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Every Ed25519 signature WAI defines is verified strictly, in order: a canonical key, a key not of small order, S < L, R not of small order, and the cofactorless equation with R compared byte for byte. OER/2's chain signature keeps the rule oer-receipts §5 settles. jwp-receipts §3.1 step 3, http-delivery's playlist receipt and packaging's receipt cite it instead of restating it; the worlds, avatars, feeds, spatial-audio, haptics, volumetric, score, film, provenance, ternary and quantum receipt texts cite it where they name their signature. CHANGELOG records the sweep. Co-Authored-By: Claude Opus 5.5 <[email protected]>
139 lines
6.9 KiB
Markdown
139 lines
6.9 KiB
Markdown
# WAI Extension: Balanced-Ternary MPS Transform (`wai.ternary.tt`)
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Status: **Draft / reference prototype.** Engine: `wai-rs/src/ternary.rs`
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(feature `ternary`), receipt `wai-rs/src/ternary_receipt.rs` (feature
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`ternary_receipt`). A **quantum-inspired** (tensor-network), classical,
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deterministic transform.
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## 0. What this is — and what it is not (read first)
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`wai.ternary.tt` is a **provenance** capability; rate reduction is not its purpose.
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It exists to demonstrate, and make usable, one property: a quantum-inspired
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ternary/tensor-network transform whose reconstruction is **byte-exact, portable,
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and receiptable**.
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It is **not** a good general media codec, and this document says so up front with
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numbers (§5). If you need compression ratio, use the zeroth menu (JPEG-XL, AVIF,
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Opus). Reach for `wai.ternary.tt` only when *determinism and provenance of the
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reconstruction outrank the ratio* — an auditable, energy-accounted transform for
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high-throughput edge streams where "what exactly did the sink reconstruct, and
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what did it cost?" must be answerable and signable.
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## 1. Lineage (ported, not invented)
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The two ingredients are established, working techniques — this extension does not
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reinvent them:
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- **Balanced-ternary weights** ({−1,0,+1}, BitNet-b1.58 style; five trits per
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byte, `3^5 = 243 < 256`, the 1.58-bit regime).
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- **Matrix-product-state (MPS / tensor-train) compression** — a signal reshaped
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into a chain of small cores with bounded bond dimension.
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Both already live as real code in the wider portfolio (ternary fabrics, MPS/MPO
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indices). Every such implementation shares one property that makes it **not**
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WAI-conformant: a **float scale** (`α·(trit·x)`, `α : f32`). A float scale
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desyncs across machines exactly as a float σ desyncs a learned entropy coder.
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**The one change that is the whole contribution:** the scale is an **integer**
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(per output column: a shared exponent + a `u16` mantissa, dequantized by a pure
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integer shift). So the entire *decode* path is `i64`/`i128` with no float, and a
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reconstruction is byte-identical on every machine. Encoder-side float (the SVD,
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the optimal per-column scale) runs once at encode and never at decode — the same
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posture as QAT and as `wai.neural.int_hyper`.
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## 2. Container (`WQTT`)
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```
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"WQTT" | u8 version | u32 n_signal | u8 n_layers | layer*
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layer := u8 n_sites | u8 n_cores | core*
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core := u16 left | u16 phys | u16 right | u8 scale_exp
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| scale_mant[right] (u16 each) | packed_trits(left*phys*right)
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```
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Little-endian; trits base-3-packed (five per byte). The container is
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self-describing and bounds-checked on parse (`from_wqtt`). This byte string is
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the canonical payload a receipt's identity hashes.
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## 3. Transform
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A left-canonical MPS per layer: sites `0..n-1` are orthonormal isometries (the
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`U` of a thin SVD), the **last** core absorbs the magnitude (the remaining
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`S·Vᵀ`). Per-column integer scales keep the isometries unit-scaled so magnitude
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never drifts multiplicatively; the last core carries the amplitude.
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**Fidelity knob — residual layers (`TernaryStack`).** RVQ over ternary-MPS: each
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layer ternary-MPS-encodes the residual of the sum so far. Decode **sums** the
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layers. A sum of byte-exact deterministic integer decodes is itself byte-exact
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deterministic, so fidelity climbs with depth while the reconstruction stays
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portable. `phys = 2` is the binary reshape; **`phys = 3` is the qutrit/base-3
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site reshape** (a ternary *site* dimension, distinct from the ternary *weights*).
