From 9048a1bd6135b40edecee2c2298027d21f62a607 Mon Sep 17 00:00:00 2001 From: Juber Shaikh <40266375+CodeWithJuber@users.noreply.github.com> Date: Sat, 11 Jul 2026 21:32:26 +0400 Subject: [PATCH 1/5] docs(research): add formal synthesis paper unifying substrate + e2e framework MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Adds research/formal-synthesis/: a formal, mathematical unification of the cognitive-substrate theory, the end-to-end reliability framework (F1/F2, Δ*, I1-I4, A1-A7, T1-T6), and the forgekit implementation. Central result (Theorem D): reliability = probabilistic instruction layer × deterministic interception layer; neither alone suffices. Three anchor identities proved: impact-oracle blast-radius ≡ change-closure Δ*; assumption gate ≡ amnesia equation; two layers ≡ the Π3-probabilistic/Π2-deterministic design law. Includes: 42-page paper (HTML+PDF), three-way crosswalk (JSON+MD) with the P1/P2/P3 → Π1/Π2/Π3 notation reconciliation, a graded reference set for 15 new sources (9 confirmed / 6 traceable / 0 unverifiable, both future-dated arXiv IDs verified by direct fetch), a merged 47-entry bibliography, and two schematics. The two runnable prototypes are cross-referenced to the existing research/python-prototypes/ trees rather than duplicated. --- research/formal-synthesis/README.md | 83 +++ research/formal-synthesis/crosswalk.json | 130 ++++ research/formal-synthesis/crosswalk.md | 42 ++ .../figures/schematic_duality.png | Bin 0 -> 136815 bytes .../figures/schematic_taskloop.png | Bin 0 -> 143744 bytes .../graded_reference_set.json | 167 +++++ .../formal-synthesis/graded_reference_set.md | 29 + .../formal-synthesis/merged_references.json | 519 +++++++++++++ .../formal-synthesis/substrate_synthesis.html | 687 ++++++++++++++++++ .../formal-synthesis/substrate_synthesis.pdf | Bin 0 -> 614206 bytes 10 files changed, 1657 insertions(+) create mode 100644 research/formal-synthesis/README.md create mode 100644 research/formal-synthesis/crosswalk.json create mode 100644 research/formal-synthesis/crosswalk.md create mode 100644 research/formal-synthesis/figures/schematic_duality.png create mode 100644 research/formal-synthesis/figures/schematic_taskloop.png create mode 100644 research/formal-synthesis/graded_reference_set.json create mode 100644 research/formal-synthesis/graded_reference_set.md create mode 100644 research/formal-synthesis/merged_references.json create mode 100644 research/formal-synthesis/substrate_synthesis.html create mode 100644 research/formal-synthesis/substrate_synthesis.pdf diff --git a/research/formal-synthesis/README.md b/research/formal-synthesis/README.md new file mode 100644 index 0000000..ee5d6da --- /dev/null +++ b/research/formal-synthesis/README.md @@ -0,0 +1,83 @@ +# Formal Synthesis — A Theory of the Cognitive Substrate for Coding Agents + +This directory contains a formal, mathematical unification of three independently +developed bodies of work that all describe the **same architecture** for making a +frozen language model reliable at coding: + +1. **The Cognitive Substrate** — five faculties a frozen model structurally lacks + (memory, learning, imagination, self-correction, impact-awareness) and six + operating mechanisms M1–M6, with two runnable prototypes. +2. **The End-to-End Agent Reliability Framework** (`FRAMEWORK.md`) — failure modes + F1 (partial work) and F2 (session amnesia), the change-closure fixpoint Δ*, + invariants I1–I4, algorithms A1–A7, and correctness theorems T1–T6. +3. **forgekit / claude-e2e-kit** — the deployed implementation: committed-file + memory, deterministic lifecycle hooks, and auto-invoked skills. + +The synthesis proves these are **one object in three vocabularies**. + +## The central result + +> **Reliability = a probabilistic instruction layer × a deterministic interception +> layer. Neither layer alone suffices.** + +Instructions (`CLAUDE.md`, rules, skills) *raise* the probability `p < 1` that the +model behaves correctly, but can never reach `p = 1` — so the residual silent-miss +rate over `n` tasks is `1 − pⁿ → 1`. A deterministic layer (hooks that execute +regardless of the model's choice) multiplies that residual down by a factor +`(1 − cⱼ)` per check — but cannot catch the *semantic* class (undecidable, by Rice's +theorem), so it needs the soft layer to shrink what reaches it. The paper states this +as **Theorem D** and proves it. It is the formal content of the practitioner's rule: +*never trust the output of a probability engine; earn trust with an external check.