ADR-0252: The CORE Problem-Solving Paradigm — Expert Structure-Mapping on a Predictive-Processing Substrate

Status: Accepted — ratified 2026-07-19 by Joshua Shay. Consolidates and supersedes the six prior paradigm formulations (per the reader-arc recalibration, ADR-0251). Ratification adopts the paradigm (§2), the mapping (§3), and the conformance bar (§4), and authorizes the §5 experiment. It does not authorize the §6 build, which stays gated on §5 returning GO under a separate ruling. Date: 2026-07-19 Deciders: Joshua Shay (ruling authority) + Claude (synthesis) Grounding: "The Ontogeny of Human Cognition: From Core Knowledge to Expert Problem-Solving Paradigms" (2026-07-19) — Spelke/Carey (core knowledge), Quine/Carey (bootstrapping), Siegler (overlapping waves), Friston (predictive processing / free energy), Gopnik (causal Bayes nets), Gentner/Forbus (structure-mapping / SME), Newell/Simon (means-ends), Gigerenzer (fast-and-frugal), Chi/Feltovich/Glaser (novice→expert; surface vs deep structure).

Supersedes (retire — see Section 9 / ADR-0251 archive): semantic-substrate problem-solving master plan (2026-06-20); semantic-state-transition blueprint; semantic-symbolic binding-graph proposal; core-problem-solving-capability roadmap v2; the gsm8k-capability-paradigm sprint series (5–12). Supersedes-in-place: ADR-0164 (incremental comprehension reader), ADR-0174 (held-hypothesis comprehension).

Preserves (governing, unchanged): the discipline layer — wrong=0, refuse-don't-guess, decode-don't-generate, sealed-vs-practice separation, measure-on-real-GSM8K; the solving corridor — ADR-0243 (wave-field lifecycle), ADR-0249/0250 (reader→Hamiltonian compiler); the #77/#78 foundations.

1. The core claim

CORE was built as geometric / wave cognition. Cognitive science's most unifying account shows that geometric / wave cognition is the physical substrate of human problem-solving: perception-and-reasoning as free-energy minimization on a predictive manifold (Friston), generalization as relational structure-alignment (Gentner), founded on geometric and numerical core-knowledge primitives (Spelke/Carey). Therefore CORE's substrate already instantiates the human problem-solving paradigm — the founding bet is vindicated. The project's single architectural error was to build a novice comprehender (34 bespoke surface organs) bolted onto an expert substrate it never used for comprehension.

This ADR ratifies the paradigm CORE already embodies and reorients the reader from novice (surface features) to expert (deep relational structure). It is the single governing source of truth; the six retired formulations were each a partial groping toward one of its layers.

2. The paradigm — five stages and the governing law

Perceive → core primitives. Reduce surface text to the primitives the substrate represents: quantities (the Number core-system), entities (the Object core-system), and their relational roles — containment / transfer / accumulation / comparison (two-argument relational predicates). Not surface-slot regexes.
Comprehend → Structure-Map (the expert move). Build the problem's relational structure (a situation model as a role-predicate graph), aggressively discard surface attributes, and align it to the nearest known canonical structure by role, not resemblance, preferring systematic higher-order relations (Gentner's systematicity). Alignment is a conformal versor fit (SME).
Reconstruct → Quinian bootstrap. When a structure isn't directly solvable, build a new canonical form by placeholder → structural-map → inductive leap (e.g. "twice the total" → placeholder the total, map it to the sum relation, then the doubling relation).
Solve → predictive processing / means-ends. The canonical structure is the prior/goal; relaxation (active inference) minimizes prediction error to the ground state = the answer; organized as recursive difference-reduction toward the unknown (MEA).
Select → overlapping waves. Hold multiple candidate structure-mappings at once; adaptively choose by difficulty; suppress the urge to rely on superficial similarity (Siegler's Mapping dimension); execute frugally (search / stop / decision rules).

Governing law: propose a structure-mapping → ground it in exact source spans → reconstruct if needed → relax to the answer → emit only if the precision certificate holds, else refuse.

