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docs(pr-x12): apply 4 canon updates from cam-pq doc §6 (R-7 / R-13 / R-14 / R-15)
The substrate-binding doc pr-x12-cam-pq-sigker-dn-tree-substrate-bindings.md §6 proposed four canon updates that PR #197 marked "should be added to canon-resolutions-delta" but never actually applied. Closing that loop. 1. R-7 path correction (both canon files): tropical-GEMM kernel lives today at lance-graph::bgz17::scalar_sparse:: tropical_spmv, not in an abstract blasgraph namespace. The blasgraph name is the eventual abstraction (post-Plan-H); until then ndarray-codec depends on bgz17 directly. Cite the symbol, not the namespace, when wiring A6. 2. R-13 expansion (both canon files): Name the implementation primitives composed by the four policy modes (LocalEphemeral / SharedClusterWide / SharedRegional / PretrainedStatic): - cam_pq::CamCodebook for training (k-means + CAM-PQ) - bgz-tensor::Codebook4096 / bgz-hhtl-d for deployed encoding - dn_tree for online plastic updates (SharedClusterWide) - merkle_tree for integrity proof (Blake3-48-bit + xor_diff) - q2 (external) for gossip protocol PR-X12 contributes the wire format + CodebookHandle trait + Option A. No new substrate code required. 3. R-14 (NEW, both canon files): Formal-correctness layer via lance-graph::jc pillars: - Pillar 10 (Pflug-Pichler, jc::pflug): nested-distance Lipschitz on Sigma DN-trees proves CAM-PQ tree quantization preserves FreeEnergy within Lε. Active in default zero-dep build. - Pillar 11 (Hambly-Lyons, jc::hambly_lyons): signature uniqueness on tree-quotient. Active under --features hambly-lyons (PR #348, 2026-05-07); probe passes (forward<1e-9, converse>0.05, ratio≥1e6). R-4 quality floors inherit Pillar 10's Lipschitz bound. R-15 gates on Pillar 11. PR #350 corrects sigker::signature_kernel_pde's Goursat-PDE math bug; until then Pillar 11 uses signature_truncated. 4. R-15 (NEW, both canon files): SignatureBasis<const DEPTH: usize>: Basis<f32> as fifth concrete Basis<T> impl alongside DctIIBasis (video), EwaSplatBasis (3DGS), ShSpectralBasis (splat SH), HadamardBasis. Wraps sigker::signature_truncated (tensor-algebra, correct today) — NOT signature_kernel_pde (buggy until PR #350). Plan G gets a fifth lane: stream signal (audio waveform / time-series / gesture / handwriting). Quality floor inherits from Pillar 11 (R-14). Compression target ~10× over raw f32 path samples (calibrate during Plan G). Also updated the compaction-preservation contract, falsifiability matrix (+3 rows for R-14/R-15), and §0 to reflect R-1..R-15 inclusive. https://claude.ai/code/session_01HbqooFZHAjaUtFEzhA1R2u
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.claude/knowledge/pr-x12-canon-resolutions-delta.md

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## 0. What's actually new
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The merged canon (`bc9da4ad`) argued the architecture; canon-resolutions makes it falsifiable. Five categories of novel content survive the delta filter:
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The merged canon (`bc9da4ad`) argued the architecture; canon-resolutions makes it falsifiable. Six categories of novel content survive the delta filter:
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1. **Concrete trait signatures** — R-1 (`Basis<T>` + `LinearReduce` split), §8 surface (`PredictiveSignal`, `CurveOrder<const N>`, `RdoMetric`)
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2. **Quantified budgets** — R-3 LoC envelope per sub-card / per consumer + audit rule; R-4 four Plan G thresholds; R-11 4K@60fps latency budget
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3. **Math identities** — R-6 SSD-via-VNNI (`||A||² - 2A·B + ||B||²`), R-7 tropical-GEMM partition (`O(4^d) → O(d²)`)
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3. **Math identities** — R-6 SSD-via-VNNI (`||A||² - 2A·B + ||B||²`), R-7 tropical-GEMM partition (`O(4^d) → O(d²)`, kernel at `bgz17::scalar_sparse::tropical_spmv`)
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4. **Type-level invariants** — R-2 bit-15/bit-14 split, R-9 topology-FREE codec
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5. **Phasing patterns** — R-8 confidence-gate framing, R-13 Option-A-then-B for federated codebook
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5. **Phasing patterns** — R-8 confidence-gate framing, R-13 Option-A-then-B for federated codebook (primitives: `cam_pq` + `bgz-hhtl-d` + `dn_tree` + `merkle_tree`)
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6. **Formal-correctness + stream lane (post-merge)** — R-14 (`jc::pflug` Pillar 10 + `jc::hambly_lyons` Pillar 11), R-15 (`SignatureBasis<DEPTH>` as fifth Plan G lane)
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Plus the synthesis layer: §9 falsifiability matrix (24 rows), §10 sequencing with named gates, §12 compaction-preservation contract.
