* docs(ADR-0172): math-domain corpus-decomposition mechanism (Learning Arc analog)
Scoping ADR for the math-domain analog of cognition's
`teaching/contemplation.py` corpus-decomposition loop (Learning Arc
milestone 2026-05-25).
## What this ADR scopes
A mechanism that reads the math audit corpus and emits
`MathReaderRefusalShapeProposal` records — structural commonalities
across N refusal cases, paired with the candidate mechanism change
that would resolve them (matcher extension, injector sub-shape,
vocabulary addition, frame reclassification).
Today the operator does this decomposition by hand (reads
audit_brief_11.md, identifies the commonality across 21 DCS
refusals, scopes the matcher/injector extension, files a focused PR).
ADR-0172 shifts the decomposition to the engine, with HITL
ratification preserved.
## Sequencing — explicit
ADR-0172 ships AFTER ADR-0170 (injector contract widening),
ADR-0168 (FrameClaim handler), and ADR-0169 (CompositionClaim
handler — reserved). Without those substrates, the decomposer can
identify patterns but cannot route them to a ratification handler
that knows how to materialize them. Cognition's learning arc
followed this same sequencing: substrate first, then decomposer.
## Why this matters
ADR-0167 LexicalClaim shipped the math-domain wire from refusal →
evidence → operator-ratification. ADR-0172 closes the gap to the
engine-decomposes loop — the moment cognition's learning arc
qualitatively shifted from "engine refuses + operator authors" to
"engine teaches itself through reviewed correction."
The Learning Arc memory entry (2026-05-25) names that moment as
when measurable progress accelerated. ADR-0172 makes the math-domain
trajectory toward the same loop explicit in the queue.
## Hard invariants preserved
- wrong=0 by construction (proposals are evidence-only)
- ADR-0166: no new eval lanes
- No teaching-store / pack mutation
- No non-deterministic mechanism (rule-based grouping, not learned
classification)
- Cross-domain partition (ADR-0167 W2-C) preserves cognition
contemplation behavior
No code, no test, no eval, no pack change in this PR.
## Cross-references
- ADR-0056/0057 — cognition contemplation/proposal substrate (template)
- ADR-0167 + FOLLOWUPS §1 — parent evidence wire
- ADR-0168 + ADR-0168.1 — FrameClaim (ratification target)
- ADR-0169 (reserved) — CompositionClaim (ratification target)
- ADR-0170 — injector contract widening (substrate prerequisite)
- Memory: Learning Arc Milestone 2026-05-25 — the moment to recreate
- Thesis: decoding, not generating — the principle preserved
* amend(ADR-0172): add Tier 2 — intensional contemplation with test-and-learn loop
Per operator feedback during ADR-0172 review: the corpus-decomposition
mechanism should not only emit explicit rules (extensional) but also
develop inference (intensional) — recognizing structural equivalence
classes across surface variations without enumerating them.
## Tier 2 — intensional contemplation
Engine recognizes that 'Sam has 5 apples' and 'Sam collected 5 apples'
carry the same canonical proposition structure, without an explicit
verb-list extension. Emits MathReaderInferenceProposal records that
name structural equivalence classes rather than enumerable rules.
This is the thesis word the original draft missed: rationalization.
Tier 1 ratifies rules; Tier 2 ratifies inference.
## Test-and-learn loop
Tier 2 proposals carry held-out test evidence:
1. Decomposer surfaces hypothesis
2. Held-out subset of corpus reserved
3. Bridge applied to held-out cases; admissibility gates run
4. Outcome scored (positive / negative / neutral)
5. Negative-evidence proposals auto-rejected before HITL
6. Operator reviews proposal + test result, not bare claim
This makes Tier 2 thesis-coherent: engine decodes a structural
pattern, tests it against unseen corpus cases, surfaces the test
result. Wrong=0 cannot leak through — held-out test failures reject
internally.
## Updated implementation outline
Tier 1 wave: W1-W4 (schema, decomposer, CLI, workbench integration)
Tier 2 wave: W5-W9 (schema, equivalence-class recognizer, test-and-learn
loop, HITL integration, bridge application path)
## Hard invariants preserved at both tiers
- wrong=0 by construction (Tier 1: evidence-only proposals; Tier 2:
held-out test rejects wrong-admitting bridges internally)
- ADR-0166: no new eval lanes
- No non-deterministic mechanism (rule-based grouping + deterministic
test-and-learn, not learned classification)
- Cross-domain partition preserves cognition contemplation behavior
* amend(ADR-0172): split Tier 2 test-and-learn into two-arm confirmation
Per operator feedback during ADR-0172 review: 'confirm against known
facts/prior solutions' is the missing arm. The Tier 2 test-and-learn
loop now has BOTH:
- Arm 1 (negative / wrong=0 on held-out refusals) — already drafted
- Arm 2 (positive / known-good preservation) — NEW
Arm 2 inherits ADR-0057's replay-equivalence contract: any
inferential bridge that would change a currently-correct outcome is
REJECTED INTERNALLY before reaching HITL, even if the new outcome is
defensible. Existing truth survives; new truth is gated.
Both arms must PASS or be neutral. Either arm rejecting → proposal
does not reach the operator. This makes the engine's reasoning
provably conservative: it confirms against truth it already knows AND
truth it hasn't yet decided.
The 5-step proposal lifecycle is updated to reflect both arms +
test-set partition + per-case verdict tables in the emitted proposal.
No code change. No runtime effect.
* amend(ADR-0172): add foundational reasoning-articulation substrate
Per operator feedback: for the engine to infer/test/learn from
feedback, it must first be able to ARTICULATE its own reasoning in a
structured, persistent, replayable form.
Articulation is the project thesis's 5th anchor ("listen → comprehend
→ recall → think → articulate → learn from reviewed correction →
replay"). Today CORE articulates SURFACE (templated realizer output)
but does not articulate REASONING — the inference chain that took the
engine from refusal corpus to hypothesis to proposal.
Without reasoning-articulation, none of the three loops can work:
- Loop 1 (self-test) has nothing to record about what it tested or why
- Loop 2 (HITL review) sees a black-box conclusion, not inference chain
- Loop 3 (feedback) has no specific step the operator can target with
a rejection rationale
## Substrate: ReasoningTrace schema
Every proposal carries a typed, content-addressable
ReasoningTrace recording each inference step:
ReasoningStep:
step_kind: observation | grouping | abstraction | hypothesis |
test_design | test_application | test_result | conclusion
input_pointers: prior steps + evidence rows
claim: human-readable assertion at this step
justification: why the engine made the claim
output_payload: type-discriminated by step_kind
The trace is byte-identical across replays of the same corpus +
verdict history. Inherits CORE's existing determinism discipline.
## Sequencing
Articulation ships FIRST (new W0 wave) — it is the prerequisite for
Tier 1 and Tier 2 and Loop 3. Each downstream wave emits or consumes
ReasoningTraces.
## Hard invariants preserved
- Deterministic-replay (trace byte-identical under same inputs)
- ADR-0057 replay-equivalence (trace IDs stable across reruns)
- No non-determinism added (rule-based step emission, not learning)
- ADR-0166: no new eval lanes
No code, no test, no eval, no pack change in this PR.
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