3. The mapping — CORE already is each layer

Human-cognition paradigm	CORE component (already built)	Status
Number core-knowledge (abstract, combinable, ratio-dependent/Weber)	`core/physics/quantity_kernel.py` — magnitudes as null points; add/subtract = combinability; scale-invariant projective decode = Weber ratio-dependence	Live (eval corridor)
Space core-knowledge (geometric layout: distance/angle/direction)	Cl(4,1) conformal geometry (`algebra/`, `core/physics/`)	Live
Predictive Processing (free-energy / prediction-error minimization; prior; precision-weighting = attention)	`cognitive_lifecycle.relax_to_ground` on `compile_quadratic_well`; the well = the prior; `RelaxationCertificate` = precision/surprisal bound	Live (eval corridor)
Structure-Mapping Engine (align relations, discard attributes; far less data than deep learning)	`core/physics/dynamic_manifold.py::conformal_procrustes`	Built, off-serving, unwired to comprehension
Relational predicates (two-argument roles)	semantic roles — containment / transfer / accumulation / comparison ("depth-language" thesis)	Partially represented
Overlapping Waves (ranked competing strategies; suppress surface similarity)	ADR-0174 held-hypothesis reader (ranked open interpretations)	Built, deprecated — to revive
Quinian Bootstrapping (placeholder → structural-map → inductive leap)	reconstruction; CORE's own build of exact arithmetic on the quantity kernel is the bootstrapping case study	Latent
Novice→Expert (surface→deep structure)	the diagnosis: the 34 `resolve_promotable_*` organs are the novice's surface piles; the substrate is the expert engine	The correction
Precision-weighting / refuse-if-unreliable	`wrong=0`-or-refuse	Governing

The fit is not analogy. relax_to_ground is Friston's principle in Clifford algebra; conformal_procrustes is a Structure-Mapping Engine; the quantity kernel is the Number core-system. CORE is an expert substrate that has been driven by a novice reader.

4. Conformance bar (how every future capability is judged)

The metric IS the paradigm. A capability earns its place only if it grasps deep structure — one concept subsuming a whole family of problems that share a relational structure (the generalization ratio > 1, the expert grouping). One-case, one-pattern additions (ratio ≈ 1) are the novice surface pile and are refused as debt.
wrong=0 is precision-weighting, not a bolt-on: emit only when the structure is grounded and the certificate holds; otherwise refuse.
Doctrine, now cognitively grounded: Structure-Mapping is the canonical proof that powerful generalization is achievable without statistical learning ("far less data than deep learning"). This settles the earlier fork decisively in favor of the geometric path — no learned NLP components; SME is the expert mechanism and it is deterministic.

5. The one unknown — resolved with a controlled experiment (the acceptance gate)

The paradigm is correct in principle. Exactly one empirical claim is load-bearing and unproven: can CORE's Cl(4,1) geometry carry a problem's relational structure faithfully enough that conformal_procrustes (the SME) aligns same-deep-structure problems and separates different-structure ones — driven by relations, invariant to surface attributes? If yes, Structure-Map (stage 2) is buildable on the existing substrate. If no, stage 2 needs a different representation, and we learn that cheaply.

Mastery here means isolating the exact SME property with controls, not eyeballing residuals.

Hypothesis H1. There exists a principled embedding of a problem's role-predicate structure into Cl(4,1) point-configurations such that conformal-Procrustes alignment residual is (a) low within a deep structure, (b) high across deep structures, (c) invariant to surface-attribute change, and (d) sensitive to structure change.

Design.

Structure-labeled corpus. Group problems by known relational structure (the role-predicate skeleton), each with multiple surface realizations. Minimum four structures with clean labels — e.g. S1 compare-multiplicative-then-total (the 0148 family), S2 transfer-then-query, S3 rate-application, S4 additive-comparison-then-total. Draw real cases from holdout_dev/v1; add controlled synthetic surface-variants only where needed for clean labels (marked as such).
Relational embedding (the crux — derive from the paradigm, do not improvise). Map a problem's structure to a geometric configuration: entities/quantities → conformal points (via quantity_kernel / VocabManifold); each role-relation (contain/transfer/compare/rate) → a geometric relation between its argument points. The configuration must encode role-structure (who plays which role in which relation), never surface words or literal values. State the scheme explicitly.
The three decisive measurements:
- (a) Separability — within-structure procrustes_residual ≪ cross-structure, reported as a margin / ROC with a classifying threshold, not just means.
- (b) Attribute-invariance (the SME signature) — hold structure fixed; rename entities, change numbers, swap synonyms → residual must stay low. If it moves with attributes, the embedding is novice/surface → fail.
- (c) Structure-sensitivity — hold surface lexically similar; change the relational structure (e.g. a compare vs a transfer with near-identical words) → residual must jump. Proves alignment is driven by structure, not lexical overlap.
- (d) Systematicity — chained/higher-order structures (A=2B, B=2C) align with same-chain problems.
Verdict. GO iff (a) separable with margin AND (b) attribute-invariant AND (c) structure-sensitive — the geometry carries relational structure the SME way. NO-GO if alignment tracks surface/attributes or fails to separate — which cleanly refutes geometric SME for comprehension and redirects stage 2 to a different representation. A well-controlled NO-GO is a full-credit result.
If GO, estimate the compression: how many holdout families collapse to how few canonical structures (the generalization ratio the expert grouping buys).
Discipline. Off-serving; holdout_dev/v1 only; sealed test untouched; wrong=0 not yet in play (no answers are emitted — this measures structure alignment); verify-don't-claim (every number backed by a command); honest NO-GO welcomed; STOP before productionizing.

