WAI Extension: Balanced-Ternary MPS Transform (wai.ternary.tt)

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Status: Draft / reference prototype. Engine: wai-rs/src/ternary.rs (feature ternary), receipt wai-rs/src/ternary_receipt.rs (feature ternary_receipt). A quantum-inspired (tensor-network), classical, deterministic transform.

0. What this is — and what it is not (read first)

wai.ternary.tt is a provenance capability; rate reduction is not its purpose. It exists to demonstrate, and make usable, one property: a quantum-inspired ternary/tensor-network transform whose reconstruction is byte-exact, portable, and receiptable.

It is not a good general media codec, and this document says so up front with numbers (§5). If you need compression ratio, use the zeroth menu (JPEG-XL, AVIF, Opus). Reach for wai.ternary.tt only when determinism and provenance of the reconstruction outrank the ratio — an auditable, energy-accounted transform for high-throughput edge streams where “what exactly did the sink reconstruct, and what did it cost?” must be answerable and signable.

1. Lineage (ported, not invented)

The two ingredients are established, working techniques — this extension does not reinvent them:

• Balanced-ternary weights ({−1,0,+1}, BitNet-b1.58 style; five trits per byte, 3^5 = 243 < 256, the 1.58-bit regime).
• Matrix-product-state (MPS / tensor-train) compression — a signal reshaped into a chain of small cores with bounded bond dimension.

Both already live as real code in the wider portfolio (ternary fabrics, MPS/MPO indices). Every such implementation shares one property that makes it not WAI-conformant: a float scale (α·(trit·x), α : f32). A float scale desyncs across machines exactly as a float σ desyncs a learned entropy coder.

The one change that is the whole contribution: the scale is an integer (per output column: a shared exponent + a u16 mantissa, dequantized by a pure integer shift). So the entire decode path is i64/i128 with no float, and a reconstruction is byte-identical on every machine. Encoder-side float (the SVD, the optimal per-column scale) runs once at encode and never at decode — the same posture as QAT and as wai.neural.int_hyper.

2. Container (WQTT)

"WQTT" | u8 version | u32 n_signal | u8 n_layers | layer*
layer  := u8 n_sites | u8 n_cores | core*
core   := u16 left | u16 phys | u16 right | u8 scale_exp
        | scale_mant[right] (u16 each) | packed_trits(left*phys*right)

Little-endian; trits base-3-packed (five per byte). The container is self-describing and bounds-checked on parse (from_wqtt). This byte string is the canonical payload a receipt’s identity hashes.

3. Transform

A left-canonical MPS per layer: sites 0..n-1 are orthonormal isometries (the U of a thin SVD), the last core absorbs the magnitude (the remaining S·Vᵀ). Per-column integer scales keep the isometries unit-scaled so magnitude never drifts multiplicatively; the last core carries the amplitude.

Fidelity knob — residual layers (TernaryStack). RVQ over ternary-MPS: each layer ternary-MPS-encodes the residual of the sum so far. Decode sums the layers. A sum of byte-exact deterministic integer decodes is itself byte-exact deterministic, so fidelity climbs with depth while the reconstruction stays portable. phys = 2 is the binary reshape; phys = 3 is the qutrit/base-3 site reshape (a ternary site dimension, distinct from the ternary weights).

4. Conformance — reconstruction-equivalence

A sink conforms iff, given a WQTT payload, it produces a decoded signal whose BLAKE3 (reconstruction_hash) matches — byte for byte, on every machine. This is the deterministic-floor *-equivalence criterion the other WAI extensions use, here over the integer decode. The registry classes it accordingly: capability_tier = Lossy (fidelity to source is lossy), replicate_class = StandardDefined (the reconstruction is fixed by WAI’s deterministic floor, not a float neural decode), license = RoyaltyFree.

5. Rate–distortion verdict (measured)

Measured on a realistic 256-sample multi-tone + noise stream (raw 2048 B, bond ≤ 4), reconstruction SNR vs on-wire bytes as residual layers accumulate:

Two limits, both recorded so the scope is stated plainly:

• Low rate–distortion. 13.3 dB at 3.8× with six layers (the table above); the noise floor is incompressible and multi-tone content out-ranks bond-4. On a toy sinusoid it reaches ~20 dB @ 2×, but that is a flattering input.
• Entropy coding of the trits is break-even. The trit stream is ~54% zeros (≈1.45 bits vs the base-3 packing’s 1.6, ~9% headroom), most of which the rANS header/state overhead eats; it is even a small loss at low layer counts. The five-trits-per-byte packing is already near-optimal.

Consistent with WAI’s own charter (SPEC Appendix B: don’t reinvent codecs). The value is not the ratio — it is that the reconstruction and its cost are byte-exact and auditable.

6. Receipt (JWP profile)

The provenance payoff (ternary_receipt.rs). A [TernaryReceipt] separates the two costs so each is trusted honestly:

seal decodes the stack (so reconstruction_hash is always the true reconstruction); verify checks the Merkle root + Ed25519; verify_reconstruction recovers the stack from the WQTT payload and confirms hash, shape, work, and reconstruction independently. Chains via parent_receipt_hash. The JWP Merkle + Ed25519 are reused verbatim — the same shape as QuantumReceipt (quantum-sim) and the world/provenance receipts. Measured energy comes from the same IOReport path as wai_quantum_meter; never fabricated. The figure’s acquisition class rides beside it as an optional signed label (energy-measurement §2.8): absent, the receipt keeps its legacy bytes and the figure is unlabelled; present, it is inside the signature. with_energy_class labels and re-signs a sealed receipt.

7. Productionize only with a use case

This capability is registered and receipt-backed, but its RD verdict means it earns a place in a deployment only where a concrete auditable-edge-stream requirement makes provenance outrank ratio. Absent that, it is a proven reference prototype — do not tune the RD further; that ceiling is not the interesting question, and it has been measured.