open-standards/wai/extensions/staged-measurement.md

WAI Extension: Staged-Delivery Measurement

Status: Draft. How a figure about staged delivery (staged-delivery) is measured and published: which bytes are counted, how quality is computed per prefix, what "first presentable" means, how layering overhead is stated, how decode time and energy are reported, how deduplication is computed, how delivery is simulated, and what a record carries. Reference impl: wai-rs — measure_framing, quality, output_tree, content_dedup, bench_env, stage_measure::{title, decode, run, sim, session}, session_recorder, energy_report::rail_liveness, energy_burst::counter_power_samples; the wai_stage_measure tool, whose bench measures a title and seals its session claim (§8.7); the corpus staged-measure-conformance/. Keywords MUST, MUST NOT, SHOULD, MAY are RFC 2119/8174.

1. Scope

§1.1 This extension binds any party that publishes a figure about WAI staged or split delivery: bytes, time, quality, overhead, decode time, energy or deduplication. It binds the reference tools. It does not bind a sink's decode behaviour, which staged-delivery states.

§1.2 A figure that does not meet this extension MUST NOT be presented as a WAI measurement.

§1.3 This extension states no price, and a record MUST NOT carry one. A deployer that derives a cost from transferred bytes does so outside WAI.

2. Terms

term	meaning
title	What a session plays: one or more bases and the layers that refine them (staged-delivery §1).
unit	A presentable output, as staged-delivery §2 fixes it per capability: a frame, a picture, an audio clip, an attribute tensor. A title numbers its units globally: a base's unit i is the title's unit first_unit + i.
stage	A unit's stage: 0 after its base decodes, k after a layer whose refines.layer is k applies to it.
prefix	The stages 0…k of a title: every object whose layer is at most k. Its layers count is k + 1.
presentation	A (unit, layers) pair a sink handed to output, with the output it presented.
counted bytes	Bytes under §3. Apart from transferred bytes, the only byte figure this extension reports.
transferred bytes	Bytes of WAI objects as a sink received them, whole or as byte ranges, without transport or receipts.

A stage's position is its layer (0 for the base). A prototype MoQ binding in this repository carries it as mrl_layer, a stage set's stage count as mrl_total_layers, and a subscriber's upper bound on the layers it accepts as max_mrl_layer; this extension names that bound layer_cap. Staged-delivery §13 says which of them a sink reads.

3. Byte accounting

§3.1 Counted bytes of an object. For a WAI1 envelope, 12 + man_len + P; for a WAI2 envelope, 8 + man_len + 2 + 8·n + Σ Pᵢ. Here man_len is the manifest's length as written, n is the component count, and P or Pᵢ is each payload's length (SPEC §2, §7.1). These are the envelope's bytes, exactly: an object with bytes after its last payload is not the envelope its lengths describe, and is not counted. Transport bytes (HTTP, QUIC, MoQ object headers, TLS) are not counted bytes; a figure that includes them MUST state them separately.

§3.2 Only a checked format is counted. An object is countable only where WAI checks the format of every payload it carries: a capability SPEC §5 pins to a binary format (WIV1, WIH1, WIA1, WIS1, and WIR1 for a refinement-only capability; Appendix A) whose payload parses as that format, by the parse a sink runs. Where a WAI1 manifest names a fallback with a pinned format, the payload must parse as the fallback's format too, since the fallback decodes the same payload (SPEC §4 step 5). Otherwise the object is not countable, with a code:

• no-format-check: a capability WAI checks no format for, a classical codestream or a string WAI does not register among them. Nothing in WAI tells such a payload's bytes from a text encoding of them (a JSON text, base64, JSON arrays of byte values), which MUST NOT be counted, as stored or as an estimate of what it would be in binary;
• the format parse's code (bad_magic, format_capability_mismatch, …: integer-payloads §8, staged-delivery A.6), for a payload that is not its capability's or its fallback's format. A JSON form of a pinned format, its base64 text, a JSON string, or the format's bytes behind a byte-order mark all fail here;
• sha256-mismatch: a WAI2 component whose sha256 is not its payload's (SPEC §7.1);
• encrypted: an encrypted payload, whose plaintext's format cannot be checked.

No byte figure is published for an object that is not countable. The JSON that the integer codecs' encode and export tools write is a converter input (integer-payloads §10); its counted bytes are those of the envelope that carries the converted payload.

§3.3 Framing label. A byte figure carries a framing label. A figure is registered when every payload it counts is in its capability's registered format, which §3.2 requires of every figure this revision defines. A later revision that counts a payload under another framing names its label. Two figures with different framing labels MUST NOT be compared, summed or placed on one curve.

