 for one that may follow another tariff, its chain continuing that tariff's (§4.14) |
| `seller` | 32 | the seller's key, which signs the tariff and every invoice under it |
| `buyer` | 32 | the buyer's key, which accepts the tariff by signing it |
| `start`, `end` | 8 each | u64: the period the tariff is good for |
| `currency` | 3 | three capitals `A`–`Z` (ISO 4217) |
| `room` | 52, in version 4 56 | thirteen u32: millionths of a minor unit per second of `publisher_us`, of `subscriber_us` for each layer class 0 to 8, of `composition_us` and of `recorded_us`, and per event sent (live-metering §4.1's order); in version 4 a fourteenth, per 10^9 bytes of `bytes_out` (§4.7) |
| `delivery` | 32 | four u64: millionths of a minor unit per 10^9 acknowledged bytes of each object class, in class order (settlement §7.1) |
| `package` | 24, in version 4 8 | three u64: millionths of a minor unit per package receipt, per entry, and per 10^9 stored bytes; in version 4 one, per 10^9 byte-days held (§4.7) |
| `ads` | 16 | two u64: millionths of a minor unit per presented impression, and per billable impression |
| `job` | 2 + Σ (18 + *c*), in versions 3 and 4 2 + Σ (19 + *c* + *o*), in version 6 2 + Σ (21 + *c* + *o* + *e* + *u*) | versions 2 to 4, absent in version 1: a u16 count *j*, then each job price (§4.5, §4.6, §4.9): `cap_len` (u8), `capability` (`cap_len` bytes), in versions 3 and 4 `op_len` (u8) and `operation` (`op_len` bytes), in version 6 `end_len` (u8) and `endpoint` (`end_len` bytes), then `unit` (u8), in version 6 `use_len` (u8) and `usage` (`use_len` bytes), then `divisor` (u64) and `price` (u64) |
| `transmission` | 1 + 18 × *t* | version 7, absent before: a u8 count *t*, then each transmission price (§4.10): `bearer` (u8), `unit` (u8), `max_bps` (u64) and `price` (u64) |
| `aggregated` | 8 | version 7, absent before: u64, millionths of a minor unit per aggregated impression (§4.11) |
| `consumption` | 8 | version 7, absent before: u64, millionths of a minor unit per object an agent consumed (§4.12) |
| `storage` | 8 | version 8, absent before: u64, millionths of a minor unit per 10^9 byte-days of storage a holder kept (§4.13) |
| `follows` | 32 | version 9, absent before: the digest of the tariff whose chain this one continues (§4.14), or zero for none |
| `scope` | 2 + 33 × *n* | a u16 count *n*, then each entry: `kind` (u8) and `id` (32), in strictly ascending order of (`kind`, `id`) |
| `seller_sig` | 64 | §4.2 |
| `buyer_sig` | 64 | §4.2 |

### 4.2 Digest and signatures

The **digest** of a tariff is SHA-256 over its bytes before `seller_sig`, the **body**. Its
`seller_sig` is Ed25519 by `seller` over the 18 bytes `wai:ledger-tariff` (ASCII) and 0x01,
followed by the body; its `buyer_sig` is Ed25519 by `buyer` over the 18 bytes `wai:ledger-accept`
(ASCII) and 0x01, followed by the body. Both are verified strictly, as [SPEC](../SPEC.md) §7
*Signatures* requires: a key that fails step 1 or 2 is `bad_key`, and a signature that fails a
later step is `bad_signature`. The buyer's signature is what binds the buyer to the prices: a
tariff the buyer did not sign bills nobody.

### 4.3 Reading and rules

A reader reads exactly the bytes it is given as one tariff, in the order of §4.1, and refuses at
the first of these that holds: fewer than 4 bytes, `truncated`; a magic other than `WLT1`,
`malformed`; no fifth byte, `truncated`; a version other than 1 to 9, `unknown_version`; the
bytes end before a field the layout requires, `truncated`; bytes after `buyer_sig`, `malformed`.
It then refuses as `tariff_invalid` a tariff that breaks any of these:

- `start` is below `end`; `currency` is three capitals `A`–`Z`;
- `seller` and `buyer` are not zero, and not the same key;
- `scope` has at least one entry, in strictly ascending order of (`kind`, `id`), each `kind` 1 to
  4 (1 to 5 in versions 2 to 6, 1 to 8 in version 7, 1 to 9 in versions 8 and 9) and each `id` not
  zero;
- in version 2, `job` has at most 255 prices, each as §4.5 requires, in strictly ascending
  order of (`capability`'s bytes, `unit`); in versions 3 and 4, at most 255, each as §4.6
  requires, in strictly ascending order of (`capability`'s bytes, `operation`'s bytes, `unit`);
  each `unit` 1 or 2, and in version 4 1 to 3;
- in version 6, at most 255, each as §4.9 requires, in strictly ascending order of
  (`capability`'s bytes, `operation`'s bytes, `endpoint`'s bytes, `unit`, `usage`'s bytes), each
  `unit` 1 to 4; and no price of any endpoint beside a price of one for the same `capability`,
  `operation`, `unit` and `usage` (§4.9);
- in version 7, `transmission` holds prices each as §4.10 requires, in strictly ascending order of
  (`bearer`, `unit`, `max_bps`), and `aggregated` and `consumption` are each at most 2^53 − 1;
- in versions 8 and 9, `storage` is at most 2^53 − 1.

Then the seller's signature, then the buyer's: `bad_key`, `bad_signature`.

### 4.4 Scope

A scope entry names whose records the tariff bills:

| kind | `id` | a source is in scope when |
|---|---|---|
| 1 | a room id | a room-session receipt's `room` is the `id` |
| 2 | a party's key | a settlement statement's `party` is the `id` |
| 3 | a packager's key | a package receipt's `signer_pubkey` is the `id` |
| 4 | an ad decider's or a stitcher's key | every receipt of an ads source has `signer_pubkey` the `id` (live-ads §3.4); a stitched source's records are accepted only when their `signer` is such an `id`: the verifier's **signers** (stitched-presentation §7.1) are the scope's entries of kind 4 |
| 5 | a router's key (versions 2 to 4) | a job source's route record has `signer` the `id` (route-record §5.1) |
| 6 | a publisher's or a node's key (version 7) | a group source's group receipt has `signer_pubkey` the `id` (jwp-receipts §2.4.1); a cache source's claims do |
| 7 | a collector's key (version 7) | an aggregated source's receipt has `signer` the `id` (telemetry-aggregation §7.1) |
| 8 | an agent's key (version 7) | a consumption source's claims have `signer_pubkey` the `id` (ai-usage §6.1) |
| 9 | a holder's key (version 8) | a storage source's record has `holder` the `id` (§4.13) |

The scope is what the buyer agreed to pay for: a record signed by a party the tariff does not name
is refused `outside_scope` (§7.2 step 5), whoever submits it.

### 4.5 Job prices (version 2)

A tariff of version 2 prices the media jobs a router routed and a hop served. A **job price**
is a `capability` (route-record §2: 1 to 128 bytes, lowercase ASCII letters, digits, `_` and
`.`, beginning `wai.`), a `unit`, a `divisor` of at least 1 and a `price`: millionths of a
minor unit per `divisor` units of the unit, for a job whose serving hop served that capability.
The units are the records' own figures, never converted:

| `unit` | name | a job's quantity |
|---|---|---|
| 1 | `jobs` | 1 |
| 2 | `subpixels` | the sum of its output receipts' `work_pixel_ops` (integer-payloads §15.1): the subpixels its output decodes to |
| 3 | `work_units` (version 4) | the sum of its output packages' `work_units` (packaging §9.1, §4.7) |
| 4 | `usage` (version 6) | what its billed hop's third-party record states the provider bills, in the price's own unit (§4.9) |

A job the tariff has no price for, by its serving capability, is billed nothing, and a buyer
pays for a capability only at a price it signed. A package job stays a package source (§5.1),
billed by §4.1's package prices.

### 4.6 Job prices per operation (version 3)

A tariff of version 3 prices jobs as §4.5 does, and each job price also names an `operation`:
an operation of WAI's catalogue in route-record §2's form (two words joined by `.`, each a
lowercase ASCII letter and then lowercase letters and digits: `media.encode`, `media.decode`),
of at most 128 bytes. A job is priced by its serving capability **and** its operation, which is
its route record's `operation`, the one its request named (route-record §5.1). The reason is the
work: within one capability, an encode (a motion search, then a codestream written) and a
decode (a reconstruction) spend different energy and compute for the same output units, so one
price per capability overprices one of them or underprices the other, and a buyer pays each at
the price it signed for it. A job the tariff has no price for, by its serving capability and its
operation, is billed nothing, as a job whose capability a tariff does not price is (§4.5): a
price for one operation never bills another.

Version 3 is a version of its own, not a change to version 2: a reader of version 2 cannot read
a job price that names an operation, and the buyer of a version-2 tariff signed version 2's
rules. Version 3 also bills a job's work rather than its output's identity (§5.2, §5.3, §6.9).
A tariff of version 2, its invoices and its sources read, verify and bill exactly as before.

### 4.7 Bytes, work and storage (version 4)

A tariff of version 4 prices jobs as version 3 does, and prices three more things by what
spending on them scales with:

1. **A room's bytes out.** Its fourteenth room price is per 10^9 bytes of a room-session
   receipt's `bytes_out`, the payload bytes the hops sent the session's sessions, summed from
   their ledgers (live-metering §4.4, a receipt of version 2). A room's time units price how
   long its sessions ran; what delivering them costs scales with the bytes carried too, and a
   viewer of a high layer and one of a low layer subscribe for the same seconds and are sent
   different bytes. The receipt states the price in its own tariff and counts it in each
   grant's funds (live-metering §4.6), so a receipt that states a tariff states this one's
   fourteen prices (§3). A receipt of version 1 states no bytes, and bills none. An egress
   that serves the room over HTTP is a hop of the room (live-metering §3.12): the bytes it
   answered are in its ledger, so the receipt's `bytes_out` bills them beside the relays', at
   this price, and no source of another kind states them.
2. **A package's work, per run.** Packaging is deterministic: the same source packed again under
   the same policy gives the same package, under the same receipt, from a run that did the work
   again with new energy (a customer asks for the work to be done and measured again). So a
   package is billed as a job is (§6.9): the **run** that made it is the work, and its receipt is
   the product, which each run that made it cites. Billing once per receipt refused a package
   made again, though the work was done again. A run is a job of the catalogue's operation
   `package.build`, routed and receipted as any job is (route-record §6): a `job` source whose
   output is the package (§5.1), billed at the tariff's job prices for its serving capability
   and `package.build`, per job and per **work unit**: the package receipt's `work_units`, the
   work its figure is expressed against (packaging §9.1, jwp-receipts), one per entry, each a
   base or a refinement the packer coded and wrote, so a price per unit bills what the run
   spent in proportion to its size. The chain bills each run's route record and hop receipts
   once, and a run replayed under a new route record is refused (`record_rebilled`,
   `record_duplicate`), as any job's; the package receipt (kind 5) is not billed once, and is
   cited by each run's line. The run's energy is its hop's figure (§6.6), and the receipt's own
   figure, the same work's, is not stated again. A `package` source is the product held: it
   bills its storage alone (below), never its work, which only a run states.
3. **A package's storage, by byte-time.** Its one package price is per 10^9 **byte-days**:
   what keeping bytes costs scales with how many are kept and for how long, which a price per
   stored byte once per receipt ignores. A package whose receipt the previous invoice of the
   chain lists is **held** through the invoice's whole period: it was written by the end of
   that invoice's period, at most this one's `start`. The invoice bills it ⌊Σ `stored_bytes` ×
   (`end` − `start`) / 86 400 000 000⌋ byte-days over its packager's held packages, the
   period in microseconds and rounded down once per line, and lists its receipt again. The
   invoice that first lists a package bills no storage for it: no record shows when within that
   period it was written, and a buyer pays only for time a record shows the bytes were kept. The period is read from the chain itself, its invoices'
   `start` and `end`, which the seller signs and the buyer holds (§6.9), and the bytes from
   the package receipt.

A version-3 reader cannot read a tariff of version 4 (its room prices are one longer and its
package prices two shorter, and a job price may be of unit 3) or an invoice of version 4 (§6.1:
it states a sixth unmetered count), so version 4 is a version of its own. A tariff of versions
1 to 3, its invoices and its sources read, verify and bill exactly as before.

### 4.8 A decode's output (version 5)

A tariff of version 5 is version 4's in its layout (§4.1), its rules (§4.3), its scope and its
prices (§4.4 to §4.7), and an invoice of version 5 is version 4's (§6.1); each bills what
version 4 bills. Where this text says version 4, or a range of versions ending at 4, version 5
is included, except as this section says.

A decode (a job whose route record's `operation` is `media.decode`) delivers its
**reconstruction**, not a codestream: the codestream is what it read. Version 4 gives every
`int_motion` output as its receipt and its `codestream` and holds the codestream to what the hop
delivered (§5.1), which is true of an encode and false of a decode, whose hop would have to state
an object it never delivered and commit its receipt to it (route-record §5.2, §6). Under a tariff
of version 5 a decode's output is held to what it delivered:

1. Each output of a decode's job source is an object of exactly `receipt` (the text of a
   `wai.video.int_motion` decode receipt's JSON form, integer-payloads §15.2), `codestream` (the
   `WIV1` payload the decode read, hex) and `frames` (one animated PNG holding its frames, hex).
   The receipt is read by integer-payloads §15.2 and re-derived from the codestream (§15.1 there):
   the codestream is the decode's input, and the receipt is the evidence of what it decodes to.
2. The animation is read whole first: its chunks as packaging §5 reads a still's (every chunk's
   type four letters and its CRC checked; `IHDR` first, of 8-bit RGB without interlace; an
   optional `PLTE` before the image data; the `IDAT`s consecutive; ancillary chunks read past;
   any other critical chunk refused; `IEND` last, empty, and nothing after it), and the chunks
   of PNG's third edition that make it an animation:
   - one `acTL` of 8 bytes, before any `fcTL` and the image data, counting at least one frame,
     and as many `fcTL`s as it counts;
   - each `fcTL` of 26 bytes, of the whole picture (its width and height `IHDR`'s, its offsets
     0), its dispose operation 0 to 2 and its blend operation 0, any delay;
   - the first `fcTL` before the `IDAT`s, so the default image is the first frame, and every
     other after them, followed by at least one `fdAT` before the next `fcTL` or `IEND`; no
     `IDAT` but the first frame's, and no `fdAT` of it;
   - the sequence numbers of the `fcTL`s and `fdAT`s 0, 1, 2, … in their order, and every
     `fdAT` at least 4 bytes long.

