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+# Epistemic State Audit — Math Subsystem Findings & Forward Plan
+
+## Context
+
+CORE's math subsystem was audited against the proposed starter epistemic taxonomy:
+
+- `PERCEIVED`
+- `EVIDENCED`
+- `VERIFIED`
+- `DECODED`
+- `UNVERIFIED-POSSIBLE`
+- `UNVERIFIED-NOVEL`
+- `CONTRADICTED`
+- `AMBIGUOUS`
+- `UNDETERMINED`
+- `EPISTEMIC_STATE_NEEDED`
+
+The audit was intentionally bounded to the math subsystem files named in the handoff:
+
+- `generate/math_problem_graph.py`
+- `generate/math_parser.py`
+- `generate/math_solver.py`
+- `generate/math_verifier.py`
+- `generate/math_realizer.py`
+- `generate/math_candidate_parser.py`
+- `generate/math_candidate_graph.py`
+- `evals/gsm8k_math/runner.py`
+- `evals/gsm8k_math/verify.py`
+
+This document records findings and a phased plan only. It proposes no runtime code changes.
+
+---
+
+## Executive Findings
+
+The math subsystem already operates with a substantial implicit epistemic model.
+
+The starter taxonomy successfully captures the majority of proposition-level semantic states in the parser -> solver -> verifier -> realizer pipeline.
+
+However, newer orchestration layers introduce a second class of states not cleanly representable by the starter taxonomy alone.
+
+Specifically:
+
+1. Proposition epistemics already exist.
+2. Operational/meta epistemics also already exist.
+3. The current starter taxonomy risks conflating these categories.
+4. The eventual ADR should likely formalize both separately.
+
+The epistemic-state effort is therefore not inventing a taxonomy from scratch. It is surfacing and naming distinctions already embedded in the engine.
+
+---
+
+## Strongly Confirmed Proposition States
+
+The following starter states mapped cleanly and repeatedly across the classic math spine.
+
+| State | Practical meaning in the math subsystem |
+|---|---|
+| `PERCEIVED` | Token/span observed before semantic lift. |
+| `EVIDENCED` | Grounded candidate or feature lifted from source spans. |
+| `VERIFIED` | Independently re-derived or cross-checked against pack/oracle/solver state. |
+| `DECODED` | Replay-equal deterministic verified trace or canonical artifact equality. |
+| `CONTRADICTED` | Proposition conflicts with typed semantic rules or verifier replay. |
+| `AMBIGUOUS` | Multiple incompatible admissible interpretations exist. |
+| `UNDETERMINED` | Insufficient structure to complete semantic lift or solve. |
+
+These states align well with:
+
+- parser grounding,
+- typed graph construction,
+- solver semantics,
+- verifier replay,
+- canonical hashing,
+- GSM8K evaluation discipline.
+
+---
+
+## Critical Taxonomy Gap
+
+The candidate-graph, recognizer, and comprehension-reader layers introduce states that are not proposition truth states.
+
+Examples include:
+
+- bounded refusal,
+- route fallthrough,
+- authoritative parser admission,
+- decoded-but-unarticulated outputs,
+- deterministic preference between multiple admissible parses,
+- grounded derivation where output values are not literal source spans.
+
+These are not adequately represented by `UNDETERMINED`, `AMBIGUOUS`, or `VERIFIED`.
+
+Flattening them into proposition states would create category errors.
+
+For example:
+
+> branch count exceeded deterministic cap
+
+is operational boundedness, not semantic ambiguity.
+
+Likewise:
+
+> realizer failed after verifier replay passed
+
+is articulation failure, not failure to decode the answer.
+
+---
+
+## Proposed Direction
+
+The taxonomy should be pressure-tested as a two-axis model rather than a single flat enum.
+
+### 1. Proposition Epistemic States
+
+Truth / grounding / replay status of a proposition.
+
+Examples:
+
+- `PERCEIVED`
+- `EVIDENCED`
+- `VERIFIED`
+- `DECODED`
+- `CONTRADICTED`
+- `AMBIGUOUS`
+- `UNDETERMINED`
+
+### 2. Operational / Meta Epistemic States
+
+States describing the engine's attempt to reach, route, bound, or surface propositions.
+
+Candidate examples:
+
+- `ROUTE_FALLTHROUGH`
+- `BOUNDED_REFUSAL`
+- `AUTHORITY_ADMITTED`
+- `DECODED_UNARTICULATED`
+- `PREFERRED_EVIDENCED`
+- `DERIVED_EVIDENCED`
+
+This preserves semantic clarity while exposing deterministic orchestration behavior.