§3.4 A record MUST state:

• the counted bytes of each object, split into envelope header, manifest and payload;
• the sums per (base, stage) and per (base, prefix), and over the title per stage and per prefix;
• the framing label;
• the bytes of each base's parameter set, separately (staged-delivery §11).

§3.5 Receipt and claim bytes are counted separately, as receipt bytes.

4. Quality per prefix

§4.1 Quality is stated per presentation and per prefix against a reference: the source, where the title pins it by SHA-256, and the final prefix's output, labelled "against the final prefix". A figure against the final prefix MUST NOT be presented as distortion against the source. A unit whose shape at a stage differs from the reference's (below an up2 or a rate layer) has no figure at that stage; a figure pooled over a prefix covers the units that have one, and says how many.

§4.2 Pictures and frames (rgb8). For two RGB8 buffers of width W ≥ 1 and height H ≥ 1:

• sse_rgb = Σ (aᵢ − bᵢ)² over the 3·W·H bytes;
• sse_y is the same sum over the luma planes, with Y = (77·R + 150·G + 29·B + 128) >> 8;
• ssim_y_q32 is the mean structural similarity of the luma planes in Q32 fixed point (2³² is 1).

The similarity's windows measure ww = min(8, W) by wh = min(8, H) pixels. Their left edges are at every multiple of 4 up to W − ww, and at W − ww itself when it is not a multiple of 4; their top edges are at every multiple of 4 up to H − wh, and at H − wh itself when it is not one. A window is at every pair of a left and a top edge, so every pixel is in at least one window. For a window of n = ww·wh pixels, with Sx = Σx, Sy = Σy, Sxx = Σx², Syy = Σy² and Sxy = Σxy over the reference's luma x and the test's luma y:

A1 = 20000·Sx·Sy + 65025·n²
A2 = 20000·(n·Sxy − Sx·Sy) + 585225·n²
B1 = 10000·(Sx² + Sy²) + 65025·n²
B2 = 10000·((n·Sxx − Sx²) + (n·Syy − Sy²)) + 585225·n²
s_w = ⌊ A1·A2·2³² / (B1·B2) ⌋                    (floor toward −∞)
ssim_y_q32 = ⌊ (Σ_w s_w) / (window count) ⌋      (floor toward −∞)

This is the structural similarity of Wang et al. (2004) with K1 = 0.01, K2 = 0.03, a peak of 255, uniform windows at stride 4 with an edge-aligned last window on each axis, and population statistics, multiplied out so that no floating-point operation occurs. Because n ≤ 64, |A1·A2·2³²| < 2¹¹⁵ and B1·B2 > 0 (the reference implementation's quality module proves both), so the computation fits signed 128-bit integers.

§4.3 Audio (pcm16). For two sequences of i16 samples, channel-interleaved and in output order: sse = Σ (aᵢ − bᵢ)² and ref_energy = Σ aᵢ² over the reference. Both are unsigned integers of at least 96 bits, written in records as decimal strings. Sequences of different lengths are refused.

§4.4 Tensors (tensor-i64), for splat attributes, volumetric attributes and haptic samples: sse over the capability's canonical integer output, written as a decimal string, and max_abs = max |aᵢ − bᵢ|.

§4.5 Pooling. A figure over several units (a clip, or a prefix) sums each sum over the units; for pictures, ssim_y_q32 is the mean of every window of every unit, one division over the pooled Σ s_w and window count, and max_abs is the largest.

§4.6 Exact outputs (state-exact), for worlds, feeds, scores, avatars, quantum and every capability whose output is a state: a prefix is equal or differs, by SPEC §7 Digests. It is never stated as a distance.

§4.7 PSNR = 10·log10(255²·N / sse) and SNR = 10·log10(ref_energy / sse) are derived for display only. A record MUST carry the integers. An sse of 0 has no finite PSNR, and is shown as exact.

§4.8 A record MAY add another full-reference metric. It names the metric's implementation and version, and the metric is informative only.

5. First presentable

§5.1 bfpf_min is the sum of the counted bytes of the smallest set of objects needed to present unit 0 at one layer: the base that holds it, and every index or manifest object a sink reads first. It is computed from the title alone. A base's parameter set is stated beside it (§3.4), not in it.

§5.2 bfpf_sched is the counted bytes that had arrived when unit 0 was first presented, under a stated delivery schedule (§10). It is at least bfpf_min.

§5.3 tfpf is the time from the session's first request to the first presentation of unit 0, in microseconds. Under §10 it is virtual and deterministic. Measured, it is a distribution over repeated runs, with the clock and the presentation event named; in a browser that event is the frame callback after the canvas write.