   It is of the receipt's `w` × `h` and holds as many frames as the receipt has. Then each frame,
   in order: its data (the `IDAT`s' for the first frame, its `fdAT`s' after their sequence
   numbers for each other, concatenated) is read as packaging §5 reads a still's image data, and
   the frame hash of its samples at its index (integer-payloads §15.1: BLAKE3 over
   `wai:video-rframe`, 0x01, the index as a u64 and the RGB8 bytes) is the receipt's frame at
   that index. Otherwise the source is refused `output_invalid`: at `outputs`, the output's
   index and `frames` where the animation breaks a rule above or differs in size or count; at
   `outputs`, the output's index, `frames` and the frame's index where that frame's data is not
   the picture's rows or its samples are not the receipt's; and at `outputs` and the output's
   index when the receipt or the codestream does not hold.
3. The objects the served attempt states it delivered (route-record §5.2) are exactly the
   decode's animations, by content hash, in the order of its outputs, and nothing else: an
   animation not stated at its place is refused `output_not_delivered` at `outputs`, the
   output's index and `frames`, and an object stated past the last, the codestream among them,
   at `outputs`. Under a route record of version 3 an animation is at its place when its proof
   holds it there (§5.1, its `index` its place), and there is none past the last when the
   attempt's `count` is the number of animations.

A decode delivers its frames as one object because a clip's frames are many and repeat: a route
record states each of a hop's outputs once, and at most 1024 of them (route-record §5.2), while
a clip runs to thousands of frames and a still scene decodes to the same frame again and again.
An animated PNG is lossless, one file every browser plays and any tool splits into stills, and
its default image is its first frame, which packaging §5's reader of a still reads. The frame
hash, not the PNG's bytes, is what the receipt binds, so any writer's animation of the right
samples holds; the reference writer is `png_still::encode_animation`. A frame is the whole
picture and its samples replace the picture's, so they are its data alone: a frame blended over
the one before, or of part of the picture, would be held to samples its data does not hold.

A decode's billed subpixels are its receipts' `work_pixel_ops` (§6.3), as in version 4: the
receipt states what the frames hold. An encode, and every other job, is held as in version 4.
A version-4 reader would read a decode's `frames` as an unknown member and refuse the source, and
a version-4 verdict on a decode must not change under it, so version 5 is a version of its own.
A tariff of versions 1 to 4, its invoices and its sources read, verify and bill exactly as
before.

### 4.9 An endpoint, a third party's usage, and what re-derives an output (version 6)

A tariff of version 6 is version 5's in its layout but for its job prices (§4.1), in its rules
but for theirs (§4.3), and in its scope and prices (§4.4 to §4.8), and an invoice of version 6 is
version 5's (§6.1) but for the records it may list; each bills what version 5 bills. Where this
text says version 4 or 5, or a range of versions ending at either, version 6 is included, except
as this section says.

**A job price names an endpoint.** Its `endpoint` is the endpoint of the attempt it prices, a
token of route-record §2's form, or empty, which prices every endpoint. Two providers of one
capability have different list prices, so one price per capability overprices one or underprices
the other, and a buyer pays each at the price it signed for it. A job is priced as §4.6 prices it
and, where a price names an endpoint, by its billed hop's. A price of any endpoint beside a price
of one, for the same capability, operation, unit and usage, would bill one job at both, so a
tariff that has both is `tariff_invalid`: its seller states one price for every endpoint or a
price for each.

**A third party's usage.** A job price of unit 4 names `usage`, a unit of route-record §2's form,
and of any other unit none. A job source may give `third_party`, a list of third-party hop
records' texts, which route-record §7.2 step 9 verifies with the rest of its document, a refusal
there being the source's. Each record contributes itself (§5.2, kind 17). A job's quantity at a
price of usage is the `usage.quantity` of its billed hop's record, when that record's `usage.unit`
is the price's `usage`, and otherwise none:

- a job given no record bills nothing at a price of usage, and bills by its other units;
- a failed hop's record, and a late hop's, state what the provider billed for it, which is what
  the router's operator owes the provider, and no line reads it: only the billed hop's usage
  reaches a line, as §5.1 holds a failed hop's figures from a line;
- a record's `charge` reaches no line. It is the provider's own figure in its own terms, and a
  line adds jobs, so it cannot be summed. The line cites the record, which states it signed, so a
  buyer reads the two side by side.

A third party's output has no WAI receipt, and a job it served gives no output receipt for it: its
record names the objects, and the route record holds them to the hop (route-record §6.2).

**An upscale.** A job whose route record's `operation` is `media.upscale` gives each output as an
object of exactly `upscale` (the text of an upscale record, exact-upscale §4.2), `object` (the
input: a `WAI1` of capability `wai.image.png` holding a PNG of 8-bit RGB that packaging §5's reader
reads, hex), `prior` (the `WSR1` it names, hex) and `picture` (the object the hop delivered: a PNG
that reader reads, hex). The record is verified by exact-upscale §7 under `require-proof`, holding
the input, its samples and the prior, and the picture is of the size the record's output is, with
the samples whose digest is its `output`. So what is billed is what the derivation gives: the
record's subpixels are the output's width × height × 3, the record contributes itself by its link
hash (§5.2, kind 18), and the picture is its object (§5.1). No residual is given, so a record that
names one is not proved here. Otherwise the source is refused `output_invalid`: at `outputs`, the
output's index and `object` where the input does not read so; at `outputs`, the output's index and
`picture` where the picture does not read or is not the output; and at `outputs` and the output's
index where the record does not read or is not proved.

**A tone mapping.** A job whose route record's `operation` is `media.tonemap` gives each output as
an object of exactly `tonemap` (the text of a rendition record, exact-tonemap §7.1), `envelope`
(the `WAI2` it read, hex) and `renditions` (each picture's rendition, its `RGB16` bytes, exact-tonemap
§2, in the record's order, hex), and under a route record of version 3 `proofs`, in place of
`proof`: one inclusion proof for each rendition (route-record §6.1). The record is verified by
exact-tonemap §8 under `require-proof`, holding the envelope and no decoded frame, so what is proved
is a still's pictures, and a record of a video's frames is refused. There is one rendition for each
picture, whose digest is the picture's `output`. So the record's subpixels are its pictures × width
× height × 3, and it contributes itself by its link hash (§5.2, kind 19). Otherwise the source is
refused `output_invalid`: at `outputs`, the output's index, `renditions` and the rendition's index
where a rendition is not its picture's; at `outputs`, the output's index and `renditions` where
their number is not the record's; and at `outputs` and the output's index where the record does not
read or is not proved. Each rendition is an object the hop delivered, and none is another output's
(§5.1): otherwise `output_not_delivered`, at `outputs`, the output's index, `renditions` and the
rendition's index. Two pictures of one record may render one picture: the hop states that object
once (route-record §5.2), and both are billed, since the record states and proves both.

A job of either operation gives its outputs in that form alone, and any other form is `malformed`.
A job's `subpixels` (§4.5) sum its output receipts' `work_pixel_ops` and these records' subpixels.
These records are the evidence of what a job delivered, as an output receipt is (§6.9): the
derivations are exact, so a run of the same request delivers the same picture, and a later invoice
may cite a record again for a new hop's work. Each is a record of the signer that made it, and what
its figure rests on is the derivation, which any holder of the source recomputes.

A version-5 reader cannot read a job price that names an endpoint, a job source's `third_party`,
these outputs or kinds 17 to 19, so version 6 is a version of its own. A tariff of versions 1 to 5,
its invoices and its sources read, verify and bill exactly as before.

### 4.10 A transmission on a shared bearer (version 7)

A tariff of version 7 is version 6's in its layout but for three fields after `job` (§4.1), in its
rules but for those fields' and its scope's (§4.3), and in its prices (§4.4 to §4.9), and an invoice
of version 7 is version 6's (§6.1) but for its seventh unmetered count and the records, lines and
rows of this section and §4.11 and §4.12; each bills what version 6 bills. Where this text says version 6, or a range of
versions ending at 6, version 7 is included, except as this section says.

**What it prices.** A publisher that sends a group over a `multicast` or `unidirectional` bearer
instance sends it once to every receiver that joins, and learns nothing of who received it
(bearer-receipts §2, §3): what the sending spends scales with the octets its passes carry and the
time they take, and no record states a quantity per receiver. A tariff of version 7 prices that
**transmission** in the two units a schedule states (carousel §4.1, §5.4): `bytes_sent`, the octets
an entry's passes send, per 10^9 octets, and `pass_us`, the microseconds of its passes, `count` ×
`duration_ms` × 1000, per 10^6 microseconds. They are rung-price §4.3's transmission units, with its
divisors and bounds.

**A price for each bearer class, unit and ceiling.** Its `transmission` field holds at most 255
**transmission prices**, 18 bytes each: `bearer` (u8), 2 `multicast` or 3 `unidirectional`,
bearer-receipts §2's classes in their order from 1; `unit` (u8), 1 `bytes_sent` or 2 `pass_us`;
`max_bps` (u64), the **ceiling**, from 1 to 2^53 − 1 bits per second; and `price` (u64), millionths of
a minor unit per the unit's divisor, at most 2^53 − 1. They are in strictly ascending order of
(`bearer`, `unit`, `max_bps`), so a class, a unit and a ceiling have one price. A `bidirectional`
bearer reaches each receiver over its own path and is priced per receiver, by the room and delivery
prices, so it has none here. A rung-price list's entry of a transmission unit transcribes into one
exactly: its bearer, unit, `max_bps` and `price` (rung-price §4.2, §4.3, §7.1).

**The tier.** An entry of a standing schedule (carousel §6.2 step 4) has a **pass rate** of ⌈8000 ×
*P* / `duration_ms`⌉ bits per second, *P* = `bytes_sent` / `count` the octets one pass sends,
computed in integers wide enough not to overflow (rung-price §7.2). In each unit it is billed at the
price of its instance's declared class and that unit whose ceiling is the least at or above its
pass rate: the seller's tier that covers it, which the buyer signed. An entry whose pass rate is
above every ceiling of its class and a unit has no price in that unit and bills nothing in it, and
the report states so (§8.3). So a line at another price of the class and unit, whether at a ceiling
below the rate or at one above the least that covers it, states a quantity no record gives at that
price, and is refused (§7.2 step 7).

**The source.** A `group` source (§5.1) is a group receipt, the object receipts given under it, and
its publisher's transmission and schedule claims about it (bearer-receipts §4, carousel §4) in their
chain's order, with `parent`, the text of the claim the first one's `parent_receipt_hash` names, or
`null` when the first is the head of its chain. A publisher's claims about all its groups are one
chain (jwp-receipts §2.4.3), so each group's source names the claim before its own. It is verified as
carousel §6.2 steps 1 to 4 verify a group and its claims: the group by jwp-receipts §3 steps 1 and
2; each object receipt against it by steps 4 to 6 with its envelope and step 5 without; `parent` by
jwp-receipts §3.1 steps 1 to 4, then held as its signer's previous claim; each claim by §3.1 steps 1
to 5, then step 6, a transmission claim by bearer-receipts §4.3 and a schedule by carousel §4.3, a
claim of another class being `context_mismatch`; then the declarations and the schedules that stand
(bearer-receipts §6.2 step 4, carousel §6.2 step 4), an instance's schedule being the last of a run
each of which extends the one before it (carousel §4.5). It is accepted only when all of them are
and no claim is set aside: otherwise it is refused with the first refusal's reason, at `group`, at
`objects` and the receipt's index, at `parent`, or at `claims` and the claim's index, and a claim set
aside with the reason it is set aside for, at the first such claim. A plan set aside is one the
publisher did not hold to, and a source billed in part would bill what it chose.

An entry is billed from the instance's last schedule alone: each schedule that one extends is its
first passes (carousel §4.5), and is cited beside it. A schedule that extends one a chain has billed
bills no pass twice, since its first pass is in a period already billed and it is in no later one
(§5.3). So the passes such a schedule adds are billed by no invoice of the chain, and neither is a
schedule whose passes cross a period's end: a schedule is billed whole, in the period that holds it,
and a seller sets its periods to hold the plans it bills.

**What it contributes.** Its group receipt (kind 20) by its link hash (jwp-receipts §3 step 3), and
each transmission claim (kind 21) and schedule claim (kind 22) by its link hash. Each instance it
declares states its energy once, in scope 7 (§6.6): its declaration's `energy`, the publisher's
figure of transmitting the group on that instance, every repetition included (bearer-receipts
§4.1), or the unmetered marker for `null`. Two declarations of one instance with one body are one,
and state the figure once; a declared instance with no schedule bills nothing and states its
figure. A bearer instance is one transmission (bearer-receipts §2), so its declaration and its
schedule are billed once in a chain, no two sources of an invoice declare one instance of a group
(§5.2), and the group receipt is the evidence each transmission of the group cites, listed again by
an invoice that bills the group sent on a new instance (§6.9).

**A cache's own instance.** A node that re-sends, over an instance of its own, objects it holds of a
group another key signed declares the instance in a `cache-transmission` claim (cache-authority §5),
may state its plan in a schedule of its own (§5.6 there), and states the bytes of the sending in a
declaration of version 2 naming that claim (settlement §4.4). A `cache` source (§5.1) is the group,
the object receipts given under it, the node's claims in their chain's order with `parent`, and those
declarations. It is verified as cache-authority §7.2 steps 1, 2 and 4 verify a group and a node's
claims: each cache-transmission claim by §5.3 there, each schedule by §5.6 there, and the instances
and schedules that stand as §7.2 step 4 and §5.6 say, every claim the same node's, never the group's
key, and a claim of another class or key being `context_mismatch`, a group source given such a claim
refuses it the same way. Each declaration reads (settlement §3.6, with that text's reasons), is of
version 2, its `upstream` the node and its `instance` the link hash of a claim the source gives,
otherwise `context_mismatch`, at `declarations` and its index. An instance with an entry to bill and
no declaration naming its claim is refused `record_missing`, at that claim. A cache-transmission
claim says what was sent and a schedule what was planned, so an entry is billed only when the
claim's bit of its `leaf_index` is set (cache-authority §7.2 step 6): an object scheduled and not sent
bills nothing. It is billed as a publisher's is, at the transmission prices of the instance's class,
in the octets and pass time its schedule states, on lines whose `source` is the node. No line reads a
declaration's bytes, which count objects and not their passes: a declaration is the node's statement
that it made the sending, in a window the period holds, and bounds no quantity. The source
contributes its claims (kind 23), its schedule claims (kind 22), its declarations (kind 4), each of
those billed once, and the group receipt (kind 20), which any number of transmissions cite, so a
publisher's transmission of a group and a node's own instance of it can be on one invoice. The
claim's `energy` is stated in scope 7 as a declaration's is.