+
+---
+
+## Proposed New Candidate States
+
+### `DERIVED_EVIDENCED`
+
+Grounded input operands exist directly in source spans, but the surfaced proposition is deterministically derived from them.
+
+Example:
+
+- `3 appointments at $400 each` -> derived value `1200`, even though literal `1200` does not appear in source.
+
+This is stronger than merely possible, but different from literal span evidence.
+
+### `PREFERRED_EVIDENCED`
+
+Multiple admissible grounded parses exist, but one is deterministically preferred by a policy such as `most-grounded-slots-wins`.
+
+This is not the same as unresolved ambiguity when the candidates collapse safely or one candidate is structurally tighter.
+
+### `AUTHORITY_ADMITTED`
+
+A subsystem admits a proposition authoritatively enough that downstream fallback parsing should not reinterpret it differently.
+
+This is route authority, not just proposition verification.
+
+### `ROUTE_FALLTHROUGH`
+
+One capability path refuses or fails, but another deterministic path is allowed to attempt the proposition.
+
+This is orchestration state, not proposition truth state.
+
+### `BOUNDED_REFUSAL`
+
+The engine refuses because deterministic bounded-computation policy was exceeded, rather than because the proposition is contradictory, ambiguous, or impossible.
+
+### `DECODED_UNARTICULATED`
+
+A proposition is replay-verified and semantically decoded, but articulation/surface realization failed.
+
+This state already effectively exists in the GSM8K runner as `decoded_unarticulated`.
+
+---
+
+## Phased Plan
+
+### Phase 1 — Separate Semantic vs Operational States
+
+Define which states belong to proposition semantics and which belong to orchestration/runtime policy.
+
+Goal: prevent category collapse.
+
+Deliverable:
+
+| State | Proposition-level? | Operational/meta? | Notes |
+|---|---:|---:|---|
+| `DECODED` | yes | no | Replay-equal verified proposition. |
+| `BOUNDED_REFUSAL` | no | yes | Deterministic computation policy boundary. |
+| `AMBIGUOUS` | yes | no | Multiple incompatible admissible propositions. |
+| `ROUTE_FALLTHROUGH` | no | yes | Route-level delegation/fallback. |
+
+### Phase 2 — Define Transition Invariants
+
+Extract deterministic transitions:
+
+| From | To | Trigger |
+|---|---|---|
+| `PERCEIVED` | `EVIDENCED` | Grounding succeeds. |
+| `EVIDENCED` | `VERIFIED` | Solver/pack/verifier cross-check succeeds. |
+| `VERIFIED` | `DECODED` | Deterministic replay equality holds. |
+| `EVIDENCED` | `AMBIGUOUS` | Multiple incompatible admissible branches exist. |
+| `EVIDENCED` | `CONTRADICTED` | Typed semantic rule or replay check fails. |
+| `PERCEIVED` | `UNDETERMINED` | Feature lift cannot complete. |
+
+This becomes the core epistemic state machine.
+
+### Phase 3 — Determine Lattice Structure
+
+Current evidence suggests the taxonomy is likely:
+
+```text
+semantic axis x operational axis
+```
+
+rather than one flat enum.
+
+A single enum may still be useful as a reporting surface, but the underlying model should preserve orthogonality.
+
+### Phase 4 — Audit Transition Sites
+
+Next bounded audit pass should enumerate every point where:
+
+- a proposition changes epistemic state,
+- a branch is refused,
+- ambiguity is introduced,
+- authority/fallthrough is applied,
+- or replay verification upgrades certainty.
+
+This likely becomes the core substrate for the epistemic-state ADR.
+
+### Phase 5 — Decide ADR Shape
+
+The ADR should decide whether CORE exposes:
+
+1. one flat state enum,
+2. a proposition state plus operational state pair,
+3. or a richer trace event model that records both.
+
+The audit currently favors option 2 or option 3.
+
+---
+
+## Architectural Importance
+
+This work is load-bearing because it directly affects:
+
+- refusal semantics,
+- replay guarantees,
+- comprehension-reader integration,
+- candidate-graph orchestration,
+- future recognition systems,
+- teaching-derived structure formation,
+- introspectable reasoning claims,
+- deterministic truth-state reporting.
+
+The math subsystem already contains the beginning of a coherent epistemic architecture. The next task is formalization and invariant discipline.
+
+---
+
+## Non-Goals For This Document
+
+This document does not:
+
+- propose runtime implementation details,
+- modify code,
+- define a final ADR,
+- audit non-math subsystems,
+- claim the starter taxonomy is final.
+
+It records bounded findings and prepares the next phase of epistemic-state design.