§5.4 tffs_k is the time to the first presentation of unit 0 at k + 1 layers, stated as §5.3 states tfpf.

6. Layering overhead

§6.1 A figure that states a saving from staging MUST be accompanied by its layering overhead.

§6.2 The single-layer reference is the same content coded by the same staged form as one layer at the final layer's operating point: the title's bases and, over each, one layer straight from stage 0 to the source, with the final layer's step and the predictor that reaches the final shape. A reference at further operating points is the same with another step.

§6.3 The overhead is two rate–quality points: (counted bytes of the full title, quality of its final prefix against the source) and (counted bytes of the reference, its quality against the source). A record MUST NOT reduce them to a ratio, and MUST NOT say "at equal quality" unless the two quality integers are equal. It SHOULD add the reference at further operating points as a curve, and state which two reference points bracket the quality of the final prefix.

7. Decode time

§7.1 Decode time is measured per (unit, stage) on a stated machine and build. A record states the runs; the minimum, median, 10th and 90th percentiles; the order in which cases ran; and the discarded warm-up runs.

§7.2 Cases MUST be interleaved, with the order rotated each round.

§7.3 A run whose output digest differs from the reference is not a timing; the bench aborts.

§7.4 A record states the machine (its processor, cores, operating system and architecture, and the build profile), its load before and after each block, its power source, and whether it was otherwise idle. Continuous integration MUST NOT assert any timing.

8. Energy

§8.1 An energy figure MUST follow energy-measurement: an acquisition class (§2); for a figure obtained under its §3, the bracket a measurement claim publishes (§6); the build (§5); and a recomputable work unit. For staged decode, the work unit is the (unit, stage) decodes of one completion.

§8.2 A figure the meter could not obtain is unmetered: it is written as null with a reason, never as 0.

§8.3 Only a figure whose attribution verdict (energy-measurement §4, §6.2) is clean is published as a figure. A bracket usable for relative comparison MAY be shown, labelled "relative comparison only, not a figure", and never as an absolute joule figure. Noisy and unusable brackets are kept in the record and not shown.

§8.4 A figure covers decode on the measured machine's processor rails. A record MUST NOT state, imply or chart energy for displays, radios, networks or other devices. A reading from a whole-system rail that includes a display is not published.

§8.5 A rail that is not live in a bracket (energy-measurement §3.1) gives no figure; the decode is unmetered.

§8.6 Before a tool brackets a decode, it reads the power reader at rest and checks that the rail is live there under the same rule: a reader that gives no sample is absent, and one whose samples do not show a live rail is stale. Either way the tool brackets nothing, and the decode is unmetered with that reason. A reader of an energy counter gives power as the counter's successive differences over the time between its reads, across the counter's wrap. A counter reset to a low value reads as a wrap of nearly its whole range in one interval, so an interval that cannot be a reading ends the samples there: one implying more power than a processor rail draws; one longer than ten sampling intervals, across which a reset implies less; and one whose difference is more than half the counter's range. The reference reader's power bound is 5 kW.

§8.7 A sink records a session's decode figure in its session claim (jwp-receipts §2.4.12): the energy of one completion of the presentations the claim commits to, under §8.1–§8.5, or null where the decode was unmetered. A tool that signs a session claim seals a figure in it only where its verdict is clean (§8.3), and publishes the bracket in a measurement claim about the session claim, signed with the same key (energy-measurement §6). The bracket's burst runs on a power of two of workers, and the session's host states them: its threads is the bracket's in_flight, so the measurement claim names no more of the machine than the session does (jwp-receipts §6.7).

9. Deduplication

§9.1 Over a set of objects:

• objects is their count, a repeated object counted each time;
• unique is the count of distinct content hashes (jwp-receipts §2.1);
• referenced_bytes is the sum of their counted bytes;
• stored_bytes is the sum over one object per content hash.

All four are recomputed, never declared. One content hash has one length; a set that gives one hash two lengths has no totals.

§9.2 Deduplication is stated per title, over every object the title and its single-layer references reference (a reference's bases counted again), and, where content repeats across titles, across the record.

10. Delivery simulation

§10.1 A deterministic delivery figure comes from the staged delivery simulator, a discrete-event model in integer microseconds defined by its model and plan (Appendix B). Its figures are labelled "simulated" with the plan. A simulated figure is never a measurement of a network, and is never presented as one.

§10.2 Delivery timeout. A plan gives each object a carriage, after the DELIVERY TIMEOUT of MoQ Transport (draft-ietf-moq-transport):

• datagram: each object is one datagram, and one not started by its deadline (its availability plus its timeout) is dropped.
• subgroup: each (base, layer) is one subgroup, whose objects are sent in order. When an object of a subgroup is not fully sent by its deadline, the subgroup is reset: the bytes already sent of it and of every later object of the subgroup are abandoned, and the bytes not yet sent are dropped, whatever the later objects' own deadlines.