**An instance is one party's.** A cache source holds the node's claims alone, so cache-authority §7.2
step 4's rule that an instance a publisher declared is no node's own reaches what a verifier is given
beside them: a cache source and a group source of one group that declare one `bearer_id` on one
invoice are refused `bearer_contradicted` at the later of them, and so are two cache sources of two
keys that do (§5.2, §7.2 step 6). A verifier given only the node's claims is shown no declaration of
the publisher's, and accepts them. The reference ledger holds every source of a chain and applies the
rule across them (§9), and a buyer that holds the publisher's claims runs cache-authority §7.2 over
both.

**Transmission, not delivery.** A transmission line bills what a publisher or a node declared it
sent, in the octets and the pass time its own schedule planned. It states nothing of any receiver: no
line reads a reconciliation (bearer-receipts §5) or a count of receivers, and a transmission line
**MUST NOT** be presented as delivery to anyone (bearer-receipts §6.3, rung-price §7.3).

### 4.11 An aggregated impression (version 7)

An impression counted over a bearer with no return path is the class **aggregated**
(impression-aggregates §9): a lower bound of what receivers reported, which no presentation claim
stands behind. It is priced in a unit of its own, `aggregated_impressions`, at the tariff's
`aggregated` price per impression, and never under `presented_impressions` or
`billable_impressions`: an invoice that states such a count under either is refused
`quantity_not_recorded` (§7.2 step 7), since no source gives that line.

An `aggregated` source (§5.1) is one aggregate receipt, `WQA1` (telemetry-aggregation §7). A verifier
reads it as data, in this order: the receipt reads (§7.2 there, at `receipt`); its `signer` is the
**collector**, whose signature verifies (`bad_key`, `bad_signature`, at `receipt`); its `task` reads
through `time_precision` (DAP §4.2), the unit its batch is stated in, which is not 0 (`task_invalid`,
at `task`); the leader's statement reads whole (`statement_invalid`, at `leader`, §6.1 there), has the
leader's role, 2 (`wrong_signer`, at `leader`, §8.1 step 5 there), and states a batch of a duration of
at least 1 (`batch_invalid`, at `leader`, §8.1 step 7 there); and the elements of `result`, summed as
integers, are its report count (`count_mismatch`, at `result`). Its **count** is that sum. Then, at
§7.2 step 5, the tariff names the collector in its scope (kind 7), so the buyer chose whose count it
pays on. A holder of the receipt and its catalogue verifies it further by impression-aggregates §8.1,
and a verifier of this extension runs no other step of that text: the receipt's count is the
collector's word to the buyer that named it.

The source contributes its receipt (kind 24) by its digest (telemetry-aggregation §7.1), and one
line of the collector's, its quantity the sum of the counts of its receipts, citing each. A receipt
is billed in the period that holds its batch (§5.3), and a chain's periods do not overlap, so a chain
bills it once, and a verifier needs no invoice but the one it is given to see that. Two receipts of
one task, by their `task` bytes, whose batches share a time unit are refused: DAP collects a bucket
once, and an impression table sets both aside (impression-aggregates §8.2). On one invoice the later
is `record_overlap` (§5.3); on two invoices of a chain one of them is `outside_period`, since one
period alone holds that time unit. A count states no energy (impression-aggregates §9), so the
source states no figure. Its line is a count of reports: it is no audience, and a party that shows
an invoice beyond the holders of its receipts holds it to impression-aggregates §8.3, a line being a
sum over a table's rows.

### 4.12 An object an agent consumed (version 7)

An agent's use of objects is stated in a consumption claim (ai-usage §6), which the agent signs. A
tariff of version 7 prices it per object, at its `consumption` price, in the unit `consumed_objects`.

A `consumption` source (§5.1) is an agent's claims, at least one, in their chain's order, with
`parent`, the text of the claim the first one's `parent_receipt_hash` names, or `null`, read as a
group source's `parent` is. Each claim is verified by jwp-receipts §3.1 steps 1 to 5, at `claims` and
its index, and held to the chain by step 5; a claim of another class, or of a key another claim of
the source does not have, is `context_mismatch`. Step 6, ai-usage §6.3, needs the objects, their
statements and the room, which the ledger does not hold: a holder of them runs it, and its outcome
bills nothing and refuses nothing here. A claim refused at that step is still its signer's statement
of what it consumed (ai-usage §6.4). The tariff names the agent in its scope (kind 8), so the buyer
pays on the word of an agent it named.

The source contributes each claim (kind 25) by its link hash, and a line of the agent's, its quantity
the objects its claims name, one for each object of each claim, an object named by two claims being
two uses, citing each claim. A chain bills a claim once. A claim states no energy, so the source
states no figure.

A version-6 reader cannot read a tariff with a `transmission`, `aggregated` or `consumption` field or
a publisher, a collector or an agent in its scope, a `group`, `cache`, `aggregated` or `consumption`
source, kinds 20 to 25 or an invoice's seventh unmetered count, so version 7 is a version of its own.
A tariff of versions 1 to 6, its invoices and its sources read, verify and bill exactly as before.

### 4.13 Storage held over time (version 8)

A tariff of version 8 is version 7's in its layout but for one field after `consumption` (§4.1), in
its rules but for that field's and its scope's (§4.3), and in its prices (§4.4 to §4.12), and an
invoice of version 8 is version 7's (§6.1) but for the records, lines and report of this section;
each bills what version 7 bills. Where this text says version 7, or a range of versions ending at 7,
version 8 is included, except as this section says.

**What it prices.** A holder that keeps objects for a buyer beyond their delivery, a stream's recent
window a player seeks back into or a clip cut from it and kept, spends on the bytes it keeps and on
how long it keeps them. No record this text reads states that: a package receipt states a package's
bytes and no time (§4.7), and a window's objects change with each one admitted and each one evicted.
A tariff of version 8 prices such storage by **byte-days**, as version 4 prices a package's, at its
`storage` price: millionths of a minor unit per 10^9 byte-days, at most 2^53 − 1. What it bills
from is the holder's own statements, signed as they are made, of what a set listed at each instant
its listing changed, and its record of the bytes the set held over an interval, which the verifier
recomputes from them.

**A stored set** is the objects a holder keeps together and states together: a stream's window,
which lists the segments a player can reach, or a clip's files. Its **subject** is 32 bytes the
holder names it by and names no other set by, the digest of a name of its own choosing: a set whose
objects change keeps its subject, so a window's snapshots over a day, each listing other segments,
are of one subject. Its **listing** at an instant names each object it lists by its content hash,
SHA-256 of its bytes, and its length; the listing's digest is SHA-256 over the 19 bytes
`wai:ledger-listing` (ASCII) and 0x01, followed by each object, in strictly ascending order of
content hash, as its content hash (32) and its length (u64). So a snapshot binds its bytes to a
list of objects, which anyone holding them recomputes, and the listing of no objects is SHA-256 over
those 19 bytes alone.

**A snapshot**, `WLS1`, is a holder's statement of what one stored set lists at one instant:

| field | size | meaning |
|---|---|---|
| `magic` | 4 | `WLS1` (ASCII) |
| `version` | 1 | 1 |
| `holder` | 32 | the holder's key, which signs it |
| `subject` | 32 | the stored set it is of |
| `at` | 8 | u64: the instant it states, a time (§2) |
| `objects` | 4 | u32: the objects the set lists at `at` |
| `bytes` | 8 | u64: their lengths, summed |
| `listing` | 32 | the digest of its listing at `at` |
| `sig` | 64 | Ed25519 by `holder` over the 20 bytes `wai:ledger-snapshot` (ASCII) and 0x01, followed by the bytes before `sig` |

**A storage record**, `WLH1`, is a holder's statement of the bytes one stored set held over an
interval:

| field | size | meaning |
|---|---|---|
| `magic` | 4 | `WLH1` (ASCII) |
| `version` | 1 | 1 |
| `holder` | 32 | the holder's key, which signs it |
| `subject` | 32 | the stored set it is of |
| `start`, `end` | 8 each | u64: its **interval**, `start` included and `end` excluded |
| `byte_seconds` | 8 | u64: the bytes the set held over the interval, in byte-seconds (below) |
| `snapshots` | 4 + 32 × *n* | a u32 count *n*, then the digest of each of its snapshots, in the order of their instants |
| `sig` | 64 | Ed25519 by `holder` over the 19 bytes `wai:ledger-storage` (ASCII) and 0x01, followed by the bytes before `sig` |

The **digest** of a snapshot or a record is SHA-256 over its bytes before `sig`. A reader reads
exactly the bytes it is given as one snapshot or one record, as §4.3 reads a tariff, with its own
magic, and a version other than 1 is `unknown_version`. It refuses as `storage_invalid` one that
breaks any of these: `holder` and `subject` are not zero; of a snapshot, one of no objects states 0
bytes and the listing of no objects; of a record, `start` is below `end` and it names at least one
snapshot. Then its signature, verified strictly as [SPEC](../SPEC.md) §7 *Signatures* requires:
`bad_key`, `bad_signature`.

**The rule.** A holder states what a set lists when its listing changes, and the bytes listed at an
instant are those of the set's latest snapshot at or before it. A record's snapshots therefore
**cover** its interval: the first is at its `start`, each later one after the one before it, and
none at or past its `end`. Its byte-seconds are what they state, the sum over its interval of the
bytes listed at each instant:

> `byte_seconds` = ⌊Σ *bytes*ᵢ × (*at*ᵢ₊₁ − *at*ᵢ) / 10^6⌋,

over its snapshots in order, *at* in microseconds and *at*ₙ its `end`, computed in integers wide
enough not to overflow and rounded down once per record. A record that states any other figure is
refused `storage_mismatch`. One that claims more bills bytes its holder never said it kept; one that
states a set's bytes as its byte-seconds, a quantity of one unit read as another, states a figure
its own snapshots contradict, and so does one that states fewer.

**The source.** A `storage` source (§5.1) is one record and its snapshots, verified in this order:
the record reads and its signature verifies, at `record`; as many snapshots are given as it names
(`snapshot_mismatch`, at `snapshots`); each snapshot, in order, reads and its signature verifies,
and it is of the record's holder and subject and its digest is the one the record names at its place
(`snapshot_mismatch`), at `snapshots` and its index; the snapshots cover the interval
(`outside_interval`, at `snapshots` and the index of the first that does not); and the record's
`byte_seconds` is what they state (`storage_mismatch`, at `record`). Then, at §7.2 step 5, the
tariff names the holder in its scope (kind 9), so the buyer chose whose word on storage it pays on,
and the record's interval lies within the invoice's period (§5.3).

**What it contributes.** Its record (kind 26) and each snapshot (kind 27), each by its digest and
each billed once in a chain (§6.9). Its line is its holder's: the quantity ⌊Σ `byte_seconds` /
86 400⌋ over the holder's storage sources, byte-seconds into whole byte-days rounded down once per
line, as version 4 rounds a package's (§4.7), at the tariff's `storage` price per 10^9 byte-days,
citing each record it counts whose `byte_seconds` is above 0 and the snapshots each names. A
snapshot states no energy, so the source states no figure. A record is billed in the period that
holds its interval, and a chain's periods do not overlap, so a set's time is billed once in a chain;
two records of one holder and one subject whose intervals overlap on one invoice bill one time twice,
and the later is refused `record_overlap` (§5.3). A holder makes a record of each set for each
period it is invoiced by, beginning with a snapshot at the period's start: a record whose interval
crosses a period's end is billed by no invoice, as a schedule crossing one is not (§4.10).

**Why the holder's snapshots.** Every other quantity this ledger bills is a figure of a record its
party signed, which the verifier reads or recomputes, and which it places in a period by the time
that record states: a room session's microseconds, a statement's period, a batch, a claim's issue.
Storage over time is a figure of the same kind, and the holder is its party, as a node is of its own
instance (§4.10). A figure signed only when it is billed would be one the buyer could take or leave.
Snapshots are signed as the listing changes, each binding its bytes to the objects listed by their
content hashes, and the record's figure is a pure function of them, so a buyer given the record and
its snapshots recomputes the line, and a record that claims more than they support is refused by
any verifier. A package's storage is billed from the chain instead (§4.7): its bytes do not change
while it is kept, and its receipt states no time. A window's bytes change by the minute, and
neither its objects' receipts nor the chain state them.

**What rests on the holder's word.** The ledger does not read a listing: it holds a record's figure
to its snapshots and each snapshot to its holder's signature. A holder of the objects, the publisher
whose segments a window lists, recomputes a snapshot's `bytes` and `listing` from them. Whether the
holder kept what it listed is its statement, as a package's storage is the seller's (§12).

A version-7 reader cannot read a tariff with a `storage` field or a holder in its scope, a `storage`
source or kinds 26 and 27, so version 8 is a version of its own. A tariff of versions 1 to 7, its
invoices and its sources read, verify and bill exactly as before.

### 4.14 A tariff that follows another (version 9)

A tariff of version 9 is version 8's in its layout but for one field after `storage` (§4.1), in its
rules, its scope and its prices (§4.3 to §4.13), and an invoice of version 9 is version 8's (§6.1);
each bills what version 8 bills. Where this text says version 8, or a range of versions ending at 7
or 8, version 9 is included, except as this section says.

**Why.** A tariff is one signed document: its scope and its prices are what both parties signed
(§4.2), and its invoices form one chain (§6.9). The parties a buyer pays for change while it is
billed: a stitcher's key is made for a new channel or retired with an old one, a packager or a
holder is added. Each change is a new tariff, which the buyer signs, and before this version each
new tariff began a chain of its own, its first invoice naming no invoice before it. What a chain
carries from one invoice to the next then did not cross: a package is billed its storage only by
an invoice whose previous lists it (§4.7), so the new chain's first invoice billed none; and a
record billed once is held to the invoice before (§6.9, `record_rebilled`), which the new chain's
first invoice did not have, so a record the old tariff's chain billed could be billed again.

**The field and the rule.** A tariff of version 9 states `follows`: zero, or the digest of the
tariff whose chain it continues. A tariff that **follows** another continues that tariff's chain:

- its first invoice names in `prev` an invoice of the tariff it follows, the last of that chain,
  and each later invoice names the one before it, as in every chain;
- every rule that reads the invoice before reads that one, across the two tariffs: a package it
  lists is held through the next period (§4.7); a record it lists that the invoice's version bills
  once is billed never again (§6.9); its period ends at or before the next one begins;
- no invoice of a tariff that follows another names zero: one that did would begin a chain of its
  own and leave behind what the chain holds and has billed, and it is refused `chain_restarted`
  (§7.2 step 4).