* + +## Three anchor identities (not analogies — the same mathematics) + +| Substrate | Framework | Relationship | +|---|---|---| +| Impact-Oracle blast-radius | change-closure `Δ*` (least fixpoint of `X ↦ X ∪ N(X)`) | **identical** — reverse reachability, run to fixpoint ⇒ perfect recall | +| M2 assumption gate | amnesia equation `assumption ≈ argmax P(convention \| training)` | **identical** — the gate supplies missing context or halts, never guesses | +| substrate's two layers | design law "Π₃ probabilistic, Π₂ deterministic" | **identical** — Theorem D | + +## Contents + +| File | What it is | +|---|---| +| `substrate_synthesis.pdf` | The formal synthesis paper (42 pp): definitions, Theorem D + proof, the unified A1–A7 TASK loop, invariants I1–I4, theorems T1–T6 with proofs, the 16-row crosswalk, the full 14-mapping Qur'anic epistemology, both prototypes with honest metrics. | +| `substrate_synthesis.html` | Same paper, self-contained HTML. | +| `crosswalk.json` / `crosswalk.md` | The three-way term-by-term correspondence (substrate ↔ framework ↔ forgekit), with the P1/P2/P3 → Π₁/Π₂/Π₃ notation reconciliation. | +| `graded_reference_set.json` / `.md` | The 15 new sources independently verified and graded (9 confirmed, 6 traceable, 0 unverifiable), including the disambiguation of the two future-dated arXiv IDs. | +| `merged_references.json` | Full 47-entry bibliography (32 original + 15 new, deduped). | +| `figures/schematic_duality.png` | The two-layer duality architecture. | +| `figures/schematic_taskloop.png` | The unified 7-stage TASK loop (each stage bound to faculty · algorithm · Qur'anic anchor). | + +The **two runnable prototypes** referenced throughout the paper already live in this +repo and are not duplicated here: + +- `../python-prototypes/impact_oracle/` — Prototype I, the impact oracle (A1 / Δ*). + Runnable, 36 tests. Perfect recall on impacted files. +- `../python-prototypes/router_gate/` — Prototype II, complexity-router + + assumption-gate (A7 + A6 / M1 + M2). Runnable, 19 tests. 62.1% real cost saved, + live-measured. + +## Honesty commitments (carried from the source work) + +- **The prototypes are demonstrations, not benchmarks.** The router/gate's perfect + accuracy is on a 30-task hand-labelled set whose thresholds were tuned against it — + it shows the rubric *can separate* the cases. The cost figures, by contrast, are + exact arithmetic on **real measured token counts** from live model calls, and the + correctness sub-experiment actually executed the cheaper models' code against tests. +- **The impact oracle does not win on F1** (0.75 vs grep's 0.79). Its property is + **perfect recall** — the safety guarantee for "what will my edit break?". +- **Every future-dated / recent citation was verified by direct fetch, not inferred.** + Both 2026 arXiv IDs resolve to real preprints; one (`2601.05111`) is a *different* + paper from the founding Agent-as-a-Judge work (`2410.10934`), and both are recorded. +- **The Qur'anic lens is framing, never technical authority.** It supplies the + vocabulary of epistemic obligation — *lā taqfu*, *tabayyun*, *al-amāna* — that names + *why* each safeguard is mandatory; the engineering stands on its own merits. + +## Relationship to forgekit + +`forgekit` is one binding of this theory (and `claude-e2e-kit` is its Claude-specific +reference realization). The paper's §11 gives the exact object-by-object mapping: +`Π₁` = the committed `docs/*.md` store, `Π₂` = the `session-context` / `docs-guard` / +`intent-router` hooks, `Π₃` = `CLAUDE.md` + `.claude/rules/`. The two prototypes here +are the mechanical cores of the `/impact` skill and the effort-router. diff --git a/research/formal-synthesis/crosswalk.json b/research/formal-synthesis/crosswalk.json new file mode 100644 index 0000000..b38506d --- /dev/null +++ b/research/formal-synthesis/crosswalk.json @@ -0,0 +1,130 @@ +{ + "meta": { + "title": "Three-way crosswalk: Cognitive Substrate theory <-> End-to-End Reliability Framework <-> forgekit / claude-e2e-kit", + "sources": { + "S": "Cognitive Substrate for Coding Agents (v2 whitepaper) \u2014 