Dropped and abandoned bytes are never delivered, and every offered byte is delivered, dropped or abandoned. The simulator models no receipt. Over a network, a relay that drops an object still forwards its receipts (jwp-receipts §4.1); a sink that holds them accounts for the object as inclusion-verified, never as delivered (jwp-receipts §4.4), and a stage claim lists it as dropped (jwp-receipts §2.4.10).

§10.3 Layer cap. An object whose layer exceeds layer_cap is never sent and never counted as offered.

§10.4 A refinement never stalls its base beyond a bound. A plan's base-only model removes every refinement. The stall of a unit is its base presentation time under the plan minus the same time under the base-only model. The stall bound is S = S_link + S_decode:

• S_link: under strict-priority, the serialisation time of one chunk; under fifo with a refinement timeout, T plus one chunk, where T is the longest timeout any refinement takes (its own, where the model gives it one, or the plan's); otherwise (a refinement that takes none) there is no bound.
• S_decode: under base-first decode, one refinement's decode time; otherwise there is no bound.

Preconditions. The bound holds for every model and every plan with no base timeout (delivery_timeout_us.base is null), a bounded link schedule (strict-priority, or fifo where every refinement takes a timeout) and base-first decode, whatever else the plan states (carriage, window, live captures, layer cap, workers, decode times, playout deadlines). A plan outside them has no bound: a base its refinements delay past its own timeout is not presented at all, and the two unbounded parts above have counter-plans.

Proof. Write c for one chunk's serialisation time, ⌈chunk_bytes·1000 / bytes_per_ms⌉, the longest any chunk takes; L = c under strict-priority and L = T + c under fifo; and d_r for one refinement's decode time. A base below is one layer-0 object (a base split into several layer-0 objects contributes each). Number the bases b_1, b_2, … in the order the sender sends them. That order is greedy under subgroup precedence: whenever the sender starts a base, it takes, of the bases available then and not held behind an unfinished earlier object of their subgroup (§10.2; under subgroup, a base's layer-0 objects form one subgroup, sent in title order), the least by the order key (Appendix B, Order), whose first part is the availability under either schedule. It is the same order under the plan and under its base-only model. By induction on k: when either starts its k-th base, the bases finished are b_1, …, b_{k−1} in both, so the same bases are held. The base-only model starts it at the first time after b_{k−1} ends at which a base is available; the plan starts it no earlier, since b_{k−1} ends no earlier under the plan and it too needs a base available. A base that becomes available after the base-only model's start has a later availability, and so a larger key, than every base eligible then, so the least is b_k in both. The order can differ from the order of the keys alone: a base listed after another of its subgroup waits for it, even when it is available earlier. A base's service time s_k (the sum of its chunks' times) is the same in both.

The link. Let a_k be b_k's availability, start_k, end_k its first chunk's start and last chunk's end under the plan, and start⁰_k, end⁰_k under the base-only model.

1. A base, once started, is sent to its end without a chunk of another object between. At each boundary while b_k is sent, the eligible objects are those eligible when it started, less any dropped or reset, and those that became available since, whose availability, and so whose key under either schedule, is larger than b_k's. None becomes eligible by its subgroup in between: an earlier object of a subgroup is finished only by being sent, which does not happen while b_k is sent, and a reset ends the whole tail. b_k was the least eligible object when it started (under strict-priority every base precedes every refinement; under fifo it was chosen), so it stays the least. So end_k = start_k + s_k.
2. In the base-only model, start⁰_k = max(a_k, end⁰_{k−1}): the bases are sent in order, and the link is idle only when no base is available.
3. Under the plan, at t_k = max(a_k, end_{k−1}) base b_k is eligible (the bases its subgroup holds it behind are among b_1, …, b_{k−1}) and, by the order above, the eligible base of least key. Under strict-priority, a base precedes every refinement, so b_k starts at the first boundary at or after t_k; a chunk in flight at t_k is a refinement's (step 1), and ends within c. So start_k ≤ t_k + c. Under fifo, objects that precede b_k are bases (all before it in the order) and refinements available no later than a_k, whose deadlines are therefore at most a_k + T. At the first boundary after a_k + T, which comes within c of it, every such refinement not yet finished has been dropped or reset (§10.2); one already finished took no longer. So start_k ≤ max(end_{k−1}, a_k + T + c), and in both cases start_k ≤ max(a_k + L, end_{k−1}), with end_{k−1} exact when it is the larger: a base that ends at a boundary where b_k is eligible is followed by b_k.
4. By induction on k, start_k ≤ start⁰_k + L: with step 3, step 1 and the hypothesis, start_k ≤ max(a_k + L, end⁰_{k−1} + L) = start⁰_k + L. Each base therefore arrives at most L later than in the base-only model, and the bases arrive in the same order in both.