A tariff whose `follows` is zero begins a chain, as every tariff of versions 1 to 8 does.

**Both signatures.** `follows` is in the body both parties sign (§4.2). A buyer that signs a
following tariff accepts its scope and its prices and that it continues the chain it names, in one
act, and a seller cannot carry a chain into a tariff the buyer did not sign, nor into one that does
not name it. A verifier needs no more than it is given: the previous invoice names its tariff by
digest, which the following tariff names, and the previous invoice's seller and buyer are held to
the invoice's (§7.2 step 4), so the chain stays one seller's and one buyer's.

**What follows the change, and what does not.** The scope and the prices are the following
tariff's alone, from its first invoice on: each source is held to the scope, the prices and the
period of the tariff its invoice names (§7.2 steps 3 and 5). A package the previous invoice holds
whose packager the following tariff does not name is no longer billed. A key the following tariff
retires bills none of its records under it, whenever they are given; a seller that may still be
given records of a retired key, a stitched record among them, which states no time (§5.3), bills
them under the tariff that names the key first, or names the key in the following tariff for as
long as they may come.

**One chain.** A tariff follows one tariff and is followed by one. Two tariffs that follow one, or
two invoices that name one `prev`, fork a chain; a verifier given an invoice and the one before it
does not see a fork, and a buyer that holds the chain does (§12). The reference ledger closes a
tariff when another follows it (§9).

**Why a following tariff, not an amendment of a scope** (decision D62). An amendment would be a
record of its own, signed by both parties, beside the tariff it amends; an invoice's scope would be
the tariff's with every amendment in force over its period, so a verifier would need every
amendment of the tariff, and an invoice whose period crossed an amendment's instant a rule to split
it. A following tariff is a tariff: its scope and its prices are read as every tariff's are, one per
invoice, and only the chain crosses. A scope that changes with prices that do not is a following
tariff with the same prices.

A version-8 reader cannot read a tariff of version 9, its `follows`, or an invoice of version 9, so
version 9 is a version of its own. A tariff of versions 1 to 8 follows none: its chain, its invoices
and its sources read, verify and bill exactly as before, and an invoice whose previous is of another
tariff is refused `tariff_mismatch` as before.

## 5. Sources

### 5.1 Kinds and their documents

A source is a JSON object (RFC 8259) whose `kind` names its extension, holding exactly what that
extension's verifier is given. Bytes are lowercase hexadecimal strings.

| `kind` | members | verified as |
|---|---|---|
| `room` | `room` (`descriptor`, `grants`, `key_log_head` (a string or `null`), `chains`, a list of lists of records), `receipt`, `hops` (each `record` and `ledger`), `descriptors`, `compositions`, `takes`, `logs` (a string or `null`) | live-metering §5.1, its receipt being `receipt` |
| `delivery` | `statement`, `records` (each `record` and its `items`, one item list per entry), `proofs`, `hops`, `rooms` (each `descriptor` and `grants`) | settlement §8.2 |
| `package` | `receipt` (the text of `package.receipt.json`), `indexes` (the index files in the receipt's component order) | packaging §9, a receipt of version 2 against its indexes |
| `ads` | `descriptor`, `grants`, `key_log`, `chains`, `policy`, `pt0_ms`, `receipts` (form-2 receipts in their JSON carriage), `pods`, `claims`, `creatives`, `issuers` | live-ads §9, with ad-presentation §9 under a policy that requires claims |
| `stitched` | `records` (pod-input records), `claims` (stitched claims), `manifests`, `responses` (VAST and VMAP documents), `receipts` (form-1 receipts in their JSON carriage), `creatives`, `issuers` | stitched-presentation §7, its signers the tariff's (§4.4) |
| `group` (version 7) | `group` (a group receipt, jwp-receipts §2.4.1), `objects` (each `receipt`, an object receipt, and `envelope`, its envelope or `null`), `claims` (the texts of its publisher's transmission and schedule claims about the group, in their chain's order) and `parent` (the text of the claim the first one follows, or `null`) | §4.10: carousel §6.2 steps 1 to 4, every claim accepted and none set aside |
| `cache` (version 7) | a `group` source's members, `claims` being the texts of one node's cache-transmission and schedule claims, at least one, and `declarations` (its `WDA1` records of version 2, settlement §4.4) | §4.10: cache-authority §7.2 steps 1, 2 and 4, every claim accepted and none set aside, and each declaration naming a claim given |
| `aggregated` (version 7) | `receipt` (an aggregate receipt, telemetry-aggregation §7) | §4.11: read as data: its collector's signature, its task's `time_precision`, its leader's statement and its count |
| `consumption` (version 7) | `claims` (the texts of an agent's consumption claims, at least one, in their chain's order) and `parent` (the text of the claim the first one follows, or `null`) | §4.12: jwp-receipts §3.1 steps 1 to 5 |
| `storage` (version 8) | `record` (a storage record, `WLH1`) and `snapshots` (the snapshots it names, `WLS1`, in its order) | §4.13: the record, each snapshot it names, their cover of its interval and its byte-seconds |
| `job` (versions 2 to 4) | `request`, `pricebook`, `policy`, `record`, `receipts`, `keys` (a route record's verification document, route-record §7.1, its `receipts` and `keys` not `null`) and `outputs`, a list of objects of exactly `receipt` (the text of a `wai.video.int_motion` decode receipt's JSON form, integer-payloads §15.2) and `codestream` (the `WIV1` payload it describes: the object the hop delivered, named by its content hash; in version 5 a decode's output also has `frames`, the animation of its frames it delivered, and its codestream is what it read, §4.8), or, in version 4, of exactly `package` (the text of a package receipt of version 2, `package.receipt.json`: the object the hop delivered) and `indexes` (its index files in its component order); under a route record of version 3, each output also has `proof`, its object's inclusion proof (route-record §6.1); in version 6, it may also have `third_party`, and an upscale's and a tone mapping's outputs have their own forms (§4.9) | route-record §7, accepted with its hop receipts checked; then each output receipt read by integer-payloads §15.2 and re-derived from its `codestream` (§15.1 there), each package verified against its indexes by packaging §9, or `output_invalid` at `outputs` and its index, an upscale's and a tone mapping's outputs as §4.9 says; then each output held to what its hop delivered, or `output_not_delivered` there |

A source is accepted when its extension's verifier accepts it; for `ads`, when the outcome is
**accept** (live-ads §9.4), a **gap** being `source_gap`. A `stitched` source is always
accepted, since its verification refuses nothing as a whole (stitched-presentation §7.5): a
record it does not accept, of a signer outside the scope among them, bills nothing, and a claim
it does not find presented counts nothing. A source that is not such an object,
whose `kind` is none of these, or whose members are not exactly its kind's, each of its form, is
refused `malformed`. Under a tariff of version 1, a `job` source is not a kind, and is
`malformed`; under a tariff of versions 1 to 6, nor are `group`, `cache`, `aggregated` and
`consumption` sources; under a tariff of versions 1 to 7, nor is a `storage` source.

A job source's **billed hop** is the attempt of its route record that is billed (route-record
§5.2), if any; its **serving capability** is that attempt's candidate's `capability`, its
**operation** is its route record's `operation`, and its **figure** is the figure of that
attempt's OER/2 receipt: the unmetered marker
(oer-receipts §3.1), or `energy.joules_total` in microjoules, rounded to the nearest and a
half to the even one, with the receipt's `energy.class`. A billed hop's receipt whose figure
has no class, or rounds below 1 µJ or past what a u64 holds, cannot be stated in a row
(§6.6): the source is refused `job_figure_invalid`, at `receipts` and the receipt's index.
Under a tariff of version 4 every attempt's figure is stated (§6.6), so the same holds of each
attempt that is not billed, a failed hop and one that served past the deadline.

**A job's output is the object its hop delivered.** An output's **object** is its
`codestream`, or a package's receipt text, named by its content hash (route-record §2,
jwp-receipts §2.1). A route record
of version 2 states the objects its served attempt delivered, by content hash, and holds that
hop's receipt to them (route-record §5.2, §6). Each output a job source gives is then one of
those objects, and no two of its outputs are one object: otherwise the source is refused
`output_not_delivered`, at `outputs` and the output's index. The reason is the subpixels a
line bills (§6.3): they are read from the output receipts, and an output receipt of an object
the hop did not deliver bills subpixels nobody delivered for this job, as a receipt given
twice bills them twice. So the chain closes: the hop's receipt names its outputs, the record
names the hop's receipt and the outputs, and each output receipt is of one of them. Under a
tariff of version 5 a decode's object is the animation of the frames it delivered, not the
codestream it read (§4.8). Under a tariff of version 4, a record that states no outputs (a
record of version 1, or one no attempt served) holds every output to none, and a job it
routed is billed by the job alone; under a tariff of version 3, a record of version 1's
outputs are read as before.

A route record of version 3 states what its served attempt delivered by its count and root,
not by a list (route-record §3.4, §5.2), so a hop may deliver any number of objects. Each
output of a job source under one gives `proof`, the inclusion proof of its object (route-record
§6.1), and is one of the objects the hop delivered when its proof holds its object's content
hash to the served attempt's `count` and `root`; an output under a record of version 1 or 2
gives none. An output without its proof, or with one under a record of version 1 or 2, or a
proof that is not an object of exactly an integer `index` and a list of content hashes'
texts, `siblings`, is `malformed`; a proof that does not hold is `output_not_delivered`, at
`outputs` and the output's index, as an object a list does not state is; and no two outputs
are one object, as before. The ledger does not hold the count to the objects, which it is not
given: the hop's receipt names the root alone (route-record §6). A count stated larger than
the objects lets the last of an odd level be proved at a second place, and that place is one
object, which no source bills twice; a decode is held to its places and its count (§4.8).
Under a record of version 3 no attempt served, the outputs are held to none.

**Routing figures are never charges.** A route record's candidates' `cost`, `energy`,
`expected_cost` and `expected_ttfb_ms`, and its price book's `price` and `failures`, are the
router's figures for choosing an endpoint (route-record §4.2, §4.4): what a hop costs the
router, and what the failures it measured cost it, per successful job. No line reads them. A
job line bills its billed attempt alone, at its list price, the tariff's job price for its
serving capability and operation, which the buyer signed: a failed attempt, what a provider
billed for it and the expected cost per successful job never reach a line, however the router
ranked, and a line that counts a failed hop as a job, or prices one at the router's figures,
does not recompute.

### 5.2 What a source contributes

Each source contributes **records**, each named by a kind and an identity. This table is the
**one registry of record kinds**: every WAI text that names a record by a kind (in a citation
digest, or in a list of records) takes the kind from here, and a new kind is assigned here, the
next free one. Kinds 10 to 13 and 28 to 44 are defined by the texts that cite or name them and are no
ledger source's; the others are the ledger's own:

| record kind | record | identity | contributed by |
|---|---|---|---|
| 1 | a room-session receipt, `WMR1` | its digest (live-metering §4.2) | a `room` source: its receipt |
| 2 | a per-hop record, `WMH1` | its digest (live-metering §3.5) | a `room` source: each record its receipt names; a `delivery` source: each record its statement names in `hops` |
| 3 | a settlement statement, `WSS1` | its digest (settlement §7.4) | a `delivery` source: its statement |
| 4 | an acknowledgement or declaration, `WDA1` | its digest (settlement §3.5) | a `delivery` source: each record its statement names in `records`; a `cache` source (version 7): each declaration it gives |
| 5 | a package receipt | its `receipt_hash` (packaging §9) | a `package` source; a `job` source (version 4): each output package |
| 6 | a `wai.video.ssai` receipt of the break form | its identity (live-ads §8.4) | an `ads` source: each receipt |
| 7 | a presentation claim, `WPC1` | its digest (ad-presentation §5.3) | an `ads` source: each claim that reads |
| 8 | a pod-input record, `WSI1` | its digest (stitched-presentation §4.4) | a `stitched` source: each record it accepts |
| 9 | a stitched claim, `WSC1` | its digest (stitched-presentation §5.3) | a `stitched` source: each claim that reads |
| 10 | a run of a channel's program-as-run | its identity ([revenue-share](revenue-share.md) §7.4) | no source: cited by revenue-share §7.4 and opportunity-report §7.3 |
| 11 | an invoice, `WLI1` | its digest (§6.7, as [revenue-share](revenue-share.md) §7.4 cites it) | no source: cited by revenue-share §7.4 |
| 12 | a cue event | its event digest ([opportunity-report](opportunity-report.md) §7.3, live-events §3.2) | no source: cited by opportunity-report §7.3 |
| 13 | a room policy | its digest ([opportunity-report](opportunity-report.md) §7.3, live-ads §3.2) | no source: cited by opportunity-report §7.3 |
| 14 | an OER/2 receipt | the 32 bytes its `receipt_id` names (oer-receipts §5) | a `job` source (versions 2 to 4): the receipt of each attempt of its record |
| 15 | a `wai.video.int_motion` decode receipt | its receipt hash (integer-payloads §15.1) | a `job` source (versions 2 to 4): each output receipt |
| 16 | a route record | its digest (route-record §5.3) | a `job` source (versions 2 to 4): its record |
| 17 | a third-party hop record | its digest (route-record §6.2) | a `job` source (version 6): each record it gives |
| 18 | an upscale record | its link hash (exact-upscale §2) | a `job` source (version 6): each upscale's record (§4.9) |
| 19 | a rendition record | its link hash (exact-tonemap §2) | a `job` source (version 6): each tone mapping's record (§4.9) |
| 20 | a group receipt | its link hash (jwp-receipts §3 step 3) | a `group` or `cache` source (version 7): its group (§4.10) |
| 21 | a transmission claim | its link hash (jwp-receipts §3.1) | a `group` source (version 7): each declaration it gives |
| 22 | a schedule claim | its link hash (jwp-receipts §3.1) | a `group` or `cache` source (version 7): each schedule it gives |
| 23 | a cache-transmission claim | its link hash (jwp-receipts §3.1) | a `cache` source (version 7): each claim it gives |
| 24 | an aggregate receipt, `WQA1` | its digest (telemetry-aggregation §7.1) | an `aggregated` source (version 7): its receipt (§4.11) |
| 25 | a consumption claim | its link hash (jwp-receipts §3.1) | a `consumption` source (version 7): each claim it gives (§4.12) |
| 26 | a storage record, `WLH1` | its digest (§4.13) | a `storage` source (version 8): its record |
| 27 | a snapshot, `WLS1` | its digest (§4.13) | a `storage` source (version 8): each snapshot its record names |
| 28 | a sink session receipt | its identity ([sink-energy](sink-energy.md) §3) | no source: cited by energy-methods §7 |
| 29 | a sink segment receipt | its identity (sink-energy §3) | no source: cited by energy-methods §7 |
| 30 | a `split-computation` claim | its link hash (jwp-receipts §3.1) | no source: cited by energy-methods §7 |
| 31 | a factor table | its identity ([energy-methods](energy-methods.md) §6.1) | no source: cited by energy-methods §7 |
| 32 | a certifier's refusal, `cert-refusal/1` | its digest ([certification](certification.md) §4.2) | no source: cited by certification §4.2 |
| 33 | a publication's manifest, `cert-publication/1` | its digest (certification §5.3) | no source: cited by certification §5.3 |
| 34 | an audit entry | its link ([audit-chain](audit-chain.md) §3.2) | no source: cited by audit-chain §3.2 |
| 35 | an audit checkpoint | its digest (audit-chain §5.2) | no source: cited by audit-chain §5.2 |
| 36 | a data export | its digest ([data-export](data-export.md) §3.4) | no source: cited by data-export §3.4 |
| 37 | a deletion record | its digest ([data-deletion](data-deletion.md) §3.2) | no source: cited by data-deletion §3.2 |
| 38 | a price document | its digest ([price-document](price-document.md) §5.3) | no source: cited by price-document §5.3 |
| 39 | a window revision, `wai-hls-window` | its identity ([hls-clips](hls-clips.md) §5.1) | no source: cited by hls-clips §9 |
| 40 | a clip record, `wai-hls-clip` | its identity (hls-clips §6.1) | no source: cited by hls-clips §9 |
| 41 | an opportunity report, `WOR1` | its digest ([opportunity-report](opportunity-report.md) §7.4) | no source: named so in a data export's record lines ([data-export](data-export.md) §3.2) |
| 42 | a statement check, `WCK1` | its digest (opportunity-report §10.5) | no source: named so in a data export's record lines (data-export §3.2) |
| 43 | an origin claim, `wai-origin` | its link hash ([synthesis](synthesis.md) §2) | no source: named so in a data export's record lines (data-export §3.2) |
| 44 | a marking, `wai-marking` | its link hash (synthesis §2) | no source: named so in a data export's record lines (data-export §3.2) |