faculties F_i, mechanisms M1-M6", + "E": "End-to-End Agent Reliability Framework (FRAMEWORK.md) \u2014 F1/F2, I1-I4, A1-A7, T1-T6, Delta*", + "K": "forgekit / claude-e2e-kit implementation \u2014 hooks, skills, agents, committed files" + }, + "notation_reconciliation": { + "collision": "Both frameworks independently use the labels P1/P2/P3.", + "substrate_P": "In the substrate paper, P1/P2/P3 are PROPERTIES of the frozen model: P1 statelessness, P2 frozen weights, P3 bounded/undifferentiated context.", + "framework_P": "In the e2e framework, P1/P2/P3 are the three required PRIMITIVES: P1 persistent store, P2 lifecycle interception, P3 instruction channel.", + "resolution": "In the synthesis, the substrate model-properties keep P1/P2/P3; the framework primitives are RENAMED Pi1 (persistent store), Pi2 (lifecycle interception), Pi3 (instruction channel). Every use of the primitives in the synthesis is written Pi-n to remove the collision." + } + }, + "rows": [ + { + "concept": "The frozen core", + "substrate": "y = f_theta(x): stateless map, fixed weights, bounded context (properties P1,P2,P3)", + "framework": "the agent/model whose behavior instructions can only raise the PROBABILITY of (p<1)", + "forgekit": "Claude / Codex / Cursor / Gemini / Aider \u2014 the model the kit wraps, never modifies", + "relation": "identical object: all three treat the model as a fixed probabilistic map to be wrapped, not retrained" + }, + { + "concept": "Impact-awareness / partial-work failure", + "substrate": "Faculty: impact-awareness gap; the developer silently simulates 'what will this edit break'. Prototype I = Impact Oracle (reverse-dependency blast radius with confidence decay)", + "framework": "F1 partial work; dependents operator N(X); required change closure Delta* = least fixpoint of X |-> X \u222a N(X); Done predicate; Algorithm A1 IMPACT-CLOSURE", + "forgekit": "/impact skill; documentation-map.md (R_declared); grep identifier sweep (R_discovered)", + "relation": "IDENTICAL MATHEMATICS. The Impact Oracle computes N(X) by reverse reachability on the dependency graph; Delta* is exactly the oracle's transitive blast-radius set. The oracle adds a confidence-decay weight the framework's set-theoretic N(X) leaves boolean." + }, + { + "concept": "Memory / session-amnesia failure", + "substrate": "Faculty: persistent memory gap; each context window is ephemeral. Validity-anchored memory (facts carry confirmed/discredited state updated by verified outcomes)", + "framework": "F2 session amnesia; continuity invariant I2 (essential(K_i) \u2286 P and loader L must load it); handoff operator H; K_{i+1}(0)=L(P)", + "forgekit": "docs/STATE.md (bounded snapshot) + docs/DECISIONS.md (append-only log); /handoff writes it; SessionStart hook injects it", + "relation": "Same failure, same fix (external bounded-compression checkpoint). Substrate adds validity-anchoring (prune by whether a past prediction was externally confirmed); framework adds the snapshot+WAL split (STATE mutable vs DECISIONS append-only)." + }, + { + "concept": "Why assumptions happen (the root the user named)", + "substrate": "M2 assumption/uncertainty gate: under-specified input -> the model confabulates a convention", + "framework": "amnesia equation: when f \u2208 essential(K) is missing from L(P), assumption \u2248 argmax P(convention | training data) \u2014 the mathematically EXPECTED result of missing context, not misbehavior. Invariant I3 (no fabrication)", + "forgekit": "CLAUDE.md No-assumptions rule; intent-router SPEC card ('state assumptions explicitly')", + "relation": "The framework gives the substrate's M2 gate its formal justification: assumption is argmax over the prior, so the fix is to supply context (raise what L loads) OR gate on missing context (halt), never to hope." + }, + { + "concept": "Self-correction / verification", + "substrate": "M6 inline verification; Prototype-II verify step; self-correction faculty", + "framework": "Algorithm A6 COMPLETION-GATE (deterministic Stop-hook floor); Hoare postcondition Done(t); the verification operator in A3 (verified-unaffected requires an actual grep, not an assumption)", + "forgekit": "docs-guard.sh Stop hook (blocks finish if code changed but no doc/state artifact did); reviewer agent verdict", + "relation": "Same verify-gate. Substrate