The decode. Number the base decode jobs in arrival order, which is the order of step 4. Under base-first the sink takes bases in the order they became ready (Appendix B, Workers), which is that order, and before any refinement. Let r_k ≤ r⁰_k + L be b_k's arrival under the plan and the base-only model, W the workers and d_b a base's decode time.

5. In the base-only model, with equal decode times and jobs started in order, u⁰_k = max(r⁰_k, u⁰_{k−1}, u⁰_{k−W} + d_b) is b_k's start (terms with an index below 1 omitted): at that time b_{k−1} has started, every base up to b_{k−W} has finished, so at most W − 1 workers are busy.
6. Under the plan, no refinement starts while a base is ready and waiting. A refinement that holds a worker after r_k + d_r therefore started after r_k and so after b_k started. At τ = max(r_k + d_r, u_{k−1}, u_{k−W} + d_b), if b_k has not started, it is the waiting base of least order, no refinement holds a worker, and at most W − 1 bases do; so u_k ≤ τ.
7. By induction, u_k ≤ u⁰_k + L + d_r: each term of τ is at most the matching term of step 5 plus L + d_r.

So every base is presented at most S_link + S_decode = L + d_r after its time in the base-only model, and a late base is presented all the same (Appendix B, Deadlines). ∎

The reference implementation checks the bound on generated models and plans drawn over the whole range of the preconditions (groups and captures in any order, objects listed in any order, slow links, zero and short timeouts, caps, one to four workers), and on draws aimed at the orders the bound depends on (captures on and beside chunk boundaries and out of order, bases split into two layer-0 objects, chunks of one byte), which fail on their own when the send or the decode order of bases is not the one above; the corpus checks it on every bounded plan it holds. For each part of the bound a plan can lose, the corpus holds a counter-plan whose stall passes the bound of the same plan with that part restored: a fifo link without a refinement timeout against the same fifo link with one, and fifo decode against the same plan with base-first decode.

11. Records

§11.1 A published figure MUST cite a dated record in wai/research/staged-measurements/ by path and commit. The record carries:

• the date and the commit;
• the title's content identity (Appendix D) and the framing label;
• the machine and build;
• every deterministic figure of §3–§6 and §9, and every measured figure of §5.3–§5.4, §7 and §8 with its method;
• the link hashes of its claims.

§11.2 Records are immutable. A correction is a new record that names the one it corrects.

§11.3 A classical baseline is a reference curve of points (counted bytes, quality per §4) from a named encoder at stated versions and settings, on the same source. A record MUST NOT state a multiplier, percentage or ratio between a WAI figure and a baseline.

12. What continuous integration asserts

§12.1 Only values that are the same on every machine:

• counted bytes, bfpf_min and simulator outputs;
• the integers of §4, output digests and the output tree's root and leaf count;
• deduplication totals and the overhead points;
• every figure a conformance corpus states.

§12.2 Measured times and energy are stored as artifacts and never asserted.

§12.3 The corpus staged-measure-conformance/ holds titles (Appendix D) and, for each, every figure of §12.1 (goldens.json) and the fixture tool's own reconstruction digests (expect.json). A conforming implementation reproduces every figure and every digest. The corpus's README names its second, independent implementation.

13. Media-class matrix

The last column follows §3.2: an object is countable only under a capability whose format WAI checks (count_object gives no-format-check for any other), so a class whose staged form or base has no checked format is not countable in this revision, whatever else it supports.