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Plus the synthesis layer: §9 falsifiability matrix (24+3 rows including R-14/R-15), §10 sequencing with named gates, §12 compaction-preservation contract.
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---
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At 4K 132K CTUs/frame: ~4 ms vs ~64 ms just for partition RDO. At 60 fps, the difference between fitting and missing budget.
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**Dep direction:** `ndarray-codec → lance-graph::blasgraph` (tropical-GEMM kernels live in blasgraph). Allowed post-Plan-H because ndarray-codec is a sibling crate, not the bottom.
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**Dep direction:** `ndarray-codec → lance-graph::blasgraph` (tropical-GEMM kernels nominally live in blasgraph). Allowed post-Plan-H because ndarray-codec is a sibling crate, not the bottom.
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**Actual kernel home (current):** `lance-graph::bgz17::scalar_sparse::tropical_spmv`. The `blasgraph` namespace is the eventual abstraction; until that lands, ndarray-codec depends on bgz17 directly. Cite the symbol when wiring A6, not the namespace.
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**Plan A6 (1 week) ships this.** λ-RDO knob scales edge weights; tropical-GEMM relaxation computes optimal mode tree.
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Wire-format hook for Option A: `WorkerId: u16` + `CodebookHash: u64` in frame header.
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**Implementation primitives** (already exist; PR-X12 only adds the wire format + `CodebookHandle` trait):
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| Concern | Crate / module |
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|---|---|
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| Codebook training (k-means + CAM-PQ) | `ndarray::hpc::cam_pq::CamCodebook` |
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| Deployed encoding format | `lance-graph::bgz-tensor::Codebook4096` / `bgz-hhtl-d` |
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| Online plastic updates (SharedClusterWide) | `ndarray::hpc::dn_tree` |
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| Integrity proof (Blake3-48 Merkle root, xor_diff) | `ndarray::hpc::merkle_tree` |
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| Gossip protocol | `q2` (external) |
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### 5.3 Streaming flush granularity (R-12)
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Per-CTU default. `FlushUnit` 2-bit tag in frame header:
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## 11. The single load-bearing paragraph (§13)
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## 11. Formal-correctness layer (R-14) — post-merge addition
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The substrate-binding doc (`pr-x12-cam-pq-sigker-dn-tree-substrate-bindings.md`) surfaced two formal proofs in `lance-graph::jc` that the codec inherits without re-proving:
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| Pillar | Crate / module | What it proves | Status |
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|---|---|---|---|
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| **Pillar 10** (Pflug-Pichler) | `jc::pflug` | Nested-distance Lipschitz on Sigma DN-trees: CAM-PQ tree quantization preserves FreeEnergy within Lε | Active in default zero-dep build |
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| **Pillar 11** (Hambly-Lyons) | `jc::hambly_lyons` | Signature uniqueness on tree-quotient: any path of bounded variation is uniquely determined by its truncated signature up to tree-like equivalence (Annals 171(1), arXiv:math/0507536) | Active under `--features hambly-lyons` (PR #348, 2026-05-07); probe passes (forward<1e-9, converse>0.05, ratio≥1e6) |
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R-4's quality-floor rows for video / KV / gradient inherit Pillar 10's Lipschitz bound. R-15's signature lane gates on Pillar 11.