Kinds 45 to 127 are unassigned. Kinds **128 to 255 are reserved for private and provisional
use**: an implementation's own records, such as a hosted service's provisional records carried
beside WAI's until WAI defines them, may name records by them, and no kind WAI assigns later will
ever be one of them. A WAI record never states one, and a WAI verifier refuses one wherever a WAI
record states a kind, `private_kind`: in this extension, an invoice's `records` (§6.8). No citation
digest WAI defines covers one.

A source's **head** is its receipt, statement or package receipt; an `ads` source's heads are its
receipts, a `stitched` source's its accepted records, a `job` source's its route record, a
`group` source's its transmission and schedule claims, a `cache` source's its cache-transmission and
schedule claims, an `aggregated` source's its receipt, a `consumption` source's its claims and a
`storage` source's its record. A head
of one source that is a head of another source of the invoice is refused `record_duplicate`. A record
that is no head of a source may be another's: a group receipt is the head of no source (§4.10), and a
package receipt is none of the run that cites it (§4.7). A per-hop record, which a room receipt and a
statement can both name, is contributed once.

An instance of a group, by the group's link hash and its `bearer_id`, is one party's one transmission
(§4.10), however many claims state it, and two groups on one `bearer_id`, a broadcast service
carrying both, are two instances. A `group` or `cache` source that declares an instance an
earlier source of the invoice declares is refused, whichever claims each gives: `record_duplicate`
when one key declared both, and `bearer_contradicted` when two did (cache-authority §7.2 step 4). So
no schedule, entry or energy figure of an instance is stated twice.

An OER/2 receipt a `job` source contributes that an earlier `job` source of the
invoice also contributes is refused `record_duplicate` too: one hop serves one job, so no hop is
billed for two. Under a tariff of version 2, so is an output receipt: one output is one job's.
Under a tariff of version 3 or 4 it is not: an output receipt is the evidence of what a job
delivered, not the work, and the same request run again on a deterministic codec delivers the
same object, of the same content hash, under the same receipt from a new hop that did the work
again (§6.9). Two lines of one invoice that cite one output receipt therefore cite different hop
receipts, whichever lines they are.

### 5.3 Placement in time

A source is **in** a period when:

- `room`: the receipt's session, placed by its room's `t0`, lies within it: `t0` + `start` ≥ the
  period's `start` and `t0` + `end` ≤ its `end`;
- `delivery`: the statement's period lies within it;
- `ads`: the `t` of the break each receipt names, placed by the room's `t0`, is within it;
- `package` and `stitched`: always: a package receipt and a pod-input record state no time, and
  the chain (§6.9) bills each once; under a tariff of version 4, a package's work once and its
  storage for the periods it is held through (§4.7);
- `job`: its route record's `accepted` is within it;
- `group`: every pass of every entry of its standing schedules is within it: `first_ms` × 1000 is
  at least the period's `start`, and the end of the last pass, (`first_ms` + (`count` − 1) ×
  `period_ms` + `duration_ms`) × 1000, at most its `end`. A source with no schedule is in every
  period;
- `cache`: every pass of every entry it bills is within it, as for `group`, an entry its claim does
  not say was sent being no pass of the source (§4.10), and each declaration's window lies within it;
- `aggregated`: its batch is within it: `start` × `time_precision` × 10^6 is at least the period's
  `start`, and (`start` + `duration`) × `time_precision` × 10^6 at most its `end`, `start` and
  `duration` the leader's statement's and `time_precision` its task's, in integers wide enough not
  to overflow. The period is when the reports were made, not when their count arrived: a batch is
  collected after a hold (impression-aggregates §7.1), so a seller invoices a period once the batches
  it bills are collected, and a batch that crosses a period's end is billed by no invoice;
- `consumption`: each claim's `issued_at`, in seconds with any fraction dropped, × 10^6, is within
  it: at least its `start` and below its `end`;
- `storage`: its record's interval lies within it: the record's `start` is at least the period's
  `start`, and its `end` at most the period's `end`.

Two room receipts of one room whose sessions overlap, two statements of one party whose periods
overlap, two receipts of the invoice's ads sources naming one break and one session, two aggregate
receipts of one task whose batches share a time unit (§4.11), two storage records of one holder and
one subject whose intervals overlap (§4.13), and, under a tariff of version 2, two
route records of one router naming one `job`, bill one thing twice: the later is refused
`record_overlap`. Under a tariff of version 3 or 4, two route records of one
job are two runs of it, each billed from its own hop, and no hop twice (§5.2): a job's id names what
was asked, not the work, and a request run again is worked again.

## 6. The invoice

### 6.1 Layout

| field | size | meaning |
|---|---|---|
| `magic` | 4 | `WLI1` (ASCII) |
| `version` | 1 | its tariff's version, 1 to 9 |
| `seller`, `buyer` | 32 each | the tariff's |
| `tariff` | 32 | the tariff's digest |
| `prev` | 32 | the digest of the invoice before it in its chain (§6.9); zero for the first |
| `start`, `end` | 8 each | u64: the period it bills |
| `currency` | 3 | the tariff's |
| `records` | 4 + 33 × *r* | a u32 count, then each record (§5.2): `kind` (u8) and `id` (32), in strictly ascending order of (`kind`, `id`) |
| `lines` | 2 + 94 × *l* | a u16 count, then each line (§6.3), in strictly ascending order of (`source_kind`, `source`, `unit`) |
| `energy` | 1 + 18 × *e* | a u8 count, then each row (§6.6): `scope` (u8), `tag` (u8), `figures` (u32), `joules` (u64, µJ), `max_ppm` (u32), in strictly ascending order of (`scope`, `tag`) |
| `unmetered` | 16, 20, 24 or 28 | four u32: the unmetered figures of scopes 1 to 4 (§6.6); in versions 2 and 3, five, scopes 1 to 5; in version 4, six, scopes 1 to 6; in versions 7 to 9, seven, scopes 1 to 7 |
| `amount` | 8 | u64: the sum of the lines' amounts |
| `sig` | 64 | §6.7 |

### 6.2 Records

`records` lists every record the sources contribute (§5.2), each once. It is what the invoice was
computed from, and what the next invoice of the chain may not bill again.

### 6.3 Lines

A line is 94 bytes:

| field | size | meaning |
|---|---|---|
| `source_kind` | 1 | 1 room, 2 delivery, 3 package, 4 ads, 5 job (versions 2 to 4), and in version 7 6 group, 7 aggregated, 8 consumption, and in version 8 9 storage |
| `source` | 32 | the room id, the delivering party, the packager, the ad decider, the router, the publisher or node, the collector, the agent or the holder |
| `unit` | 1 | the unit (below) |
| `quantity` | 8 | u64: the quantity of the unit the records state |
| `price` | 8 | u64: the tariff's price for the unit |
| `amount` | 8 | u64: §6.4 |
| `cited` | 4 | u32: the records the line cites (§6.5) |
| `cites` | 32 | their **citation digest** (§6.5) |

The units, the quantity each sums over the sources of its `source`, and the price and divisor of
each:

| `source_kind` | `unit` | name | quantity | price | divisor |
|---|---|---|---|---|---|
| 1 | 1 | `publisher_us` | the receipts' `publisher_us` | `room` 0 | 10^6 |
| 1 | 2–10 | `subscriber_us_0`–`subscriber_us_8` | their `subscriber_us` of layer class `unit` − 2 | `room` 1–9 | 10^6 |
| 1 | 11 | `composition_us` | their `composition_us` | `room` 10 | 10^6 |
| 1 | 12 | `recorded_us` | their `recorded_us` | `room` 11 | 10^6 |
| 1 | 13 | `events_sent` | their `events_sent` | `room` 12 | 1 |
| 1 | 14 | `bytes_out` (version 4) | their `bytes_out`, of receipts of version 2 (§4.7) | `room` 13 | 10^9 |
| 2 | 1–4 | `live`, `fetch`, `fill`, `ancillary` | the bytes of the statement's delivery lines of that class that are not free (settlement §7.2) | `delivery` `unit` − 1 | 10^9 |
| 3 | 1 | `packages` | the number of package receipts | `package` 0 | 1 |
| 3 | 2 | `entries` | their `total_entries` | `package` 1 | 1 |
| 3 | 3 | `stored_bytes` | their `stored_bytes` | `package` 2 | 10^9 |
| 3 | 3 | `byte_days` (version 4, its only package unit) | ⌊Σ `stored_bytes` × (`end` − `start`) / 86 400 000 000⌋ over the package receipts the previous invoice lists, which are held (§4.7) | `package` 0 of version 4 | 10^9 |
| 4 | 1 | `presented_impressions` | under a policy that requires claims, the impressions that count (ad-presentation §9.2); of a stitched source, the presentations of its accepted records' ads (stitched-presentation §7.4), one per session | `ads` 0 | 1 |
| 4 | 2 | `billable_impressions` | under a policy that does not, the billable impressions (quartile at least 1) | `ads` 1 | 1 |
| 5 | *k* | the *k*-th job price's unit | over the router's job sources with a billed hop whose serving capability is that price's `capability` (and, in versions 3 and 4, whose operation is its `operation`, and, in version 6, whose endpoint is its `endpoint`, when it names one): one per job (`jobs`), each job's output receipts' `work_pixel_ops` (`subpixels`), in version 6 with its upscale and rendition records' subpixels, or, in version 4, its output packages' `work_units` (`work_units`), or, in version 6, its billed hop's record's usage in the price's unit (`usage`, §4.9) | the *k*-th job price's `price` | its `divisor` |
| 6 | *k* | the *k*-th transmission price's unit, `bytes_sent` or `pass_us` (version 7) | over the publisher's group sources, or the node's cache sources, each entry of a standing schedule on an instance of that price's `bearer` that §4.10 bills at that price: its `bytes_sent`, or its `pass_us` | the *k*-th transmission price's `price` | 10^9 for `bytes_sent`, 10^6 for `pass_us` |
| 7 | 1 | `aggregated_impressions` (version 7) | over the collector's aggregated sources, each receipt's count (§4.11) | `aggregated` | 1 |
| 8 | 1 | `consumed_objects` (version 7) | over the agent's consumption sources, the objects each claim names (§4.12) | `consumption` | 1 |
| 9 | 1 | `byte_days` (version 8) | ⌊Σ `byte_seconds` / 86 400⌋ over the holder's storage records (§4.13) | `storage` | 10^9 |

In version 4 a package source bills only its `byte_days`, and its work is its run's job line.
There is one line for each source and unit whose
quantity is above 0, a price of 0 included, and none for a quantity of 0. A delivery line's bytes are those its party's downstream parties signed
for (settlement §3.7): a declared byte and a free retrieval are never billed, and the delivery
report states both (§8.2). An ad line counts impressions under one rule or the other, never both:
a policy that requires claims bills only what the players' own claims show presented, and one that
does not bills on the decider's beacons, under a unit of its own.

### 6.4 Amounts

A line's **amount** is ⌊`quantity` × `price` / divisor⌋, computed in integers wide enough not to
overflow, and the invoice's `amount` is the sum of its lines' amounts. A line amount or a sum past
what a u64 holds cannot be stated, and a ledger refuses to compute such an invoice.

### 6.5 Citations

Each line cites the records it came from:

- a room line: the receipts of its room whose figure of the unit is above 0;
- a delivery line: the statements of its party with a delivery line of the class that is not free,
  and each acknowledgement (mode 1) they name with an entry of the class that is not free (a
  retrieval class with a zero `grant` is free);
- a package line: the package receipts of its packager whose figure of the unit is above 0; in
  version 4, the held receipts its `byte_days` count;
- an ad line: the receipts of its decider with at least one impression counted under the unit, and,
  for `presented_impressions`, each counted impression's own claim; of a stitched source, its
  stitcher's accepted records, and each presented own claim of their ads;
- a job line: for each job it counts, its route record and its billed hop's OER/2 receipt, and,
  for `subpixels`, each of its output receipts whose `work_pixel_ops` is above 0. In versions 3
  and 4, an output receipt that two jobs of the line delivered is cited once and its
  `work_pixel_ops` counted for each (§6.9); in version 4, for `work_units`, each of its output
  packages whose `work_units` is above 0, a package that two runs of the line made cited once
  and counted for each; in version 6, for `subpixels`, each of its upscale and rendition records,
  counted as an output receipt is, and for `usage`, its billed hop's third-party record;
- a transmission line (version 7): for each standing schedule with an entry the line bills, the
  group receipt, the schedule's claims and its instance's transmission claims, or, of a cache source,
  its cache-transmission claims and the declarations naming them (§4.10);
- an aggregated line (version 7): each receipt it counts (§4.11);
- a consumption line (version 7): each claim it counts (§4.12);
- a storage line (version 8): each record it counts whose `byte_seconds` is above 0, and each
  snapshot those records name (§4.13).