class	unit	staged form	edge operation	quality kind	in this revision
image	a picture	pinned integer base (wai.neural.int_hyper) + WIR1 layers (wai.image.int_refine: identity, up2)	serve a prefix of layers	rgb8	measured (corpus); a classical base (PNG and the like) is not countable in this revision
video, WAI-native	a frame	wai.video.int_motion or wai.video.int_hyper base + WIR1 layers, per frame or per span (wai.video.int_refine)	drop layers above a cap	rgb8 per frame, pooled per clip	measured (corpus)
audio	the clip	wai.audio.int_codec base + WIR1 layers (wai.audio.int_refine: rate, identity)	drop layers above a cap	pcm16	measured (corpus); a wai.audio.flac base is not countable in this revision
splat	the attribute tensor	wai.splat.int_codec base + WIR1 layers (wai.splat.int_refine)	drop layers above a cap	tensor-i64	measured (corpus)
video, enhancement layer	a frame	registered base + wai.video.lcevc companion (SPEC §7.1)	drop the companion	rgb8 after the sink's decode	not countable in this revision (the companion's format is not checked); quality needs a sink-supplied decoder
image, progressive passes	a picture	byte prefixes of one progressive codestream	serve a byte prefix	rgb8 after the sink's decode	a staged form not yet registered (staged-delivery §6.4); not countable in this revision
audio, codebook prefix	the clip	the further codebooks of a residual-vector-quantised code	drop codebooks above a cap	pcm16	a staged form not yet registered; not countable in this revision
volumetric (4D splat)	a keyframe span	keyframe refinement	serve a prefix	tensor-i64	a staged form not yet registered; not countable in this revision
world / feed / film / avatar	a segment	snapshot and operation deltas	snapshot and tail	state-exact	a staged form not yet registered; not countable in this revision
score	a section	none	none	state-exact (mixdown digest)	not countable in this revision
haptics	an envelope	keyframe refinement	serve a prefix	tensor-i64	a staged form not yet registered; not countable in this revision
quantum	a circuit	none	none	state-exact	not countable in this revision
text and records	an object	none	none	none	not countable in this revision

Appendix A. Counted formats

The formats §3.2 counts, and how the reference implementation (measure_framing::count_object) checks each before it counts it. A payload that fails its check is not countable, with the check's code.

capabilities	format	check
wai.video.int_motion (keyframe 0), wai.video.int_hyper (keyframe 1)	WIV1	integer-payloads §2–§3, in its order
wai.neural.int_hyper	WIH1	integer-payloads §2, §4
wai.audio.int_codec	WIA1	integer-payloads §2, §5
wai.splat.int_codec	WIS1	integer-payloads §2, §6
wai.image.int_refine, wai.video.int_refine, wai.audio.int_refine, wai.splat.int_refine	WIR1	staged-delivery Appendix A.1–A.3, for the capability's unit kind
every other capability	—	none: not countable (no-format-check)

A WAI1 fallback with a pinned format is checked as its capability is. Parameter sets (SPEC §3.1) are not objects and are never counted bytes; §3.4 states them separately. The corpus's counting.json holds an object for each outcome.

Appendix B. Delivery simulator wai-sim/1

A model is a title's objects in title order, the object index, as delivery sees them (wai-sim-model/1):

{ "format": "wai-sim-model/1", "unit_us": 40000,
  "objects": [ { "id": "base.wai", "base": 0, "layer": 0, "units": [0, 5], "bytes": 2519, "capture_us": null }, … ] }

units is [from, count] over the title's units and bytes the object's counted bytes (§3). A refinement MAY carry timeout_us, a delivery timeout of its own in place of the plan's for its layer: what a MoQ track's DELIVERY_TIMEOUT sets for every object on it (packaging §8, its deadlines). A model is well formed when every object has at least one byte and one unit, no base carries timeout_us, no two objects cover one unit at one layer, and every unit an object of layer k ≥ 1 covers is covered at layer k − 1 by an object of the same base. A measured title's model is its objects with their counted bytes, and its bases' capture times.

A plan (every member required, none other allowed):

{ "plan": "wai-sim/1", "mode": "vod" | "live",
  "link":   { "rtt_us": 40000, "bytes_per_ms": 2500, "chunk_bytes": 1200 },
  "sender": { "schedule": "strict-priority" | "fifo", "carriage": "datagram" | "subgroup",
              "layer_cap": null, "delivery_timeout_us": { "base": null, "refinement": 30000 },
              "vod_window_us": null },
  "sink":   { "workers": 1, "decode_order": "base-first" | "fifo",
              "decode_us": { "base": 4000, "refinement": 2000 },
              "playout_start_us": null, "late_refinement": "discard" | "present" } }

bytes_per_ms, chunk_bytes, workers and both decode times are at least 1. Every integer of a model or plan is at most 2⁵³ − 1. All arithmetic is in integer microseconds, and h = ⌊rtt_us / 2⌋; a time or a byte sum past 64 bits is refused (overflow), never wrapped.

The sender.