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**Open work (G-4):** PR #350 corrects `sigker::signature_kernel_pde`'s known Goursat-PDE math bug; Pillar 11's probe deliberately uses `signature_truncated` (tensor-algebra) until PR #350 lands. Production-scale benchmarking pending.
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---
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## 12. Stream-signal codec lane (R-15) — post-merge addition
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`SignatureBasis<const DEPTH: usize>: Basis<f32>` is the fifth concrete `Basis<T>` impl, complementing the four lanes in §1's table:
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```rust
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// New: ndarray::hpc::signature (~1 wk, wraps sigker::signature_truncated)
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impl<const DEPTH: usize> Basis<f32> for SignatureBasis<DEPTH> {
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fn dim(&self) -> usize { /* truncated tensor-algebra dim */ }
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fn apply(&self, path: &[f32], signature: &mut [f32]) {
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// iterated-integral truncation via sigker::signature_truncated
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}
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fn invert(&self, _sig: &[f32], _path: &mut [f32]) {
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unimplemented!("path-from-signature is unique only up to tree-like \
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equivalence per R-14 Pillar 11")
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}
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}
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```
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**Plan G gets a fifth lane: "stream signal"** — audio waveforms / time-series / gesture / handwriting paths. Codec is `SignatureBasis<DEPTH=3>` + standard rANS over the four-mode taxonomy; quality floor inherits from Pillar 11 (R-14); compression target ~10× over raw f32 path samples (calibrate during Plan G).
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**Why `signature_truncated` not `signature_kernel_pde`:** the PDE form ships a known divergence bug (PR #350). The tensor-algebra path is correct today and is what Pillar 11 cites.
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---
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## 13. The single load-bearing paragraph (canon-resolutions §13)
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> *The merged canon committed to the right architectural synthesis (M:E-A, M:E-D, M:E-G, M:E-I) but left the load-bearing contracts unsigned. Canon-resolutions commits them: `Basis<T>` + `LinearReduce` are two traits not one (R-1); bit 14 of the leaf header is consumer-typed and bit 15 universal (R-2); generic codec body ≤1500 LoC with ≤200 LoC per consumer (R-3); four threshold pairs gate Plan G's pass criteria (R-4); the trajectory is Plan G (2 wks) → Plan A7 critical path (1.5 wks) → Phase 2 consumers parallel (3 wks); end state is one binary, four loads, ~2 KLoC stack demonstrating M:H-NEW-1 in ~10.5 weeks of wall-clock. Every claim in §9 has a test; Plan G's bench-harness binary is the audit. The falsifiability is the point.*
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> *The merged canon committed to the right architectural synthesis (M:E-A, M:E-D, M:E-G, M:E-I) but left the load-bearing contracts unsigned. Canon-resolutions commits them: `Basis<T>` + `LinearReduce` are two traits not one (R-1); bit 14 of the leaf header is consumer-typed and bit 15 universal (R-2); generic codec body ≤1500 LoC with ≤200 LoC per consumer (R-3); four threshold pairs gate Plan G's pass criteria (R-4); the trajectory is Plan G (2 wks) → Plan A7 critical path (1.5 wks) → Phase 2 consumers parallel (3 wks); end state is one binary, four loads, ~2 KLoC stack demonstrating M:H-NEW-1 in ~10.5 weeks of wall-clock. Every claim in §9 has a test; Plan G's bench-harness binary is the audit. The falsifiability is the point. The substrate-binding follow-up (R-14, R-15) adds a formal-correctness layer via `jc` pillars and a fifth stream-signal lane via `SignatureBasis<DEPTH>`.*
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.claude/knowledge/pr-x12-substrate-canon-resolutions.md

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(R-5 through R-7 restorations)
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- **§6** — three pieces of detail from session B the merge underrepresented
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(R-8 through R-10 restorations)
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- **§7** — three commitments missing from both originals and from the
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merge (R-11 through R-13 new specs)
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- **§7** — five commitments missing from both originals and from the
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merge: R-11 through R-13 (latency, flush granularity, federated
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codebook) plus R-14 (formal correctness via `jc` pillars) and R-15
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(`SignatureBasis<DEPTH>` as fifth Plan G lane), the latter two
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surfaced post-merge by the substrate-binding docs
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Then five integration pieces that make the resolutions actionable:
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- **§11** — end-state + trajectory (think it from the end)
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- **§12** — compaction-preservation contract
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Citation IDs: `R-1` through `R-13` for resolutions. Canon IDs (`M:E-*`,
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`A:E-*`, `B:E-*`, `M:H-*`, `M:T-*`) remain stable; this doc adds, does
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not renumber.