`cited` is their number, and `cites` is SHA-256 over the 17 bytes `wai:ledger-cites` (ASCII) and
0x01, followed by each cited record's `kind` and identity, in ascending order of (`kind`,
identity). Every cited record is in `records`. A buyer recomputes a line from the records it
cites alone, and shows one line to an auditor with its records and nothing else. One line is
the exception: a job line of version 3 or 4 two of whose jobs delivered one output receipt names each job
and that output once, and how many of its jobs delivered the output is stated by their sources,
each of which pairs its job with its outputs (§5.1).

### 6.6 Energy

Each record that states an energy figure states it once, in one **scope**:

| scope | figures |
|---|---|
| 1 `room_hops` | the per-hop records named by the room receipts (each restated by its receipt, live-metering §4.5) |
| 2 `delivery_hops` | the per-hop records named by the statements and by no room receipt of the invoice |
| 3 `packaging` | the package receipts' `joules_micro` and class; in version 4 none: a package's figure is its run's, which the run's hop states (§4.7) |
| 4 `ad_decisions` | the ad receipts' `joules_micro` and class; a pod-input record states no figure |
| 5 `jobs` (versions 2 to 4) | each job source's billed hop's figure (§5.1): the hop that served the job, in the class its OER/2 receipt states; a job with no billed hop states none |
| 6 `unbilled_hops` (version 4) | each job source's attempts that are not billed (route-record §5.2): a failed hop and one that served past the deadline, each its OER/2 receipt's figure (§5.1) |
| 7 `transmissions` (version 7) | each instance a group or cache source declares, its declaration's or claim's figure, once (§4.10): what transmitting on it spent, every repetition included |

A failed hop spent energy and delivered nothing, and a hop that served late spent it and
delivered too late: neither is billed, and before version 4 neither appeared in any row, so an
invoice's energy for its jobs was less than their hops spent. Version 4 states them in a scope
of their own, beside the billed hops' and never summed with them: the jobs' energy is scope 5
and scope 6 together, per class, and what the buyer was billed for is scope 5 alone. No line
reads scope 6.

For each scope, `unmetered` counts its figures that are the unmetered marker, which are in no row
and **MUST NOT** be presented as zero joules. For each scope and each tag among its metered
figures there is one **row**: `figures`, their number; `joules`, their sum; and `max_ppm`, the
largest `relative_ppm` among them for tags 4 and 5, which carry a declared uncertainty, and 0 for
tags 2 and 3, which do not. When each figure's error is within its declared relative uncertainty,
the sum's is within `max_ppm` of the sum. A row never sums figures of two classes, and no row sums
two scopes: a relay's counter reading, a packager's model and a decider's estimate are three rows,
since a sum of a model and a counter reading is neither. A row whose `tag` is 0 is refused
`classes_summed`, and so is a row whose `joules` is the sum of the figures of its class and of at
least one other class of its scope, while not the sum of its own (live-metering §4.5's rule). A
scope's energy is **whole** when its `unmetered` is 0 and it has a row, **partial** when it has an
unmetered figure, and **none** when it has no figure; a partial total **MUST NOT** be presented as
the scope's energy.

### 6.7 Digest and signature

The **digest** of an invoice is SHA-256 over its bytes before `sig`. Its signature is Ed25519 by
`seller` over the 19 bytes `wai:ledger-invoice` (ASCII) and 0x01, followed by the bytes the digest
covers, verified strictly (SPEC §7 *Signatures*).

### 6.8 Reading and rules

A reader reads exactly the bytes it is given as one invoice, as §4.3 reads a tariff with `WLI1`
for `WLT1` (`truncated`, `malformed`, `unknown_version`), and refuses as `classes_summed` an
invoice with a row of tag 0. It refuses as `private_kind` an invoice with a record of a kind 128 to 255 (§5.2), and as
`invoice_invalid` one that breaks any of these:

- `start` is below `end`; `currency` is three capitals `A`–`Z`;
- each list is in the strictly ascending order §6.1 gives it; each record's `kind` is 1 to 9 (in
  versions 2 to 4, also 14 to 16: kinds 10 to 13 are no ledger source's, §5.2; in version 6, also
  17 to 19; in version 7, also 17 to 25; in versions 8 and 9, also 17 to 27);
- each line's `source_kind` is 1 to 4 (1 to 5 in versions 2 to 4, 1 to 8 in version 7, 1 to 9 in
  versions 8 and 9), its `unit`
  a unit of its kind in its version (§6.3; for kinds 5 and 6, at least 1), its `quantity` and
  `cited` above 0;
- each row's `scope` is 1 to 4 (1 to 5 in versions 2 and 3, 1 to 6 in version 4, 1 to 7 in versions
  7 to 9), its `tag` 2 to 5 and its `figures` above 0.

Then the signature (§6.7): `bad_key`, `bad_signature`.

### 6.9 Chains

The invoices of one tariff form a **chain**: each names in `prev` the invoice before it, the first
names zero, and their periods do not overlap. A tariff of version 9 that follows another (§4.14)
continues that tariff's chain: its first invoice names the last invoice of the chain it follows, no
invoice of it names zero, and every rule of this section reads across the two tariffs as within
one. A ledger keeps one chain per tariff, and a chain a following tariff continues is one chain.
No record is in
the `records` of two invoices of a chain, but, under a tariff of version 3 or 4, an output receipt
(kind 15), under one of version 6 an upscale record and a rendition record (kinds 18 and 19, §4.9),
under one of version 7 a group receipt (kind 20), which each transmission of the group cites
(§4.10), and under one of version 4 a package receipt (kind 5), which each run that made it
cites and each invoice whose period it is held through lists again to bill its storage (§4.7): a record billed once is billed never again, whatever period a later invoice states (a storage record and a snapshot among them, §4.13), and
a package receipt, which states no time, is billed in the invoice that first holds it.

What a chain bills once for a job is its **work**, and its output's receipt is the **evidence**.
A run of a job is a hop that did it: new energy, and a new OER/2 receipt and route record, new
on every run. An output receipt is not the work: the codecs are deterministic, so the same request
run again delivers the same objects, of the same content hashes, under the same receipt. Under a
tariff of version 3 or 4, therefore:

- the records a chain bills once for a job are its route record and its hops' OER/2 receipts,
  the billed hop's among them, and in version 6 its hops' third-party records, each of one hop;
- an output receipt is cited, and carried in its lines' citation digests, but is not billed once:
  a later invoice may list it again for another job's hop;
- a re-run whose route record and hop receipt are new is billed, in the invoice that holds it;
- a source with a hop receipt or a route record the previous invoice holds is refused
  `record_rebilled`, and one with a hop receipt an earlier source of the invoice gives is refused
  `record_duplicate` (§5.2): a replay of either is never billed;
- two lines of one invoice may cite one output receipt only under different hop receipts.

Under a tariff of version 2, an output receipt is billed once as well, and a re-run of a job
whose output an invoice of the chain holds is refused, as that tariff's buyer signed it. A
package keeps its rule in versions 1 to 3: it is billed as a delivered product, once per package
receipt, which is a rule of its own and not a job's. In version 4 it has a job's shape: the run
that made it is the work, billed once per run, and its receipt the product, cited by each run;
its storage is billed for each period it is held (§4.7).

## 7. Verification

### 7.1 Inputs

A verifier is given the **tariff**, the **invoice**, the invoice its `prev` names (the
**previous**, or none), and the **sources**, a list. The ledger's verification document holds them
as one JSON object: `tariff` and `invoice` (hexadecimal), `previous` (hexadecimal or `null`) and
`sources` (§5.1).

### 7.2 Steps

It runs these steps and stops at the first refusal, which it reports with the reason and where:

1. **The tariff** (§4.3), at `tariff`, or `tariff` and `seller` or `buyer` for a signature:
   `truncated`, `malformed`, `unknown_version`, `tariff_invalid`, `bad_key`, `bad_signature`.
2. **The invoice** (§6.8), at `invoice`: `truncated`, `malformed`, `unknown_version`,
   `classes_summed`, `private_kind`, `invoice_invalid`, `bad_key`, `bad_signature`.
3. **The binding**, at `invoice`: its `tariff` is the tariff's digest, and its `version`,
   `seller`, `buyer` and `currency` the tariff's: otherwise `tariff_mismatch`; its period lies within the tariff's:
   otherwise `outside_tariff`.
4. **The previous**, at `previous`. Under a tariff that follows another (§4.14), `prev` is not
   zero (`chain_restarted`). When `prev` is not zero: an invoice whose digest is `prev` is given
   (`record_missing`); it reads and its signature verifies (§6.8, with those reasons); its `tariff`
   is the invoice's, or, under a tariff that follows another, the digest it follows, and its
   `seller` and `buyer` are the invoice's (`tariff_mismatch`); and its `end` is at most the
   invoice's `start` (`invoice_overlap`).
5. **Each source**, in order, at `source` and its index: it is verified as §5.1 says, a refusal
   being that extension's reason with that extension's place after the index (an `ads` gap is
   `source_gap`, a `storage` source's reasons and places §4.13's, and a source that does not read
   `malformed`); then it is in the scope (§4.4, `outside_scope`); a room receipt or a statement
   that states a tariff states this one (§3, `tariff_conflict`); and it is in the invoice's period
   (§5.3, `outside_period`).
6. **Across sources**, at `source` and the index of the later: a head of two sources
   (`record_duplicate`); an instance of a group that an earlier source declares (§5.2,
   `record_duplicate`, or `bearer_contradicted` when another key declared it); a receipt, statement,
   ad receipt or storage record overlapping an earlier one, or, in
   version 2, a route record of the router and job an earlier one names (§5.3,
   `record_overlap`); and a record that is in the previous invoice's `records`, in versions 3 and
   4 an output receipt excepted, in version 4 a package receipt, in version 6 an upscale or
   rendition record, and in version 7 a group receipt (§6.9, `record_rebilled`).
7. **The figures**, at `invoice`, recomputed from the sources as §6.2 to §6.6 compute them and
   compared in this order:
   1. a line whose source and unit no source gives, or that states a larger quantity than the
      sources give: `quantity_not_recorded`, a quantity no signed record covers;
   2. a row that §6.6 calls summed across classes: `classes_summed`;
   3. a line whose `cited` or `cites` is not the records it came from: `citation_mismatch`;
   4. any other difference (the records, a line missing, a smaller quantity, a price, an amount, a
      row, `unmetered`, the `amount`): `invoice_mismatch`.

A figure that cannot be held in its field is a difference.

### 7.3 Outcome

- **refuse**: the reason and where.
- **accept**: the invoice's digest; the tariff's digest, and, under a tariff that follows another,
  the digest it follows (§4.14); the currency and the period; the number of
  records; each line with its source kind, source, unit name (and, for a job line, the job
  price's `capability`, in versions 3 and 4 its `operation`, and in version 6 its `endpoint` and,
  for a usage, its `usage` as `usage_unit`; for a transmission line, its transmission price's
  `bearer` and `max_bps`), quantity, price, amount and its
  cited records; each energy row by scope and class label with its figures, joules and `max_ppm`;
  each scope's unmetered figures and coverage (scopes 1 to 4, in versions 2 and 3 scope 5, in
  version 4 scopes 5 and 6, and in versions 7 to 9 scopes 5 to 7); the
  amount; and the reports of §8, in versions 7 to 9 with §8.3's, and in versions 8 and 9 with
  §8.4's.

## 8. Reports

The reports are computed from the verified sources, as the lines are, and are stated with every
accepted invoice. They are not signed: anyone holding the sources computes them, and a verifier
compares them.

### 8.1 Ad decisions against presentation claims

For each `ads` source, in order: its room, whether its policy requires claims, and each receipt in
its list's order, with its identity, decider, `cue` and `session`, and each impression's `slot`,
`ad_id`, `price_micros` and `quartiles_reached`, whether it is **billable** (the decider's beacons:
a quartile of at least 1), whether it **counts**, and its **verdict**: under a policy that requires
claims, `presented` or the reason its own claim did not count, `claim_absent` among them
(ad-presentation §9.2); under one that does not, `beacons`. Then the receipt's billable impressions
and their spend, `budget_spent_micros`, the seller's figure; and its counted impressions and their
spend, the presented spend (ad-presentation §9.3), the buyer's. Then, over the source: the
billable and the counted impressions, the billable and the counted spend, and, for each verdict
other than `presented`, the billable impressions that did not count with it.

So a seller's receipts and a buyer's claims are reconciled from the same signed bytes: what the
seller billed, what the players presented, and why each impression that was billed and did not
count did not.

For each `stitched` source, in order, the report is the statement of stitched-presentation §7.5 as
that extension's verifier gives it, unchanged: each record's verdict, each ad's presentations,
quartiles and presented spend, and, for a checked form-1 response, the receipt's own quartile and
spend beside them; each claim's verdict; and the spend by currency, never summed across currencies.
That statement is the seller-against-buyer reconciliation of a stitched stream, and the ledger
computes no second one.

### 8.2 Delivery by party

For the `delivery` sources together, each party in ascending order of key: the digests of its
statements; their `currency` (the stated one, or `null`); the acknowledged objects and bytes of
each class; the free retrieval bytes; the declared declarations, objects and bytes (settlement §4),
never billed; the sum of its statements' own `amount`s; the sum of the invoice's lines of the party;
and its energy rows and unmetered figures over its per-hop records.

Then the **overlaps**: for each pair of acknowledgements (mode 1) of two different parties, signed
by one downstream key, whose windows overlap, and each content hash that an item of each names with
byte ranges that share bytes, one overlap. It states the content hash, the downstream key, the bytes
shared, summed over every such pair of items, and the two parties with their acknowledgements'
digests, the lower party first. The overlaps are in ascending order of (content hash, downstream,
first party, first record, second party, second record). An overlap is billed by both parties, since each was acknowledged; it is what a buyer
using several delivering parties disputes with them, and the report names the signatures it rests
on.

### 8.3 Transmissions (version 7)

For each `group` and `cache` source, in order: its group's link hash as `group`, its publisher or
node as `publisher`, `cache`, whether it is a `cache` source, and each entry billed of each of its
standing schedules, the schedules in ascending order of `bearer_id` and each schedule's
entries in its order: its `bearer_id`, its instance's declared `bearer`, its `leaf_index`,
`bytes_sent` and `pass_us`, its pass rate as `rate_bps` (`null` above 2^53 − 1, every ceiling's
bound), and, as `bytes_sent_price` and `pass_us_price`, the index from 1 in the tariff's
`transmission` of the price it is billed at in each unit (§4.10), or `null` where its pass rate is
above every ceiling of its class and that unit. An entry with no price in a unit was sent and is
billed nothing in it: the report says which, so a buyer sees what the tiers it signed leave
unpriced.