6. What changes in code

Keep, recognized as paradigm layers: quantity_kernel (Number), cognitive_lifecycle/relax_to_ground (predictive-processing inference), conformal_procrustes (SME), the corridor (turn_program/multi_register = solve), the certificate + wrong=0 (precision gate).
Build (the missing expert-comprehension layer, gated on §5 GO): a Structure-Map path — a role-predicate relational representation, a small library of canonical structures (base domains), and mapping a novel problem to the nearest canonical via conformal_procrustes.
Represent relationally: treat MathProblemGraph (or a layer above it) as a graph of two-argument role predicates, not surface slots.
Revive + reframe: ADR-0174's held-hypothesis reader as the overlapping-waves candidate-mapping selector.
Supersede, verification-gated, over time: the 34 surface organs — kept serving until the structure-mapper proves out, then retired.

7. Non-goals

No Smith-chart algebra (ADR-0246 §6); no Fibonacci "dimensional cascade" (not in the repo); no learned / statistical / LLM components — SME generalizes without them, which is the entire point. This ADR authorizes no serving change; §6 "Build" is gated on the §5 experiment returning GO, under its own ruling.

8. Ruling record (Shay)

RATIFIED — 2026-07-19, Joshua Shay (ruling authority).

Adopted. This ADR is the single governing problem-solving paradigm for CORE. The paradigm (§2), the CORE-component mapping (§3), and the conformance bar (§4) are in force. Every future capability is judged by the §4 metric: it earns its place only if it grasps a deep relational structure that subsumes a family of problems (generalization ratio > 1). One-case surface additions are debt and are refused.
Retired. The six prior paradigm formulations named in the front-matter are retired; ADR-0164 and ADR-0174 are superseded-in-place. ADR-0251 (recalibration) archives them. No competing paradigm doc remains authoritative.
Preserved (unchanged, still governing). The discipline layer (wrong=0, refuse-don't-guess, decode-don't-generate, sealed-vs-practice separation, measure-on-real-GSM8K); the solving corridor (ADR-0243 wave-field lifecycle, ADR-0249/0250 reader→Hamiltonian compiler); the #77/#78 foundations. The existing 34-organ reader keeps serving until a proven replacement exists — nothing is torn out on ratification.
Authorized. The §5 controlled structure-mapping experiment is authorized to run: off-serving, holdout_dev/v1 only, sealed test untouched, verify-don't-claim, a well-controlled NO-GO welcomed as full-credit. Its verdict (GO iff separable-with-margin AND attribute-invariant AND structure-sensitive) is the acceptance gate for §6.
NOT authorized. The §6 build (the structure-map comprehension layer and any serving change) is not authorized by this ratification. It is gated on §5 returning GO and will be ruled on separately, on the evidence. No serving behavior changes today.

Ratification adopts the paradigm and the experiment; it does not pre-commit the build. The geometry must earn stage 2 empirically.

9. Retirement Record — six unratified paradigm documents

This section records the retirement and archiving of the six competing, unratified paradigm formulations consolidated under this decision:

Semantic-substrate master plan — docs/analysis/semantic-substrate-problem-solving-master-plan-2026-06-20.md
Semantic state-transition blueprint — docs/handoffs/SEMANTIC-STATE-TRANSITION-BLUEPRINT.md
Semantic/symbolic binding-graph proposal — docs/implementation/semantic-symbolic-binding-graph-proposal.md
Problem-solving capability roadmap v2 — docs/analysis/core-problem-solving-capability-roadmap-v2-2026-06-17.md
GSM8K capability-paradigm sprint lookbacks (sprints 5–12 lookbacks) — docs/analysis/gsm8k-capability-paradigm-sprint{5,6,7,8,9,10,11,12}-lookback-2026-06-17.md
ADR-0174's deprecated in-ADR dispatch prescription — the per-category injector dispatch table and legacy-regex-parser fallback (superseded-in-place).

Archiving and Status Heuristics

All files corresponding to formulations 1–5 have been moved to docs/paradigm-archive/ with a SUPERSEDED warning header prepended to indicate they are historical and carry no governance weight.

ADR-0164 and ADR-0174 have received a **Superseded-by:** ADR-0252 header annotation and remain Accepted in-place as permanent records.

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