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Citation IDs: `R-1` through `R-15` for resolutions (R-14, R-15
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appended post-merge from the substrate-binding doc; numbering remains
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append-only). Canon IDs (`M:E-*`, `A:E-*`, `B:E-*`, `M:H-*`, `M:T-*`)
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remain stable; this doc adds, does not renumber.
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Sister docs (read order):
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this is dep-allowed because ndarray-codec is a sibling, not the bottom).
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**Actual kernel home (current).** The tropical-GEMM kernel lives today
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at `lance-graph::bgz17::scalar_sparse::tropical_spmv` — NOT in an
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abstract `blasgraph` namespace. The codec's tropical-GEMM call is
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`bgz17::scalar_sparse::tropical_spmv(edge_weights, dag)`. The
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`lance-graph::blasgraph` name above is the eventual abstraction layer
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(post-Plan-H extraction); until that lands, ndarray-codec depends on
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bgz17 directly. Cite the symbol, not the namespace, when wiring A6.
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**Plan A6 RDO (1 week) ships this.** The λ-RDO knob (per A:§10.3) and
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R-4 gradient threshold (8× compression at <0.5% loss delta). At that
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**Implementation primitives (current substrate, no new code required):**
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| Concern | Crate / module |
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|---------|----------------|
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| Codebook training (k-means + CAM-PQ) | `ndarray::hpc::cam_pq::CamCodebook` (`train_geometric` / `train_semantic` / `train_hybrid`) |
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| Deployed encoding format (per-shard) | `lance-graph::bgz-tensor::Codebook4096` and the `bgz-hhtl-d` shared-palette variant |
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| Online plastic updates (`SharedClusterWide`) | `ndarray::hpc::dn_tree` (quaternary plastic memory, partial-Hamming descent) |
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| Integrity proof for distributed updates | `ndarray::hpc::merkle_tree` (Blake3-48-bit, 1 KB root, `xor_diff` panCAKES compression) |
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| Gossip protocol (cluster-wide) | `q2` (external — implements the wire protocol) |
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The four policy modes (`LocalEphemeral` / `SharedClusterWide` /
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`SharedRegional` / `PretrainedStatic`) compose these primitives
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differently; the codec body exposes a `CodebookHandle` trait, and the
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primitives plug in via that trait. **PR-X12 contributes the wire format
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+ trait + Option A; the primitives above already exist.**
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**Cite as R-13 in Plan F PR description.**
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### R-14 — Formal correctness via `lance-graph::jc` pillars
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**Problem.** Canon and resolutions describe the codec's empirical
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behaviour (R-4 thresholds, R-11 latency) but never name the formal
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correctness proofs the substrate already carries. Without a citation,
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"the codec is correct" is unverifiable; with citations, the codec
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inherits machine-checked guarantees from existing crates.
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**Resolution.** Pin both pillars and what each proves.
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**Two formal proofs in `lance-graph::jc`:**
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- **Quantization correctness (Pillar 10, Pflug-Pichler):**
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nested-distance Lipschitz on Sigma DN-trees. Proves that CAM-PQ tree
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quantization preserves the FreeEnergy functional within a Lipschitz
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factor Lε. **This is the proof PR-X12 cites for "wire-format
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quantization is faithful."** Implementation: `jc::pflug` (active in
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default build, zero-dep).