• Availability. The sink requests at 0 and the sender holds the request at h. An object is available at h + max(0, from·unit_us − vod_window_us) on demand (h with no window), and at max(h, capture_us) live; a live plan over an object with no capture time is refused.
• Deadline. An object's availability plus its layer's timeout (base for layer 0, refinement otherwise, or a refinement's own timeout_us); none when that timeout is null.
• Cap. An object above layer_cap is capped: never sent, never offered.
• Datagrams. Under datagram, an object of more than chunk_bytes that is not capped is refused (datagram-too-large).
• Link. The link carries one chunk at a time. At each boundary — time 0, and the end of each chunk — the sender first applies the timeouts, then sends the next chunk:
  • Timeouts. In object order, each object still pending whose deadline is before the boundary's time: under datagram it is dropped; under subgroup its subgroup is reset from it (§10.2).
  • Eligibility. An object is eligible when it is pending, available, and, under subgroup, no earlier object of its subgroup is pending.
  • Order. Of the eligible objects, the least by (layer, then for a base its availability, from, object index) under strict-priority, and by (availability, object index) under fifo: under either, bases go in the order they became available.
  • Chunk. c = min(chunk_bytes, bytes not yet sent), occupying the link ⌈c·1000 / bytes_per_ms⌉ µs from the boundary, and arriving h after it ends. An object's sent_first_us is its first chunk's start. An object whose last chunk ends at e is delivered, arriving at e + h, under datagram, with no deadline, or when e is at most its deadline; otherwise it stays pending and the next boundary resets its subgroup.
  • With nothing eligible, the time moves to the next availability of a pending object, which is a boundary too; the run ends when nothing is pending.

The sink.

• Ready. A delivered object is ready when it has arrived and, for layer k ≥ 1, every unit it covers is at stage k − 1; it became ready at the later of its arrival and the time the last of those units reached that stage.
• Workers. The sink has workers non-preemptive workers. At each event time it first completes the jobs ending then, then gives each free worker the least ready job: by (layer, then for a base the time it became ready, from, object index) under base-first, so bases are decoded in the order they arrived, and by (the time it became ready, object index) under fifo. A job lasts decode_us.base or decode_us.refinement, once per object whatever its units. The next event is the next job end or the next time a job becomes ready.
• Presentation. When a job ends at t, every unit it covers is presented at layers = k + 1 at t, and reaches stage k.
• Deadlines. With playout_start_us set, unit u's deadline is playout_start_us + u·unit_us. Each unit a job presents after its deadline counts one missed: a base is presented all the same; a refinement is presented under present, and under discard is not presented and the unit stays at its stage.

Outputs.

• per object: sent_first_us, arrived_us, and its state: delivered, dropped, abandoned or capped;
• the presentations (unit, layers, t_us), ordered by unit, then layers;
• bfpf_sched, the bytes of the chunks arrived by unit 0's first presentation; tfpf_us, that presentation's time; and tffs_us, unit 0's first presentation at each layer count, null where none;
• offered, delivered, dropped, abandoned and never_sent_capped, in bytes, with offered = delivered + dropped + abandoned;
• missed;
• each unit's stall (§10.4), null where the plan or the base-only model never presents its base.

A case of the corpus names a model, a plan, and its claim: within-bound (every stall at most the plan's bound), exceeds:<plan> (the plan has no bound, and its largest stall passes the named plan's), or unbounded (the plan has no bound, and only its figures are checked).

Appendix C. Output tree

A commitment to every presentation of a session or a title: one leaf per (unit, layers), so that a record or a claim commits to its outputs by the pair (root, leaf_count) and any one output is provable by an inclusion path.

out_digest = SHA-256(canonical output)            SPEC §7 Digests: RGB8, s16le PCM, the attribute tensor, a 32-byte state hash
leaf = SHA-256("wai:out-leaf\x01" ‖ u64_be(unit) ‖ u16_be(layers) ‖ u16_be(decoder) ‖ out_digest)
node = SHA-256("wai:out-node\x01" ‖ left ‖ right)

• decoder is the index of the decoder entry that produced the output: entries are (capability, pin, object) triples in first-use order, presentations taken by (layers, unit), the object being the content hash (jwp-receipts §2.1) of the envelope decoded. For a title, each base's capability with the parameter set its decode read, named as a decoder entry's pin names it (jwp-receipts §2.4.12: the pin it verified, where it verified one), and its envelope, then each layer's refinement capability and envelope. For a session claim, the entries are its decoder entries (jwp-receipts §2.4.12), in the same order.
• Leaves are ordered by (unit, layers), and a (unit, layers) given twice is refused.
• The root over n ≥ 1 leaves is RFC 6962's Merkle tree hash: one leaf is itself; otherwise node(MTH(D[0:k]), MTH(D[k:n])), with k the largest power of two below n. No leaf is ever duplicated, so two leaf lists never give one root.
• A commitment is the root with its leaf count; a root alone is not one. A record or a claim that commits to an output tree states both.
• An inclusion proof is RFC 6962's audit path, checked as RFC 9162 §2.1.3.2 checks one under the leaf count the commitment states, never a count the proof's holder supplies. An audit path does not fix the tree's size: leaf 0's path in a tree of 7 leaves also walks to that root when 8 is taken as its size.
• layers is 16 bits, so it holds any stage count.