framed it as a mechanism; framework proves it terminates (T1) and is sound (T3) and makes it the deterministic layer of the duality." + }, + { + "concept": "Complexity routing", + "substrate": "M1 complexity-aware router (transparent additive rubric); Prototype-II router", + "framework": "Algorithm A7 KNOWLEDGE-ROUTER (where every fact lives, keeps always-loaded context bounded); System 1/System 2 effort routing; intent DFA", + "forgekit": "intent-router.sh (UserPromptSubmit hook, keyword DFA, <10ms, zero-token); effort-routing rule in CLAUDE.md; per-agent model: fields", + "relation": "Two facets of one routing principle. Substrate M1 routes by TASK COMPLEXITY -> model tier (cost). Framework A7 routes by KNOWLEDGE TYPE -> storage home (context budget). Both are transparent/deterministic, both reject an opaque-LLM classifier for the same reason." + }, + { + "concept": "Task decomposition", + "substrate": "M3 task/session decomposition", + "framework": "HTN closure -> ordered task list (A1 output is the worklist); the meta-algorithm TASK(t)", + "forgekit": "sdlc-pilot 7-phase skill; subagents; git worktrees", + "relation": "Same: decompose the goal into the closure's ordered worklist before building." + }, + { + "concept": "Goal-anchoring", + "substrate": "M4 goal-anchoring (goal drift: to a text model a long story and long code are the same object)", + "framework": "BDI Desires = written goal + acceptance criteria in STATE.md; I2 keeps them across sessions; acceptance criteria written at SPEC, consumed at VERIFY", + "forgekit": "docs/STATE.md 'Current goal' + 'Acceptance criteria'; sdlc-pilot SPEC->VERIFY gate", + "relation": "Substrate names the drift; framework anchors it in a persisted, re-injected Desire so every session optimizes the same target." + }, + { + "concept": "Anti-over-engineering", + "substrate": "M5 anti-over-engineering (scope minimality; the residual whitespace)", + "framework": "amana / scope-boundedness (agent may not exceed asked scope); I3 (no invented structure)", + "forgekit": "CLAUDE.md effort routing 'trivial -> do it directly, no ceremony'; least-privilege defaults", + "relation": "Weakest-covered in all three; substrate marks it residual-gap, framework encodes it as a stewardship bound, kit as an effort-routing default." + }, + { + "concept": "World-model of the codebase", + "substrate": "Faculty: world-model; Prototype-I codebase world-model (AST -> persistent dependency graph)", + "framework": "the typed artifact graph (A, tau, R = R_declared \u222a R_discovered)", + "forgekit": "documentation-map.md + the repo itself + ARCHITECTURE.md", + "relation": "Same graph. Substrate builds it from AST for code; framework generalizes the node type to {code,test,doc,config,diagram} so DOCS become first-class dependents \u2014 the key generalization that turns 'impact on code' into 'impact on all artifacts'." + }, + { + "concept": "Continual learning from outcomes", + "substrate": "Faculty: learning without touching theta (non-parametric always-on + parametric LoRA/EWC)", + "framework": "Reflexion loop made cross-session (I3/I4); DECISIONS.md as precedent DB; A4 mirrors durable lessons", + "forgekit": "Reflexion rule in CLAUDE.md; STATE gotchas; agents' memory: project", + "relation": "Same 'learn without retraining' stance. Both store verbal lessons externally and re-inject; substrate adds the parametric option, framework keeps it purely non-parametric (committed files)." + }, + { + "concept": "Rehydration (session start)", + "substrate": "closed-loop write-back/read-back band in the substrate architecture", + "framework": "Algorithm A5 CONTEXT-REHYDRATE; loader L; records git baseline for the gate", + "forgekit": "session-context.sh SessionStart hook; /catchup skill (deep variant)", + "relation": "The read side of the substrate's memory loop, made deterministic (inject, don't hope the agent reads)." + }, + { + "concept": "Independent verification / judge", + "substrate": "self-correction faculty; the honest-negative-result caution (models correct poorly alone)", + "framework": "LLM-as-Judge applied: reviewer agent (fresh context, explicit criteria, adversarial); self-consistency for critical changes (majority of N)", + "forgekit": "reviewer.md agent; DoD item 7", + "relation": "Substrate cited the finding that self-correction