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- **Path-signature correctness (Pillar 11, Hambly-Lyons):**
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signature uniqueness on tree-quotient. Proves that any path of
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bounded variation is uniquely determined by its truncated signature
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up to tree-like equivalence (Annals of Mathematics 171(1):109–167,
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arXiv:math/0507536). **This is the proof PR-X12 cites for the
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`SignatureBasis<DEPTH>` lane (R-15).** Implementation:
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`jc::hambly_lyons` (active under `--features hambly-lyons`, since
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PR #348 landed on 2026-05-07).
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**What the codec inherits.** Both pillars exist; the codec cites them
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and does not reprove. R-4's "Quality floor" rows for video / KV /
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gradient inherit Pillar 10's Lipschitz bound automatically. R-15's
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signature-lane gates on Pillar 11.
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**Status.**
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- Pillar 10: active in default zero-dep build.
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- Pillar 11: active under `--features hambly-lyons`; passes its probe
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(forward < 1e-9, converse > 0.05, discrimination ratio ≥ 1e6 over
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N=100 random pairs in d=3 at depth-2).
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- Production-scale benchmarking + PR #350 (`signature_kernel_pde`
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Goursat-PDE math correction) remain open — see Gap G-4 in
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`pr-x12-cam-pq-sigker-dn-tree-substrate-bindings.md`. Pillar 11's
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probe deliberately uses `signature_truncated` (tensor-algebra path),
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not the buggy PDE form.
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**Falsifies if.** Pillar 10 ever flips state (a regression in the
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Pflug-Pichler proof bound) — Plan G's video / KV / gradient quality
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floors lose their formal underwriting and become empirical-only.
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**Cite as R-14 in any PR claiming "codec output is faithful to
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input" or wiring `SignatureBasis` (R-15).**
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---
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### R-15 — `SignatureBasis<const DEPTH: usize>` as `Basis<f32>` impl
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**Problem.** R-1 commits the `Basis<T>` shape; the canon lists three
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concrete impls (`DctIIBasis<N>` for video, `EwaSplatBasis` for 3DGS,
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`ShSpectralBasis<L>` for splat SH). No `Basis<T>` impl targets
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*streams* — audio waveforms, time-series, gesture/handwriting paths.
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Plan G has only four lanes; path-structured signals are unaddressed.
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**Resolution.** Commit `SignatureBasis<const DEPTH: usize>: Basis<f32>`
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as the fifth concrete impl, wrapping the path-signature kernel from
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the external `lance-graph::sigker` crate.
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```rust
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// Concrete impl, lives in ndarray::hpc::signature (new module, ~1 wk)
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impl<const DEPTH: usize> Basis<f32> for SignatureBasis<DEPTH> {
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fn dim(&self) -> usize { /* truncated tensor-algebra dim at DEPTH */ }
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fn apply(&self, path: &[f32], signature: &mut [f32]) {
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}
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fn invert(&self, _sig: &[f32], _path: &mut [f32]) {
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unimplemented!("signature inversion is N/A — path unique only up to \
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tree-like equivalence per R-14 / Pillar 11")
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}
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}
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```
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**Why `signature_truncated` and not `signature_kernel_pde`.** The
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diverges from the true kernel `I₀(2·√⟨u, v⟩)` at moderate inner
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products). The tensor-algebra path (`signature_truncated`) is correct
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today and is what jc Pillar 11 cites. R-15 wraps the truncated path;
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the PDE form becomes available after PR #350 lands.
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**Plan G gets a fifth lane.** "Stream signal" mode:
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- Input: audio waveform / time-series / gesture stream
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- Codec: `SignatureBasis<DEPTH=3>` truncates path signature, residuals
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go through standard rANS via the four-mode taxonomy
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- Quality floor: signature-uniqueness preservation per Pillar 11
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- Compression target: ~10× over raw f32 path samples (estimate;
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calibrate during Plan G)
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**Falsifies if.** `SignatureBasis<DEPTH=3>` plus rANS fails to
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At that point, raise DEPTH or fall back to per-block DCT-II for the
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stream lane.