The JWP group root (jwp-receipts) is a separate, fixed wire format and is not this tree.

Appendix D. Measured titles

A measured title is a fixture directory with a title.json:

{ "format": "wai-measure-title/1", "title": "still", "about": "…",
  "unit_us": 40000,
  "bases": [ { "case": "staged-conformance/cases/image_int_hyper_2l", "base": 0,
               "first_unit": 0, "capture_us": null } ],
  "layers": [ "L01.wai", "L02.wai", "L03.wai" ],
  "source": { "file": "source.bin", "sha256": "<64 hex>" },
  "references": [ { "label": "one layer, q 1", "layers": [ "R0_00.wai" ] } ],
  "expect": "expect.json" }

• The stage structure is the staged set's own. Each base is a base of a staged-conformance case, named by the case directory and its index there: the case states its envelope, the parameter set it decodes against (by member and path) and its stage-0 output. Each layer's refines names its base, producers, layer and span (staged-delivery §3). title.json adds only what that model does not carry.
• unit_us is one unit's duration, and capture_us a base's capture time for a live delivery plan (null for one delivered on demand).
• source holds each unit's canonical buffer at its final shape, in unit order, with its SHA-256.
• references are the single-layer references of §6.2: each is the title's bases with the layers it lists.
• expect.json holds, from the fixture tool's own encoder, the SHA-256 of every unit's output at every stage, and of every reference's final units. An evaluation MUST reproduce them.
• A base MAY instead be named by its envelope alone, { "envelope": <path>, "set": { <member>: <path> }, "first_unit", "capture_us" }: it has no stage-0 output or case to check its decode against.
• limits (optional) lowers the limits the title is measured under: cost, four figures (output bytes, symbols, working bytes, multiply-accumulates), and chain_budget, each null for the tool's limit below. A title lowers a limit and never raises one (below).
• refused (optional) names the code the title's evaluation MUST be refused with: a title that exists to be refused has no figures.
• Every path is below wai/; a layer, source and expectation file is a file name in the fixture directory.

A title's content identity is BLAKE3 over "wai:measure-title\x01" and then, in path order, each measured file's path and bytes, each prefixed by its length as a 64-bit big-endian integer. The measured files are its objects (bases, layers and the references' layers), its bases' parameter-set files and its source; labels, title.json, stage-0 outputs and expect.json are not part of it.

Evaluation. Each base is decoded as a sink decodes one (SPEC §4: its capability, then its fallback, a refinement-only or companion-only capability making the envelope inert), against the parameter set its pin names (SPEC §3.1), and under the cost limit, which its payload's declared cost (integer-payloads §7) is compared with before any symbol is decoded or any output allocated. It must give the case's stage 0, and the capability, fallback, tier and pin the case states. Its layers are applied as a sink applies them (staged-delivery §4) under the chain budget, with the same limit on each layer's declared cost (Appendix A.5), one layer index at a time and, within one, in the order the title lists them; every layer MUST apply to every unit it covers, as in a set delivered whole and in order. The figures of §3–§6 and §9 and the output tree follow from the outputs at every stage. A refusal on the way names its code: the base decode's (cost_over_limit, missing_capability, a pin refusal) or the sink's (chain-over-limit, a layer's §4.2 reason). This composition of library functions is for measurement, not a sink's dispatch path.

The tools' limits. The reference tools (wai stage, wai_stage_measure, wai_stage_bench) decode every base under these cost figures, hold every layer to their output, symbols and working bytes (staged-delivery Appendix A.5), and hold every chain to the chain budget. A tool's --limit OUT,SYMBOLS,WORKING,MACS replaces the four cost figures. A title is measured under the lower, figure by figure, of its own limits and the tool's: a title lowers a limit and MUST NOT raise one, because whoever writes a title is not whoever runs the tool, and raising a limit takes the tool's own --limit.

figure	default	why
output bytes	2²⁵ (32 MiB)	five 1920 × 1080 RGB8 frames, or minutes of 48 kHz stereo PCM: more than one stage set's base carries, and below the declared clips a tool must refuse
symbols	2²⁵	one entropy-decode step per output byte at the output limit
working bytes	2²⁸ (256 MiB)	eight bytes per network activation, for networks a few times the output's size
multiply-accumulates	2³⁸	a learned decode of several megapixels
chain budget	2²⁸ (256 MiB)	eight times the output limit, for a base's units and the layers retained over them