audit(L0): algebra primitives — CLOSED
First per-layer audit of the substrate-liveness program. Establishes the registry shape and standard of evidence for subsequent layers. L0 (algebra primitives) is foundation; verdict CLOSED: - 4 ADRs in scope (ADR-0001 versor invariant, ADR-0003 coordinate dissolution, ADR-0004 rotor as operator, ADR-0009 compositional physics). - 6 modules (versor, rotor, cga, cl41, holonomy, backend); every module has at least 2 live-import sites outside the package and outside tests (38 distinct caller files overall). - core test --suite algebra exercises every L0 module: 82 passed, 50 skipped (Rust-parity tests, Python-only env — not a closure gap). - Cross-layer contract pass 1 (mechanical): every exposed symbol has at least one downstream consumer. - Cross-layer contract pass 2 (semantic): versor_condition < 1e-6 invariant is measured per turn (core/cognition/trace.py:34), folded into deterministic trace payload, surfaced to operator via CLI, and gated at the eval boundary (evals/cognition/runner.py:60). Matches CLAUDE.md discipline of "measure and surface, don't weaken." No cleanup performed — no dead code, no redundant modules, no orphaned tests found at L0. Foundation is honest. One scope-hypothesis correction: layering table cited "algebra/backend/" (directory); reality is "algebra/backend.py" (file). Hypothesis drift, recorded for amendment if it matters elsewhere. Three forward-pointing notes left for downstream auditors: - L1 should verify field propagation correctness is tested independently of L5's downstream versor_condition measurement. - L2 should verify vault honors exact-CGA-recall end-to-end, not just at the algebra layer. - ADR-0020 (Rust parity) is cross-cutting; audit when Rust integration is live rather than at any single layer. Format established for subsequent per-layer commits. Audit progress table in registry root tracks pending layers; resume-after-interruption is "look at the progress table, start with the first pending layer."
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# Substrate Liveness Registry
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**Scope:** [substrate-liveness-audit-scope](../decisions/substrate-liveness-audit-scope.md) (v2)
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**Status:** Active audit — append-only as layers are completed.
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**Discipline:** [feedback-adr-cross-reference-discipline](../../../.claude/projects/-Users-kaizenpro-Projects-core/memory/feedback-adr-cross-reference-discipline.md), [feedback-cleanup-as-you-find](../../../.claude/projects/-Users-kaizenpro-Projects-core/memory/feedback-cleanup-as-you-find.md)
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## Audit progress
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| Layer | Status | Verdict | Cleanup performed | Last audited |
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|---|---|---|---|---|
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| L0 — Algebra primitives | ✅ Audited | **CLOSED** | None — no dead code found | 2026-05-24 |
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| L1 — Field substrate | ⏳ Pending | — | — | — |
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| L2 — Vault | ⏳ Pending | — | — | — |
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| L3 — Language packs | ⏳ Pending | — | — | — |
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| L4 — Recognition | ⏳ Pending | — | — | — |
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| L5 — Cognition pipeline | ⏳ Pending | — | — | — |
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| L6 — Chat runtime + surface composition | ⏳ Pending | — | — | — |
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| L7 — Teaching loop | ⏳ Pending | — | — | — |
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| L8 — Inter-session memory + contemplation | ⏳ Pending | — | — | — |
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| L9 — Epistemic state + verdicts | ⏳ Pending | — | — | — |
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L10 / L11 are not audit targets (no design to audit; flagged in scope as
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gaps the audit will surface need for).
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---
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## L0 — Algebra primitives
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**Audit date:** 2026-05-24
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**Auditor:** primary agent (Claude)
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**Verdict:** **CLOSED**
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### Scope-hypothesis correction (per audit step 0)
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The scope's layering table cited `algebra/backend/` (directory). Reality:
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`algebra/backend.py` (single 267-line file). Hypothesis drift, not a
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finding — recorded so the scope's layering map can be amended if it
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matters elsewhere.