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**Cost.** ~1 week wrapper around `sigker::signature_truncated` +
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basis-trait plumbing + Plan G fifth-lane wiring.
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**Cite as R-15 in any PR adding a stream-signal codec lane or
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wiring `SignatureBasis`.**
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---
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## 8. The canonical contracts — concrete trait signatures
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| R-11 (4K 60fps SIMD-batched) | this doc | Plan G video latency assert | Per-CTU encode time | ≤210 ns/CTU on Sapphire Rapids |
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| R-12 (per-CTU flush) | this doc | A8 frame-header parse + decode | First-CTU latency | First CTU decodable before frame complete |
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| R-13 (Option A per-shard) | this doc | Plan F on BERT-glue | 8× compression + accuracy | Holds; else escalate to Option B |
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| R-14 (Pillar 10 active) | this doc | `cargo test -p jc` (default features) | Pflug-Pichler Lipschitz bound | Pillar 10 probe green |
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| R-14 (Pillar 11 active) | this doc | `cargo test -p jc --features hambly-lyons` | Signature uniqueness probe | forward < 1e-9, converse > 0.05, ratio ≥ 1e6 |
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| R-15 (SignatureBasis lane) | this doc | Plan G stream-signal lane | path reconstruction under Pillar 11 | ε within discrimination ratio of Pillar 11 |
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**Every row of this matrix is a test.** Plan G's bench harness binary
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1. **The five "merged well" items** from §3 (M:E-A / M:E-D / M:E-G /
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M:E-I / M:E-F) — these are the canon's load-bearing synthesis.
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2. **The thirteen resolutions** R-1 through R-13 with their summary
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2. **The fifteen resolutions** R-1 through R-15 with their summary
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commitments:
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- R-1: `LinearReduce<Basis>` two-trait shape
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- R-2: bit 15 universal, bit 14 consumer-typed
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- R-3: ≤1500 LoC generic, ≤200 LoC per consumer
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- R-4: 4 threshold pairs (video, splat, kv, grad)
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- R-5: DCT crossover ~64 blocks
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- R-6: SSD via VNNI ≥30× over SAD
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- R-7: tropical-GEMM partition O(4^d) → O(d²)
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- R-7: tropical-GEMM partition O(4^d) → O(d²) via
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`bgz17::scalar_sparse::tropical_spmv`
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- R-8: Plan G is confidence gate
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- R-9: topology-FREE codec layer
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- R-10: ~4 bits/Gaussian near target, ~1 bit stretch
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- R-11: 210 ns/CTU SIMD-batched encode
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- R-12: per-CTU flush default; per-bucket Plan F
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- R-13: Option A (per-shard codebook) for Plan F v1
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- R-13: Option A (per-shard codebook) for Plan F v1; primitives are
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`cam_pq` + `bgz-hhtl-d` + `dn_tree` + `merkle_tree`
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- R-14: formal correctness via `jc::pflug` (Pillar 10) +
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`jc::hambly_lyons` (Pillar 11, feature-gated)
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- R-15: `SignatureBasis<DEPTH>: Basis<f32>` as fifth Plan G lane
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(stream signal)
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3. **The trajectory** from §2 — Phase 0 → A7 → parallelise → Phase 2
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4. **The five-category architecture** including `ndarray-codec`
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5. **The four traits** as the canonical contracts:
@@ -1258,7 +1404,7 @@ When this doc is summarised across context windows, preserve at minimum:
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7. **The falsifiability matrix in §9** — every claim has a test;
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not every claim will pass; that's the design
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**Citation IDs in this doc** (R-1 .. R-13) are stable. Canon IDs
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**Citation IDs in this doc** (R-1 .. R-15) are stable. Canon IDs
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(M:E-*, M:H-*, M:H-NEW-*, M:T-*, A:E-*, A:H-*, A:T-*, B:E-*, B:HG-*,
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B:D-*) remain stable per canon's §10. Append, never renumber.
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