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## 4. Conformance — reconstruction-equivalence
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A sink conforms iff, given a `WQTT` payload, it produces a decoded signal whose
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BLAKE3 (`reconstruction_hash`) matches — byte for byte, on every machine. This is
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the deterministic-floor `*-equivalence` criterion the other WAI extensions use,
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here over the integer decode. The registry classes it accordingly:
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`capability_tier = Lossy` (fidelity to *source* is lossy), `replicate_class =
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StandardDefined` (the reconstruction is fixed by WAI's deterministic floor, not a
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float neural decode), `license = RoyaltyFree`.
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## 5. Rate–distortion verdict (measured)
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Measured on a realistic 256-sample multi-tone + noise stream (raw 2048 B, bond
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≤ 4), reconstruction SNR vs on-wire bytes as residual layers accumulate:
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| layers | SNR | payload (entropy-coded) |
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|---|---|---|
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| K=1 | 3.6 dB | 104 B (19.7×) |
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| K=2 | 5.7 dB | 194 B (10.6×) |
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| K=3 | 7.6 dB | 280 B (7.3×) |
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| K=4 | 10.1 dB | 370 B (5.5×) |
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| K=6 | 13.3 dB | 546 B (3.8×) |
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Two limits, both recorded so the scope is stated plainly:
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- **Low rate–distortion.** 13.3 dB at 3.8× with six layers (the table above); the
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noise floor is incompressible and multi-tone content out-ranks bond-4. On a toy
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sinusoid it reaches ~20 dB @ 2×, but that is a flattering input.
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- **Entropy coding of the trits is break-even.** The trit stream is ~54% zeros
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(≈1.45 bits vs the base-3 packing's 1.6, ~9% headroom), most of which the rANS
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header/state overhead eats; it is even a small loss at low layer counts. The
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five-trits-per-byte packing is already near-optimal.
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Consistent with WAI's own charter (SPEC Appendix B: *don't reinvent codecs*). The
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value is **not** the ratio — it is that the reconstruction and its cost are
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byte-exact and auditable.
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## 6. Receipt (JWP profile)
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The provenance payoff (`ternary_receipt.rs`). A [`TernaryReceipt`] separates the
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two costs so each is trusted honestly:
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| field | what | trust |
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|---|---|---|
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| `payload_hash` | BLAKE3 of the `WQTT` bytes | re-checkable (tamper-evidence) |
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| `reconstruction_hash` | BLAKE3 of the decoded signal | **re-checkable** (re-decode) |
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| `trit_macs` | Σ trit-tensor sizes — the decode work | **verified** by recomputation |
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| `joules_micro` | measured marginal energy | **attested** by signature |
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`seal` decodes the stack (so `reconstruction_hash` is always the true
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reconstruction); `verify` checks the Merkle root + Ed25519 (as SPEC §7 *Signatures*
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requires); `verify_reconstruction`
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recovers the stack from the `WQTT` payload and confirms hash, shape, work, and
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reconstruction independently. Chains via `parent_receipt_hash`. The JWP Merkle +
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Ed25519 are reused verbatim — the same shape as `QuantumReceipt`
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([quantum-sim](quantum-sim.md)) and the world/provenance receipts. Measured
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energy comes from the same IOReport path as `wai_quantum_meter`; never fabricated.
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The figure's acquisition class rides beside it as an optional signed label
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([energy-measurement](energy-measurement.md) §2.8): absent, the receipt keeps
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its legacy bytes and the figure is unlabelled; present, it is inside the
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signature. `with_energy_class` labels and re-signs a sealed receipt.
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## 7. Productionize only with a use case
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This capability is registered and receipt-backed, but its RD verdict means it
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earns a place in a deployment **only** where a concrete auditable-edge-stream
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requirement makes provenance outrank ratio. Absent that, it is a proven reference
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prototype — do not tune the RD further; that ceiling is not the interesting
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question, and it has been measured.
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