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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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## 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:
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.
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.
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:
// iterated-integral truncation via sigker::signature_truncated
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}
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fninvert(&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>`.*
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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reconstruct the path within ε under Pillar 11's discrimination ratio.
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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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All three plug-points (per M:E-E) get concrete signatures here. These
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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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emits a JSON report containing the actual measurement for each row;
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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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