alone is weak; framework operationalizes the fix (an EXTERNAL judge), which is the same 'trust only an external check' principle as the gate." + }, + { + "concept": "The two-layer duality (THE central new insight)", + "substrate": "implicit: the substrate wraps a probabilistic core with deterministic external structure, but v2 never states it as a law", + "framework": "DESIGN LAW: instructions (Pi3) are PROBABILISTIC (raise p); interception (Pi2) is DETERMINISTIC (guarantee a floor c->1). P(silent miss) = (1-p)\u00b7prod_j(1-c_j). Since p<1 always, neither layer alone suffices.", + "forgekit": "the split itself: CLAUDE.md/rules/skills = soft layer; hooks (docs-guard, session-context, intent-router) = hard layer", + "relation": "THIS is what the kit gives the substrate theory: the reason the substrate must be TWO layers, stated as a theorem. The user's own discipline ('never trust AI output \u2014 it is calculated probability') is exactly (1-p)>0, which forces the deterministic layer." + }, + { + "concept": "The probabilistic failure model", + "substrate": "eval honesty: perfect accuracy shows separation not a benchmark; p<1", + "framework": "P(>=1 miss) = 1 - p^n over n tasks (0.9 -> 65% at 10, 96% at 30); layered: P(silent miss)=(1-p)\u00b7prod(1-c_j)", + "forgekit": "the lattice of gates: turn-level (hook) \u2282 commit-level (pre-commit) \u2282 PR-level (CI)", + "relation": "The math that makes 'it works sometimes then forgets' a geometric certainty rather than bad luck \u2014 and quantifies why each added deterministic gate multiplies down the residual." + }, + { + "concept": "Stewardship / governance boundary", + "substrate": "STEWARDSHIP/amana wrapper (33:72) around the whole architecture", + "framework": "amana in I3/I4 as no-fabrication + verified-currency; least privilege, reversibility, logged rationale, scope-boundedness", + "forgekit": "committed-files-only (auditable), block-at-most-once (no nagging), fail-open safety (T2), DOCS_GUARD_DISABLE auditable escape hatch", + "relation": "The ethical frame the substrate draws from the lens is realized as concrete safety properties in the framework (fail-open, reversibility) and kit (auditable hooks)." + } + ] +} \ No newline at end of file diff --git a/research/formal-synthesis/crosswalk.md b/research/formal-synthesis/crosswalk.md new file mode 100644 index 0000000..12ddb3f --- /dev/null +++ b/research/formal-synthesis/crosswalk.md @@ -0,0 +1,42 @@ +# Three-Way Crosswalk + +**Cognitive Substrate theory ↔ End-to-End Reliability Framework ↔ forgekit / claude-e2e-kit** + +This map is the spine of the formal synthesis: every unified concept, shown in all three vocabularies, plus the relationship that justifies treating them as one object. + +## Notation reconciliation (the P1/P2/P3 collision) + +> Both frameworks independently use the labels P1/P2/P3. + +- **Substrate P1/P2/P3** — P1 statelessness, P2 frozen weights, P3 bounded/undifferentiated context. +- **Framework P1/P2/P3** — P1 persistent store, P2 lifecycle interception, P3 instruction channel. +- **Resolution** — In the synthesis, the substrate model-properties keep P1/P2/P3; the framework primitives are RENAMED Pi1 (persistent store), Pi2 (lifecycle interception), Pi3 (instruction channel). Every use of the primitives in the synthesis is written Pi-n to remove the collision. + +## The map + +| # | Unified concept | Substrate (S) | E2E Framework (E) | forgekit / kit (K) | Why they are one object | +| --- | --- | --- | --- | --- | --- | +| 1 | **The frozen core** | y = f_theta(x): stateless map, fixed weights, bounded context (properties P1,P2,P3) | the agent/model whose behavior instructions can only raise the PROBABILITY of (p<1) | Claude / Codex / Cursor / Gemini / Aider — the model the kit wraps, never modifies | identical object: all three treat the model as a fixed probabilistic map to be wrapped, not retrained | +| 2 | **Impact-awareness / partial-work failure** | Faculty: impact-awareness gap; the developer silently simulates 'what will this edit break'. Prototype I = Impact Oracle (reverse-dependency blast radius with confidence decay) | F1 partial work; dependents operator N(X); required change closure Delta* = least fixpoint of X \|-> X ∪ N(X); Done predicate; Algorithm A1 IMPACT-CLOSURE | /impact skill; documentation-map.md (R_declared); grep identifier sweep (R_discovered) | IDENTICAL MATHEMATICS. The Impact Oracle computes N(X) by reverse reachability on the dependency graph; Delta* is exactly the oracle's transitive blast-radius set. The oracle adds a confidence-decay weight the framework's set-theoretic N(X) leaves boolean. | +| 3 | **Memory / session-amnesia failure** | Faculty: persistent memory gap; each context window is ephemeral. Validity-anchored memory (facts carry confirmed/discredited state updated by verified outcomes) | F2 session amnesia; continuity invariant I2 (essential(K_i) ⊆ P and loader L must load it); handoff operator H; K_{i+1}(0)=L(P) | docs/STATE.md (bounded snapshot) + docs/DECISIONS.md (append-only log); /handoff writes it; SessionStart hook injects it | Same failure, same fix (external bounded-compression checkpoint). Substrate adds validity-anchoring (prune by whether a past prediction was externally confirmed); framework adds the snapshot+WAL split (STATE mutable vs DECISIONS append-only). | +| 4 | **Why assumptions happen (the root the user named)** | M2 assumption/uncertainty gate: under-specified input -> the model confabulates a convention | amnesia equation: when f ∈ essential(K) is missing from L(P), assumption ≈ argmax P(convention \| training data) — the mathematically EXPECTED result of missing context, not misbehavior. Invariant I3 (no fabrication) | CLAUDE.md No-assumptions rule; intent-router SPEC card ('state assumptions explicitly') | The framework gives the substrate's M2 gate its formal justification: assumption is argmax over the prior, so the fix is to supply context (raise what L loads) OR gate on missing context (halt), never to hope. | +| 5 | **Self-correction / verification** | M6 inline verification; Prototype-II verify step; self-correction faculty | Algorithm A6 COMPLETION-GATE (deterministic Stop-hook floor); Hoare postcondition Done(t); the verification operator in A3 (verified-unaffected requires an actual grep, not an assumption) | docs-guard.sh Stop hook (blocks finish if code changed but no doc/state artifact did); reviewer agent verdict | Same verify-gate. Substrate framed it as a mechanism; framework proves it terminates (T1) and is sound (T3) and makes it the deterministic layer of the duality. | +| 6 | **Complexity routing** | M1 complexity-aware router (transparent additive rubric); Prototype-II router | Algorithm A7 KNOWLEDGE-ROUTER (where every fact lives, keeps always-loaded context bounded); System 1/System 2 effort routing; intent DFA | intent-router.sh (UserPromptSubmit hook, keyword DFA, <10ms, zero-token); effort-routing rule in CLAUDE.md; per-agent model: fields | Two facets of one routing principle. Substrate M1 routes by TASK COMPLEXITY -> model tier (cost). Framework A7 routes by KNOWLEDGE TYPE -> storage home (context budget). Both are transparent/deterministic, both reject an opaque-LLM classifier for the same reason. | +| 7 | **Task decomposition** | M3 task/session decomposition | HTN closure -> ordered task list (A1 output is the worklist); the meta-algorithm TASK(t) | sdlc-pilot 7-phase skill; subagents; git worktrees | Same: decompose the goal into the closure's ordered worklist before building. | +| 8 | **Goal-anchoring** | M4 goal-anchoring (goal drift: to a text model a long story and long code are the same object) | BDI Desires = written goal + acceptance criteria in STATE.md; I2 keeps them across sessions; acceptance criteria written at SPEC, consumed at VERIFY | docs/STATE.md 'Current goal' + 'Acceptance criteria'; sdlc-pilot SPEC->VERIFY gate | Substrate names the drift; framework anchors it in a persisted, re-injected Desire so every session optimizes the same target. | +| 9 | **Anti-over-engineering** | M5 anti-over-engineering (scope minimality; the residual whitespace) | amana / scope-boundedness (agent may not exceed asked scope); I3 (no invented structure) | CLAUDE.md effort routing 'trivial -> do it directly, no ceremony'; least-privilege defaults | Weakest-covered in all three; substrate marks it residual-gap, framework encodes it as a stewardship bound, kit as an effort-routing default. | +| 10 | **World-model of the codebase** | Faculty: world-model; Prototype-I codebase world-model (AST -> persistent dependency graph) | the typed artifact graph (A, tau, R = R_declared ∪ R_discovered) | documentation-map.md + the repo itself + ARCHITECTURE.md | Same graph. Substrate builds it from AST for code; framework generalizes the node type to {code,test,doc,config,diagram} so DOCS become first-class dependents — the key generalization that turns 'impact on code' into 'impact on all artifacts'. | +| 11 | **Continual learning from outcomes** | Faculty: learning without touching theta (non-parametric always-on + parametric LoRA/EWC) | Reflexion loop made cross-session (I3/I4); DECISIONS.md as precedent DB; A4 mirrors durable lessons | Reflexion rule in CLAUDE.md; STATE gotchas; agents' memory: project | Same 'learn without retraining' stance. Both store verbal lessons externally and re-inject; substrate adds the parametric option, framework keeps it purely non-parametric (committed files). | +| 12 | **Rehydration (session start)** | closed-loop write-back/read-back band in the substrate architecture | Algorithm A5 CONTEXT-REHYDRATE; loader L; records git baseline for the gate | session-context.sh SessionStart hook; /catchup skill (deep variant) | The read side of the substrate's memory loop, made deterministic (inject, don't hope the agent reads). | +| 13 | **Independent verification / judge** | self-correction faculty; the honest-negative-result caution (models correct poorly alone) | LLM-as-Judge applied: reviewer agent (fresh context, explicit criteria, adversarial); self-consistency for critical changes (majority of N) | reviewer.md agent; DoD item 7 | Substrate cited the finding that self-correction alone is weak; framework operationalizes the fix (an EXTERNAL judge), which is the same 'trust only an external check' principle as the gate. | +| 14 | **The two-layer duality (THE central new insight)** | implicit: the substrate wraps a probabilistic core with deterministic external structure, but v2 never states it as a law | DESIGN LAW: instructions (Pi3) are PROBABILISTIC (raise p); interception (Pi2) is DETERMINISTIC (guarantee a floor c->1). P(silent miss) = (1-p)·prod_j(1-c_j). Since p<1 always, neither layer alone suffices. | the split itself: CLAUDE.md/rules/skills = soft layer; hooks (docs-guard, session-context, intent-router) = hard layer | THIS is what the kit gives the substrate theory: the reason the substrate must be TWO layers, stated as a theorem. The user's own discipline ('never trust AI output — it is calculated probability') is exactly (1-p)>0, which forces the deterministic layer. | +| 15 | **The probabilistic failure model** | eval honesty: perfect accuracy shows separation not a benchmark; p<1 | P(>=1 miss) = 1 - p^n over n tasks (0.9 -> 65% at 10, 96% at 30); layered: P(silent miss)=(1-p)·prod(1-c_j) | the lattice of gates: turn-level (hook) ⊂ commit-level (pre-commit) ⊂ PR-level (CI) | The math that makes 'it works sometimes then forgets' a geometric certainty rather than bad luck — and quantifies why each added deterministic gate multiplies down the residual. | +| 16 | **Stewardship / governance boundary** | STEWARDSHIP/amana wrapper (33:72) around the whole architecture | amana in I3/I4 as no-fabrication + verified-currency; least privilege, reversibility, logged rationale, scope-boundedness | committed-files-only (auditable), block-at-most-once (no nagging), fail-open safety (T2), DOCS_GUARD_DISABLE auditable escape hatch | The ethical frame the substrate draws from the lens is realized as concrete safety properties in the framework (fail-open, reversibility) and kit (auditable hooks). | + +## The three anchor identities + +Three rows are not analogies but *the same mathematics under two names*: + +1. **Impact Oracle blast-radius ≡ change-closure fixpoint Δ\*.** Reverse reachability on the dependency graph is the least fixpoint of `X ↦ X ∪ N(X)`. The oracle computes `N(X)` with a confidence-decay weight; the framework's `N(X)` is its boolean core. +2. **M2 assumption gate ≡ the amnesia equation.** `assumption ≈ argmax P(convention | training)` is *why* an under-specified prompt is answered with a confabulated convention — so the gate either supplies the missing context or halts; it never hopes. +3. **The substrate's two layers ≡ the design law.** Instructions raise `p<1`; interception guarantees a floor `c→1`. `P(silent miss) = (1−p)·∏(1−cⱼ)`. 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