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### ADRs in scope for L0
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Triaged from the broader algebra/versor/CGA keyword grep against
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`docs/decisions/`:
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| ADR | Title | Status | Belongs at L0? |
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|---|---|---|---|
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| ADR-0001 | VocabManifold Versor Invariant | Accepted | Yes — defines the `versor_condition < 1e-6` invariant L0 must preserve |
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| ADR-0003 | Coordinate System Dissolution | Accepted | Yes — algebraic foundation |
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| ADR-0004 | Rotor as Operator, Not Vocabulary Property | Accepted | Yes — defines rotors as L0 primitives |
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| ADR-0009 | Compositional Physics | Accepted | Yes — versor composition rules |
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Other ADRs surfaced by the grep but assigned to higher layers (not
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audited at L0): ADR-0006 (L1), ADR-0019 (L2), ADR-0010 (L3 identity),
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ADR-0021/0022/0023/0024/0025 (L5 policy), ADR-0020 (cross-cutting Rust
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parity, audit when relevant).
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### Modules in scope for L0
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| Module | Lines | Live-import sites (outside `algebra/`, outside `tests/`) | Test-import sites |
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|---|---|---|---|
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| `algebra/__init__.py` | 5 | (re-export shim) | — |
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| `algebra/backend.py` | 267 | 21 | 16 |
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| `algebra/cga.py` | 84 | 16 | 17 |
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| `algebra/cl41.py` | 165 | 8 | 10 |
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| `algebra/holonomy.py` | 100 | 2 | 5 |
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| `algebra/rotor.py` | 179 | 5 | 8 |
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| `algebra/versor.py` | 180 | 20 | 19 |
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Every module has at least 2 live-import sites outside `algebra/`. No
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dormant modules at L0.
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### Caller-trace evidence
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Sample of live callers (full grep: `grep -rn "from algebra\|import algebra" --include="*.py" | grep -v "^algebra/" | grep -v "tests/"` — 38 distinct caller files):
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- `field/propagate.py:23` — versor application during field propagation (L1 → L0)
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- `ingest/gate.py:33` — versor/energy at injection boundary (L1 → L0)
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- `language_packs/compiler.py:14` — versor construction during pack compilation (L3 → L0)
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- `chat/runtime.py` — versor operations in the live turn loop (L6 → L0)
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- `generate/intent_ratifier.py`, `generate/admissibility.py`, `generate/proposition.py` — versor-gated generation (L5 → L0)
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- `core/cli.py:446-469` — versor diagnostics surfaced to operator (CLI → L0)
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Every live caller traces back to the runtime entry through at least one
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of: `core chat`, `core eval cognition`, or the field/ingest pipeline.
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### Exercising suite lane
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`core test --suite algebra` — 13 test files, every L0 module covered:
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| Module | Tests in algebra suite |
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|---|---|
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| `versor.py` | test_versor_closure, test_holonomy, test_energy, test_motor, test_versor_condition_rust_parity, test_versor_apply_rust_parity |
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| `rotor.py` | test_versor_closure, test_energy |
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| `holonomy.py` | test_holonomy, test_holonomy_resonance |
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| `cga.py` | test_holonomy_resonance, test_null_cone, test_vault_recall |
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| `cl41.py` | test_vault_recall_vectorised |
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| `backend.py` | test_vault_recall_vectorised, test_vault_recall_rust_parity, test_cga_inner_rust_parity, test_geometric_product_rust_parity, test_versor_condition_rust_parity, test_versor_apply_rust_parity |
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**Verification:** `python3 -m core.cli test --suite algebra -q` →
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**82 passed, 50 skipped** (skipped are Rust-parity tests on a Python-
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only environment; not a closure gap).
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### Cross-layer contract check
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**Pass 1 — mechanical (consumer-exists per exposed symbol):**
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| Exposed symbol | Consumer evidence |
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|---|---|
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| `versor_apply` | `field/propagate.py`, `generate/stream.py`, `chat/runtime.py` (3+ live consumers) |
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| `versor_condition` | `core/cognition/trace.py:34`, `evals/cognition/runner.py:60` (gated in evals at `< 1e-6`) |
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| `normalize_to_versor` | `generate/intent_ratifier.py`, `generate/admissibility.py` |
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| `cga_inner` | `vault/store.py`, `algebra/backend.py` (`_CGA_INNER_METRIC`), `evals/lab/vault_epistemic_trace.py` |
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| `embed_point`, `is_null`, `null_project` | `vault/store.py`, `language_packs/compiler.py`, `field/operators.py` |
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| `using_rust`, `vault_recall` (backend) | `vault/store.py`, all Rust-parity tests |
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| `word_transition_rotor`, `make_rotor_from_angle` | `field/operators.py`, `generate/intent_ratifier.py` |
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| `holonomy_encode`, `holonomy_similarity` | `vault/store.py`, `evals/lab/` |
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| `N_COMPONENTS` (cl41) | `algebra/backend.py`, `algebra/cga.py` |
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No exposed L0 symbol with zero downstream consumers.