### 8.4 Storage (version 8)

For each `storage` source, in order: its record's `holder` and `subject`, its interval as `start`
and `end`, the number of its `snapshots`, and its `byte_seconds`. A line sums a holder's records
into byte-days, rounded down once; the report states each set's own figure, so a buyer sees what
each window and each clip held, and recomputes the line from them.

## 9. The reference ledger service

`wai/wai-ledger` runs the ledger as an HTTP service over a directory it owns:

| request | does |
|---|---|
| `GET /v1` | the service, its seller key, its limits |
| `GET /v1/health` | `ok` |
| `POST /v1/tariffs` | `{"tariff": hex}`: a tariff whose seller is the service's key, both signatures verified (§4), kept by its digest; a tariff that follows another (§4.14) continues the chain of a tariff the service holds, of its buyer, that no other follows and whose chain has an invoice (`record_missing` or `tariff_mismatch` at `tariff`, `follows`), and closes it |
| `POST /v1/sources` | `{"tariff": digest, "source": {...}}`: the source verified (§7.2 steps 5 and 6 against what the tariff's chain holds), kept by its heads |
| `POST /v1/invoices` | `{"tariff": digest, "start", "end"}`: the invoice of the period over the sources held and not yet billed, chained, signed and kept, with its outcome (§7.3) |
| `GET /v1/invoices/{digest}` | the invoice, its outcome and its verification document (§7.1) |
| `POST /v1/verify` | a verification document: its outcome |

A tariff that follows another takes over the chain of the tariff it follows: its first invoice names
that chain's last, the records every invoice of the chain lists are billed (§6.9), and every source
the closed tariff holds that its next invoice would bill is held under the following one, each
verified again under it (§7.2 steps 5 and 6). A package that chain holds whose packager the
following tariff does not name is left behind, billed no more. Any other source the following
tariff refuses, or one some of whose records it would no longer bill (`outside_scope`), refuses the
following tariff, at `tariff`, `follows`, `source` and the source's index, so the seller bills it
under the tariff that names it first. A source or an invoice under a closed tariff is refused
`tariff_mismatch`.

Each refusal names its reason and place. The service writes every file whole (to a temporary name,
synced, then renamed), holds a lock on its directory so that one process writes it, and recovers
each tariff's chain and held sources from the directory when it starts. A buyer fetches an
invoice's verification document and checks it with any verifier of this extension, the service's
own not among them.

## 10. Reasons

The codes this extension adds, each with where it is raised:

| reason | raised at |
|---|---|
| `tariff_invalid` | §4.3, §7.2 step 1 |
| `invoice_invalid` | §6.8, §7.2 step 2 |
| `tariff_mismatch` | §7.2 steps 3 and 4 |
| `outside_tariff` | §7.2 step 3 |
| `invoice_overlap` | §6.9, §7.2 step 4 |
| `source_gap` | §5.1, §7.2 step 5 |
| `outside_scope` | §4.4, §7.2 step 5 |
| `tariff_conflict` | §3, §7.2 step 5 |
| `outside_period` | §5.3, §7.2 step 5 |
| `record_duplicate` | §5.2, §7.2 step 6 |
| `record_overlap` | §5.3, §7.2 step 6 |
| `record_rebilled` | §6.9, §7.2 step 6 |
| `quantity_not_recorded` | §7.2 step 7 |
| `citation_mismatch` | §6.5, §7.2 step 7 |
| `invoice_mismatch` | §7.2 step 7 |
| `private_kind` | §5.2, §6.8, §7.2 step 2 |
| `output_invalid` | §4.8, §4.9, §5.1, §7.2 step 5 |
| `job_figure_invalid` | §5.1, §7.2 step 5 |
| `output_not_delivered` | §4.8, §4.9, §5.1, §7.2 step 5 |
| `storage_invalid` | §4.13, §7.2 step 5 |
| `snapshot_mismatch` | §4.13, §7.2 step 5 |
| `outside_interval` | §4.13, §7.2 step 5 |
| `storage_mismatch` | §4.13, §7.2 step 5 |
| `chain_restarted` | §4.14, §6.9, §7.2 step 4 |

A verifier of this extension also raises `truncated`, `malformed` and `unknown_version` for a
tariff, an invoice, a snapshot or a storage record that does not read, and `malformed` for a source that does not read (§5.1); `bad_key` and `bad_signature` for their signatures;
`record_missing` (live-metering §9) for a previous invoice not given; `classes_summed`
(live-metering §9) for a row over classes; `bearer_contradicted` (bearer-receipts §10) for an instance
two keys declare across sources (§5.2); and, at a source, every code its extension's verifier
raises: live-metering §9 and the codes it lists, settlement §11 and the codes it lists, packaging
§12, live-ads §10 with ad-presentation §11, at a `job` source, route-record §8 and the
codes it reuses, at a `group` source, jwp-receipts §3's and §3.1's codes, bearer-receipts §10's and
carousel §9's, at a `cache` source, those and cache-authority §11's and settlement §3.6's, at an
`aggregated` source, `statement_invalid`, `task_invalid`, `wrong_signer` and `batch_invalid`
(telemetry-aggregation §11) and `count_mismatch` (age-assurance §7.3), and, at a `consumption` source, jwp-receipts §3.1's and ai-usage §9's. A `stitched` source raises none: the codes of
stitched-presentation §9 are the verdicts of its records and claims, stated in its report (§8.1).

## 11. Conformance

[`live-conformance/ledger/`](../live-conformance/ledger/) holds the corpus, in one file,
`vectors.json`, written by `wai_receipt_ledger_vectors gen` from fixed seeds and from sources taken
from the corpora of the extensions it reads (`live-conformance/metering/`,
`live-conformance/settlement/`, `live-conformance/ads/`, `live-conformance/presentation/`,
`live-conformance/stitched/`, `live-conformance/routes/` and `pack-conformance/packs/`), with
delivery statements of two parties signed for it and, for each media job, a sink's
`wai.video.int_motion` decode receipt of its output over a payload of
`wai-rs/tests/vectors/int_video/`, and, for version 3, the route records of a decode, a re-run, a
replayed hop receipt and a claimed one, routed and sealed under the route corpus's own seeds, as
are jobs routed under the route record's version 2, its price book of version 2 with its
per-operation entries and measured failures, the served hop stating its outputs, and, for version
7, a broadcaster's groups with their declarations and carousel schedules, a node's own instance of
one with its schedule and settlement declaration and an agent's consumption claims, signed for
them from fixed seeds, and the aggregate receipts of
[`live-conformance/impressions/`](../live-conformance/impressions/), and, for version 8, a holder's
snapshots and storage records of a window and a clip over two days, signed for it from fixed seeds. The sources are held once, by name, and each vector is a verification document (§7.1) naming its sources, with the
outcome §7.3 gives it:

- **Accepted**: an invoice of one day billing a lesson room, two delivering parties and a viewer
  that forwarded sealed objects under no tariff of its own, a package, ads under a policy that
  requires claims and under one that does not, with both reports, one viewer acknowledging one
  object from both parties among the overlaps; the next invoice of its chain, billing a relay's
  session whose energy is unmetered, and a second package; and an invoice whose room hops are of
  three classes, one row each; and an invoice of streams stitched by others, one with a form-1
  receipt whose own figures the report states beside the presented ones; and, under a tariff of
  version 2, a month of media jobs one router routed, beside a package: an `int_motion` job billed
  per job and per subpixel of its output's receipt, a failover billed at the fallback's price, a
  job served past its deadline and one every allowed hop failed, which bill nothing, and a job
  whose serving hop was unmetered, counted unmetered in the jobs' scope; and, under a tariff of
  version 3, the same jobs priced per operation with an `int_motion` decode beside the encodes,
  each at its own price; the next invoice of that chain, billing the first job run again, its
  route record and hop receipt new and its output receipt one the first invoice holds; the job
  and its re-run in one invoice, their shared output receipt cited once and its subpixels billed
  for each; and a decode under a tariff that prices only the encode, which bills nothing; jobs
  routed under the route record's version 2 billed under version 3 (an encode, a failover billed
  at the endpoint that served, a decode, a hop past the deadline and three that failed); and,
  under a tariff of version 4, a lesson room's receipt of version 2 billed by its bytes out
  beside its time, a package listed and the run of `package.build` that made it, billed per run
  and per work unit, and those jobs with every hop's energy, the failed and late hops' in their
  own scope, one of them unmetered; and the next invoice of that chain, billing the package it
  holds for the byte-days of its own period and the same package made again by a new run, its
  work billed again and its receipt cited again, beside a second package listed; and, under a
  tariff of version 5, an `int_motion` decode whose served hop states it delivered one animated
  PNG of the clip's frames, its receipt re-derived from the codestream it read, beside an encode
  held to its codestream; and jobs whose route records are of version 3, each output proved
  among what its hop delivered: an encode whose clip is the second of two objects, a decode of
  version 5 whose animation is its one object, and a package's run whose receipt is the first
  of 1,501 objects; and, under a tariff of version 6, a third party's jobs billed per job and by
  what each record states the provider bills, each endpoint at its own price: a served hop,
  another provider's, a failover whose failed hop's billed usage reaches no line, a job with no
  record, a job in another unit at that unit's price, and one in a unit no price names; an encode,
  a decode held to its frames and a package's run, billed as version 5 bills them; an upscale of
  two pictures and two tone mappings, one of whose records states two pictures of one rendering,
  each re-derived from what it read; the next invoice of that chain, billing the upscale run again
  and citing its records again; and an upscale and a tone mapping whose route records are of
  version 2; and, under a tariff of version 7 that prices multicast octets at two ceilings and pass
  time at one and broadcast octets at one ceiling and pass time at two, a month of a broadcaster's
  transmissions in four invoices chained a week apart: a group simulcast on a broadcast and a
  multicast instance, each entry at the least ceiling covering its pass rate, each declaration's
  energy in its class's row; a faster broadcast, one entry above every ceiling of its class's
  octets, billing its pass time alone, beside the first week's group sent again on a new instance,
  its group receipt listed again; a multicast entry above every ceiling of its class, billing
  nothing, and a declaration with no figure; a broadcast beside a relay chain declared and
  scheduled nowhere; and a fifth invoice after the month, billing a broadcast whose schedule a later
  one extends, a node's own multicast instance of that group with an object scheduled and not sent,
  the counts of two aggregate receipts whose aggregators state different `rejected` counts, and an
  agent's two chained consumption claims; two sources of one group on one invoice, each of an
  instance of its own; two groups on one broadcast service; an aggregate receipt in the hour its batch
  fills, and one of statements of version 1; and a node's plan with an
  entry past the period that its claim does not say it sent, billing what it did; and, under a
  tariff of version 8, a day of a holder's storage, a stream's window empty at the day's start and
  then listing three, five and four segments, one snapshot a microsecond after noon so that its
  byte-seconds round down, and a clip cut at 13:00, on one line of byte-days; the next day of its
  chain, each set's record from the day's start and the clip's ending at its deletion; that day at a
  storage price of 0; a record of 1,000 byte-seconds, which bills no line and is listed; and the
  window's day beside an agent's consumption claims and an aggregate receipt's count, each billed as
  version 7 bills it; and, under tariffs of version 9, one buyer's chain across three tariffs, each
  following the one before it: the first day billing signer 1's stitched stream and first listing a
  package, the next day under a tariff that adds signer 2's key billing the storage of the package
  the first day's invoice holds and signer 2's interstitials, and the day after under a tariff that
  retires signer 1's key billing the package's storage again; and the second day's scope under a
  tariff that follows none, whose first invoice bills no storage for the package, as before.
- **Refused**: each reason of §10 at least once, each vector a control of one defect; a source of
  each kind outside the scope, a room receipt and a statement under other prices, and a source of
  each timed kind outside the period; a refusal of each source kind by its own extension; and, for
  version 2, job prices out of order, a router in a version-1 tariff's scope, a job source under a
  version-1 tariff, a version-1 invoice under a version-2 tariff, a job given twice, routed twice,
  and claiming another job's output, and a job line and a jobs row that do not recompute; and an
  invoice of each version listing a record of a kind reserved for private use, and one listing
  another text's kind; and, for version 3, job prices out of order by operation, a version-2
  invoice under a version-3 tariff, a hop receipt the previous invoice billed brought again
  under a new route record, and one hop receipt claimed by two jobs billed on two lines; and,
  under a tariff of version 2, the same re-run, refused because its output receipt was billed;
  and, for a job routed under the route record's version 2, an output receipt of a clip its hop
  did not deliver and one output given twice (`output_not_delivered`); and, for version 4, a
  price of bytes other than the receipt's and a receipt of version 1 under a price of bytes
  (`tariff_conflict`), bytes out above the receipt's, storage billed for a package first listed,
  a held package's storage over the tariff's period rather than the invoice's, a package's run
  replayed under a new route record in the next invoice (`record_rebilled`) and in the same one
  (`record_duplicate`), a failed hop billed as a job and a job line at the router's list price, the unbilled
  hops' energy left out or added to the billed hops' row, an unbilled hop whose figure states no
  class (`job_figure_invalid`), an output of a route record of version 1, and an invoice of
  version 3 under a tariff of version 4; and, for version 5, a decode whose record states the
  codestream it read, and one whose record states it after the animation
  (`output_not_delivered`), a decode in version 4's form (`malformed`), a frame with one sample
  changed, two frames swapped, a still for the animation, a frame missing, frames of another
  shape holding the same samples, a codestream not the receipt's, and an animation that blends
  a frame over the one before, disposes of one by no defined operation, holds a frame of part of
  the picture, skips a sequence number, keeps its default image apart from its frames, counts a
  frame more than it holds, or has a frame with no data (`output_invalid`), a decode in
  version 5's form under a tariff of version 4, and an invoice of version 4 under a tariff of
  version 5; and, for jobs routed under the route record's version 3, an output without its proof,
  a proof under a record of version 2 and a proof whose index is text (`malformed`), a proof of
  another place, one past the count, one a sibling short, an output its hop did not deliver, one
  output twice, a decode's animation at another place, a decode with an object past its animation,
  and an output of a job no hop served (`output_not_delivered`); and, for version 6, job prices out
  of order by endpoint, a price of any endpoint beside one, a price of usage naming no unit, a
  price per job naming one, an endpoint not of its form and a unit past `usage`
  (`tariff_invalid`); a price of usage under version 5, and an invoice of version 5 listing a
  third-party record (`invoice_invalid`), and an invoice of version 5 under a tariff of version 6;
  a job given third-party records, and an upscale and a tone mapping in version 6's form, under
  version 5 (`malformed`); another job's record (`third_party_mismatch`); a failed hop's usage added to a
  line, a usage line for a job with no record, and subpixels above a record's
  (`quantity_not_recorded`); a usage at another endpoint's price and a record left out of the
  invoice's (`invoice_mismatch`), and a usage line not citing its records (`citation_mismatch`);
  an upscale whose picture is altered, of another shape or not a PNG, under another prior, of
  another input, whose input is not an envelope, of another capability or not RGB, whose record
  states another output, names a residual or does not verify (`output_invalid`), whose picture its
  hop did not deliver or given twice (`output_not_delivered`), in an encode's form (`malformed`);
  and a tone mapping with a rendition altered, one missing, renditions out of order, of another
  envelope, whose record does not verify (`output_invalid`), with a rendition its hop did not
  deliver or given twice (`output_not_delivered`), a proof short, without its proofs, with proofs
  under a list, or in an encode's form (`malformed`); and, for version 7, transmission prices out
  of order, one ceiling priced twice, a price of a bidirectional bearer, a unit past `pass_us`, a
  ceiling of 0, a ceiling and a price past 2^53 − 1, and a publisher in a tariff of version 6
  (`tariff_invalid`); an invoice of version 6 listing a group receipt (`invoice_invalid`) and one
  under a tariff of version 7 (`tariff_mismatch`); a group under version 6 (`malformed`); a line
  at a ceiling below its entry's pass rate, one at a dearer ceiling than the least that covers it,
  and an entry above every ceiling billed (`quantity_not_recorded`); the transmissions' rows left
  out and an unmetered transmission left out (`invoice_mismatch`); a line not citing its
  declaration (`citation_mismatch`); a publisher outside the scope, a group outside the period, a
  group given twice and a declaration billed again; and, by the texts a group source is verified
  by, a schedule contradicted, one with no declaration, one on a relay chain, declarations
  contradicted, a schedule of another group, a chain not held and one broken, a group receipt
  altered, and an object receipt of another group; an aggregated count stated under
  `presented_impressions` and under `billable_impressions`, one above its receipts' count, a node
  billed an object it did not send and a consumption line above its claims (`quantity_not_recorded`);
  a collector and an agent outside the scope, overlapping batches on one invoice and on two of a chain,
  a receipt billed again in the next invoice and two invoices on, a batch a microsecond before and past
  its period and one past any instant, a schedule extended after it was billed, a claim issued at the
  period's end and one in the year 0000, a node's declaration outside the period, and a node's entry past the period that its
  claim says it sent; one schedule and one instance of a node's in two sources, one instance of a
  publisher's in two sources of its group (`record_duplicate`), and a node naming the publisher's
  instance, before and after the group's source, and two nodes naming one
  (`bearer_contradicted`); a node's instance with no declaration, with one of another claim or key, its claims and
  schedules contradicted or undeclared, signed by the publisher or by another key, or given a
  publisher's claim; an aggregate receipt that does not read, of a version not defined, with its
  signature failing or its result not its count; a task cut short and one of no precision
  (`task_invalid`); a leader's statement of another magic, of a version not defined at either version's
  length, of version 2's length stating version 1, of no role, a byte short and a byte over (`statement_invalid`), of the
  helper's role (`wrong_signer`) and of a batch of no time (`batch_invalid`); a consumption source of two agents, of another
  class, of no claim, without its parent or after another claim; each of the three kinds under
  version 6 (`malformed`); and an aggregated and a consumption price past 2^53 − 1
  (`tariff_invalid`); and, for version 8, a record stating a byte-second more than its snapshots
  support and a clip's record stating its bytes as its byte-seconds (`storage_mismatch`); a line a
  byte-day above its records and a clip's bytes billed as byte-days (`quantity_not_recorded`), and a
  storage line of a second unit (`invoice_invalid`); a second record of the window overlapping the
  day's in one invoice (`record_overlap`), and, in the next invoice, a record reaching back into the
  day before, the first day's record again, and that day's records in another day (`outside_period`);
  a snapshot an hour after its record's interval, a first snapshot after its start and two out of
  order (`outside_interval`); a snapshot whose bytes were raised after it was signed, a record whose
  byte-seconds were, and a snapshot signed as a record (`bad_signature`); a snapshot left out,
  another of the set at the instant of the one named, one of another set and one of another holder
  (`snapshot_mismatch`); a record of no time and a snapshot of no objects stating bytes
  (`storage_invalid`); a record a byte short (`truncated`), of a version not defined
  (`unknown_version`), a snapshot given as a record, a snapshot with a byte after its signature
  and a source with no `snapshots` (`malformed`); a record given twice (`record_duplicate`); a
  holder outside the scope; a storage line not citing its snapshots (`citation_mismatch`) and a
  snapshot left out of the invoice's records (`invoice_mismatch`); a storage price past 2^53 − 1
  and a holder in a tariff of version 7 (`tariff_invalid`); a storage source under version 7
  (`malformed`); an invoice of version 7 listing a storage record (`invoice_invalid`); and an
  invoice of version 7 under a tariff of version 8 (`tariff_mismatch`); and, for version 9, an
  invoice of a following tariff that names no invoice before it (`chain_restarted`), one naming an
  invoice of a tariff it does not follow (`tariff_mismatch`), one beginning before the invoice of
  the chain it follows ends (`invoice_overlap`), signer 1's stream billed again under the tariff
  that follows the one whose chain billed it (`record_rebilled`), a retired key's records billed
  under the tariff that retires it (`quantity_not_recorded`), and an invoice of version 8 under a
  tariff of version 9 (`tariff_mismatch`); the control of an undefined invoice version is of
  version 10.

