core/docs/sessions/SESSION-2026-05-29-multistep-build-arc.md

Session 2026-05-29 — The Multi-Step Build Arc: from "another matcher" to a comprehension composer

Status: In progress (EX-2 landing) ✓ through GB-2 Companion: SESSION-2026-05-28 — risk/reward learning architecture (the design discussion that opened this arc) Headline: Took the GSM8K work from "build another recognizer per shape" to a safe, inspectable, comprehension-guided multi-step solver — and, just as importantly, proved with measurement exactly where coverage is gated (extraction richness × cue precision × scale), so the remaining roadmap is honest rather than hopeful.

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TL;DR

Across one long session we:

1. Shipped ADR-0175 Phases 1–3b (the two-regime calibrated-learning substrate) and Phase 5a (retired the inert reader; net −1,038 LOC; serving byte-identical at 3/47/0).
2. Did a lookback review of the 5-PR stack (no live hazards; recorded drift); landed it.
3. Built the multi-step machine end-to-end: MS-1 (question-targeting) → MS-2 (chain model + comparatives) → MS-3 (target-guided search) → GB-1 (clause segmentation) → GB-2 (list-sum-then-scale) → EX-2 (decimal grounding).
4. Scoped the full remaining roadmap as ADRs 0176–0179.
5. Kept wrong=0 on serving (3/47/0) byte-identical the entire time — every attempt-and-eliminate ran in the sealed practice lane.

The arc's intellectual payoff: each phase's measurement told us the next lever, and they converged on a clean dependency chain rather than a guessing game.

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The converged architecture (what we now believe)

ADR-0175  Two-regime calibrated learning      serving wrong=0  |  sealed practice attempt+eliminate
ADR-0176  Multi-step grounded search          extract → chain → self-verify gate (grounding ∧ cue ∧ unit ∧ completeness ∧ uniqueness)
ADR-0178  Comprehension-guided structure      read clause-by-clause; structure-from-reading, not enumeration
ADR-0177  Cue-precision learning              trust gate + search prune (closes "self-verification necessary-not-sufficient")
ADR-0179  Extraction richness                 feed the composer real quantities (the unblock prerequisite)
                                              × SCALE (ADR-0163 §F) to compound

The honest dependency chain (the session's central finding):

extraction richness (0179) → unblocks the built structure (MS-3/GB-2) → produces gold-matching chains → feeds cue-precision (0177) → coverage; all gated by wrong=0 and amplified by scale.

Coverage does not come from more search — it comes from reading the structure and feeding it real quantities, with the self-verification gate keeping every attempt honest.

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What shipped to main

PR	What	Result
#430	Phase 5a — retire inert reader	net −1,038 LOC; 3/47/0 byte-identical
#432	Phase 1 — reliability ledger + gate (core/reliability_gate/)	inert substrate; invariants #3/#4 proven
#433	Phase 2 — sealed practice lane (evals/gsm8k_math/practice/v1/)	diagnosis: 35 skill / 12 knowledge / 0 ambiguity
#434	Phase 3a — self-verification gate (generate/derivation/)	invariant #2 proven (spurious refuses)
#435	Phase 3b — multiplicative search	first attempts live; the "necessary-not-sufficient" finding
#436	self-verification completeness clause	practice wrongs 9→2
#438	en_core_comparatives_v1 pack	irreducible world-facts (twice→×2, half→×0.5)
#439	MS-1 — question-targeting (Target)	search pruning + stopping signal
#440	MS-2 — chain model (text + comparative operands)	0024/0033 mixed chains self-verify
#441	MS-3 — target-guided bounded search	flips 0021; honest 4/9/37 practice
#444	GB-1 — clause segmentation + clause-local sub-derivation	per-clause structure
#445	GB-2 — same-unit list-sum-then-scale	clean-case capability; extraction-gated on practice
#447	EX-2 — bare-decimal grounding (shared primitive)	0003 unblocked (+1 practice flip); serving byte-identical

Proposed (doc) PRs: #437 (ADR-0176), #442 (ADR-0177), #443 (ADR-0178), #446 (ADR-0179).

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The findings the microscope produced (in order)

1. Per-shape matchers can't compound — 79% need multiplication, 0% single-step; phrasings are unbounded. (Killed the "another matcher" path.)
2. Self-verification is necessary but not sufficient (3b) — 9/13 self-verified attempts were wrong; the gap is which composition, not can we multiply.
3. Completeness catches multi-step-incomplete attempts (correct first-steps mistaken for answers) — wrongs 9→2.
4. Two gaps: A = cue→op precision; B = compositional structure. Gap B dominates.
5. Structure-from-reading (Gap B) resolves the rich-search-vs-uniqueness tension: every gold case fits a sequential clause read.
6. Cue-precision is bottlenecked — it can only learn from gold-matching chains (~4/50 on blunt shapes); it's the trust substrate + prune, not the coverage unlock.
7. Extraction is the wall — non-uniform units, decimals, word-numbers, multi-word units block the built machinery. (EX-2 proved it: fixing decimal grounding flipped 0003.)

Each finding came with a deterministic trace — the microscope, exactly as the design predicted.

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wrong=0 discipline held throughout

• Serving 3/47/0 byte-identical across all 13 PRs — verified at each landing (and EX-2, the one shared-primitive touch, gated by the pinned lane-SHA check).
• Every attempt-and-eliminate ran in the sealed practice lane; practice "wrongs" are gold-checked eliminations (learning signal), never served.
• Invariants proven by failing-under-violation tests at each phase (#1 seal, #2 spurious-refusal, #3 determinism, #4 no-self-authorization, completeness, target-match).
• A 5-PR lookback review caught and recorded drift before it compounded.

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Next levers (honest, in order)

1. Finish EX (extraction richness) — EX-1 word-numbers, EX-3 multi-word units, EX-4 list-unit inheritance (unblocks 0024's same-unit list). EX-2 (decimals) just proved the pattern.
2. Cue-precision (ADR-0177) — once richer extraction produces more gold-matching chains, the ledger has signal to learn from.
3. Scale (ADR-0163 §F) — volume is what makes the learning compound; 50 cases is mechanism-demonstration.
4. CI-hosted contemplation loops (recorded) — run the sealed practice loop on CI minutes, mobile-triggered, once the learning config stabilizes.

The eval headline (3/47/0) moves once extraction + structure + cue-precision compose on enough volume — and the substrate to make that lift trustworthy is now built and proven.