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**Pass 2 — semantic (judgment-required):**
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ADR-0001's `versor_condition < 1e-6` invariant is the primary semantic
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contract. Verified:
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- **Measured per turn:** L0's `versor_condition()` is computed and
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folded into the deterministic trace payload (`core/cognition/trace.py:34,70`)
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on every turn.
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- **Surfaced to operator:** displayed by `core chat` and `core` info
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commands (`core/cli.py:398,461,469`).
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- **Gated at eval boundary:** evals refuse to count a turn as
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`versor_ok` if `versor_condition >= 1e-6` (`evals/cognition/runner.py:60`,
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`evals/run_cognition_eval.py:54`).
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- **NOT enforced inline as exception:** a turn with `vc >= 1e-6` still
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completes; the violation is visible in trace + eval, not raised as
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an error. This matches CLAUDE.md's discipline ("Do not weaken this
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threshold to make tests pass. Fix the operator/construction
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boundary that violated it.") — violations are surfaced for fix,
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not catastrophically refused at runtime.
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**Semantic mismatches flagged for human review:** none. The contract
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is consistently consumed.
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### Closure criteria scorecard
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| Criterion | Status | Evidence |
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|---|---|---|
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| 1. Design artifact | ✅ | ADR-0001, ADR-0003, ADR-0004, ADR-0009 |
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| 2. Code artifact | ✅ | `algebra/{backend,cga,cl41,holonomy,rotor,versor}.py` |
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| 3. Live caller | ✅ | 38 distinct caller files outside `algebra/` and `tests/` |
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| 4. Exercised by suite lane | ✅ | `core test --suite algebra` — 82/82 non-skipped pass; every L0 module covered |
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| 5. Cross-layer consistency | ✅ | All exposed symbols consumed; `versor_condition` invariant measured + traced + gated |
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**Verdict:** **CLOSED.**
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### Cleanup performed
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**None.** Audit found no dead, redundant, superseded, or orphaned code
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at L0. Every module has live callers; every exposed symbol is consumed;
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the suite lane exercises every module; the invariant is preserved
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end-to-end.
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### Findings / notes for downstream layers
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- **L1 (Field substrate) auditor:** L0's `versor_condition` is consumed
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at L5 (trace) and at the eval boundary, but L1 itself does not appear
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to enforce the invariant — L1's propagation produces field states
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that may later violate the invariant, with measurement deferred to
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L5. Worth verifying that L1's propagation correctness is itself
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tested independently of L5's downstream measurement.
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- **L2 (Vault) auditor:** `vault/store.py` is one of the heaviest
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consumers of L0 (cga_inner, embed_point, is_null, holonomy_encode).
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L2's closure depends on L0's exact-CGA-recall guarantees; the L2
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audit should verify the vault honors the exact-match discipline
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end-to-end, not just at the algebra layer.
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- **L6 (Chat runtime) auditor:** ADR-0020 (Phase 5 / Rust Parity
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Sequencing) is cross-cutting; the 50 skipped tests in the algebra
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suite are Rust-parity tests skipped in a Python-only environment.
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Audit ADR-0020 wherever Rust integration is live (when it lands)
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rather than at any single layer.
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### Audit method footnote
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This entry follows the per-layer audit format established here:
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ADRs in scope → modules in scope → caller traces → suite lane
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exercise → cross-layer contract (mechanical + semantic) → closure
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scorecard → cleanup → notes for downstream. Subsequent layers should
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follow the same format so the registry is uniformly machine- and
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human-scannable.
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---
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