`wai_receipt_ledger_vectors verify` and the test `tests/receipt_ledger.rs` check that the file
regenerates byte for byte, that `wai-rs` gives every vector its outcome, that every reason of §10
refuses a vector, that §10 lists exactly the reference's codes, and that the month of version 7,
the two days of version 8 and the chain across three tariffs of version 9 are made again byte for
byte from their tariffs, the invoices before them and their sources.
`live-conformance/receipt_ledger_verify.py` is the second implementation, written from this text:
it shares no code with `wai-rs`, verifies signatures with WAI's strict rule written from RFC 8032
(`claim-conformance/_ed25519.py`), verifies each source with that corpus's own second
implementation (`live_metering_verify.py`, `settlement_verify.py`, `live_ads_verify.py` with
`ad_presentation_verify.py`, `stitched_presentation_verify.py`, `route_record_verify.py`,
`upscale_verify.py`, `tonemap_verify.py`, `carousel_verify.py` and `cache_authority_verify.py` with
`jwp-conformance/jwp_verify.py` and `claim-conformance/claim_verify.py`,
`telemetry_aggregate_verify.py`'s reader of a receipt, and `pack-conformance/pack_verify.py`) and each output receipt by `_int_motion_receipt.py`, written
from integer-payloads §15, computes each output's content hash with BLAKE3 written from its
specification (`claim-conformance/_blake3.py`), recomputes every line,
citation, row and report itself, gives every vector the same outcome, and requires every mutated
copy of the corpus to fail.

## 12. Security and privacy considerations

- **Who signs what.** The buyer signs the prices and the scope; each record's own party signs its
  figures; the seller signs the invoice. A seller cannot bill a unit at a price the buyer did not
  sign, a record of a party the buyer did not name, or a quantity no record states: the verifier
  recomputes every line.
- **Double billing.** A head is billed once in an invoice (`record_duplicate`), so is an instance of
  a group (§5.2), one session, one statement period, one viewer's break and one stored set's time once (`record_overlap`),
  and a record once in a chain (`record_rebilled`), a chain a following tariff continues being one
  chain, whichever of its tariffs billed the record (§4.14). An aggregate receipt and a batch sharing a time
  unit with it are in one invoice of a chain at most, by their period (§5.3). An instance's claims
  are billed once in a chain; a party that declares one instance again in a new claim for a later
  period gives a record no invoice holds, which a verifier given one invoice bills for that period's
  passes alone, its energy figure stated again, and which the reference ledger, holding every source
  of the chain, refuses (§9). A verifier given one invoice checks it against the one before it; a
  buyer holding the chain checks every link.
- **Work, not identity.** Under a tariff of version 3 a job is billed for the work done, its
  route record and its hops' OER/2 receipts, once per chain, and its output's receipt is the
  evidence of what it delivered (§6.9). A deterministic re-run does the work again, a new hop,
  new energy, a new receipt, and is billed; a replayed hop receipt or route record is refused,
  which is what keeps a job from being billed twice. A seller cannot bill a job again by citing
  its output again: every billing needs a hop receipt no invoice of the chain holds. What a re-run
  rests on is that hop's receipt: a router and a hop that collude can bill a re-run that never
  ran, as a party and a downstream key can bill bytes (settlement §13). Whether a request is
  worked again or answered from outputs still kept is the router's decision, not the ledger's;
  the ledger bills what was worked. A tariff of version 2 keeps billing an output once.
- **Bytes, work and storage.** Under a tariff of version 4 a room's bytes out rest on its hops'
  ledgers, which each hop signs by their root (live-metering §3.4), as its time rests on their
  records; a package's work rests on the run that made it, its route record and its hop's
  receipt, new on every run, and on its receipt's work units, which its indexes recompute; and
  its storage on the chain: a package is billed a period's storage only when the invoice before lists it,
  so it was written by the start of the period billed, and a buyer holding the chain sees each
  period billed once. Whether the seller kept the bytes through the period is the seller's
  statement, as a delivery is the acknowledging parties' (settlement §13).
- **A third party's usage.** Under a tariff of version 6 a job may be billed by what a third
  party's record states the provider bills. That figure is the router's statement: no provider
  signs anything, so the record holds what the router read, with the provider's response kept
  where it was JSON and every byte named by digest (route-record §6.2), and a router can state a
  usage the provider did not bill. A buyer holds the price it signed and the record the router
  signed, each line cites that record, and the provider's own `charge` is stated beside it, so a
  dispute is about a signed figure; it is not recomputable, as a re-derived subpixel is.
- **What re-derives an output.** Under a tariff of version 6 an upscale's and a tone mapping's
  subpixels are recomputed by the verifier from the record, what it read and what the hop
  delivered. That binds the picture to its input, and nothing binds the input to what the buyer
  asked for: the hop's receipt names its inputs by digest, which a holder of them checks.
- **Transmission, never delivery.** Under a tariff of version 7 a transmission line rests on the
  publisher's own declaration and schedule (bearer-receipts §4, carousel §4): what it planned to
  send and says it sent, which no receiver signs, as a declaration is a party's own word
  (settlement §4.2). The pass rate that picks a price is a pure function of the signed schedule,
  and its octets are recomputed from the schedule's parameters, so a seller cannot bill a faster
  rate's octets at a slower tier's price. What the passes reached is a reconciliation's
  (bearer-receipts §5), which no line reads. A node's line rests on its own claim, plan and
  declaration in the same way, and an object it scheduled and does not say it sent bills nothing. Its
  declaration is evidence that it stated the sending, and no line is held to its bytes (§4.10). An
  invoice holds an instance to one party across its own sources, and what a verifier is not given it
  does not read: a buyer holding the group's other claims runs cache-authority §7.2 over them.
- **An aggregated count is the collector's word.** Under a tariff of version 7 a line of
  `aggregated_impressions` rests on the signature of a collector the buyer named, on a receipt the
  buyer is given. The ledger holds its result to its count and bills it once; it does not run
  impression-aggregates §8.1, which needs the receipt's catalogue, so a collector that signs a
  receipt no aggregator stood behind is found by a holder running that text, not by this one. That
  check is the buyer's to run, with the receipt the source gives it.
- **A consumption line is the agent's word.** It rests on a claim an agent the buyer named signed. The
  ledger does not check the claim against the objects and their statements (ai-usage §6.3), so a
  line bills a use whether the governing statements allowed it or not, and says nothing of that.
- **Storage is the holder's word, held to itself.** Under a tariff of version 8 a storage line rests
  on a holder the buyer named, on snapshots it signed as a set's listing changed and on records it
  signed over intervals. The verifier recomputes every record's byte-seconds from its snapshots, so
  a holder cannot bill more time or more bytes than its own snapshots state, nor bill one set's time
  twice in a chain. It does not see the objects: a holder can sign snapshots of bytes it did not
  keep, or of a listing it did not have, as a seller can state a package kept that it deleted
  (§4.7). A holder of the objects recomputes each snapshot's bytes and listing from them, and a
  dispute is about a signed statement. A holder that signs no snapshot when its listing changes
  bills the bytes of its last one until its next, more or less than it kept: the buyer that names
  it accepts its cadence.
- **A following tariff.** Under a tariff of version 9, a scope or a price changes only by a tariff
  both parties sign, and the chain crosses only into a tariff that names the one it follows. A seller
  that begins a chain anew under a following tariff is refused (`chain_restarted`), so it cannot
  leave a chain's billed records behind to bill them again. A seller that offers two tariffs
  following one, or issues two invoices after one, forks the chain: a verifier given one invoice
  and the one before it does not see it, and a buyer holding the chain sees two invoices naming one
  `prev`, as within one tariff. A retired key bills nothing under the tariff that retires it, so a
  buyer is not billed for a key it no longer names.
- **Every hop's energy.** Under a tariff of version 4 an invoice states the energy every hop of
  its jobs spent, the hops the buyer was not billed for in a scope of their own, so a seller
  whose router fails often shows it in the energy it states, and is not paid for it.
- **What the figures rest on.** An invoice is as true as its records: a delivery line rests on
  acknowledgements, so a party and a downstream key that collude can bill bytes that never moved,
  as settlement §13 says; a room line rests on per-hop records and the room's events; an ad line
  under claims rests on players' session keys. The reports name the signatures each figure rests
  on, so a dispute is about records, not about logs.
- **Energy.** A row states figures as their parties signed them, with their class: it is
  attributable and its sum recomputable, not true (energy-measurement §5). `max_ppm` bounds the
  declared part of a sum's uncertainty and says nothing of a class's undeclared systematic error.
- **What an invoice reveals.** Its records list names every record by identity, and its lines name
  rooms, parties, packagers and deciders. A verification document holds the records themselves:
  acknowledgements name downstream keys, and ad receipts name sessions. They travel between the
  seller, the buyer and an auditor they choose; the service serves an invoice's document by its
  digest and lists nothing.