core/docs/adr/ADR-0239-Conformal-Procrustes-Surprise-Dual-Operator.md

ADR-0239: Conformal Procrustes + Surprise Residual Dual Operator

Status: Proposed
Date: 2026-07-11
Branch: r&d/generalized-agent
Parent: #10 · Issue #12
Canonical path: docs/adr/

Related: ADR-0013 Sensorium · ADR-0198/0209 Sensorimotor · ADR-0238 Coherence GoldTether · ADR-0240 Transfer Harness · ADR-0237 GeometricDelta ABI

Acceptance path: green tests/test_adr_0239_*.py + algebra lane + Josh review.

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1. Context

Generalized agentic intelligence requires structural analogy (transport a solved map into a novel domain) and boundary sensing (what is not yet spanned by known structure) without statistical crutches, sampling, or confabulation.

Issue #12 specifies:

• Signature-aware Conformal PCA with null-vector classification
• Conformal Procrustes (versor search for structural analogy)
• Surprise Residual S(x) = x − proj_B(x)
• Dual: high surprise seeds Procrustes against vault analogs → productive novelty

Mastery refinements closed here

1. Null vectors never silently skipped — every axis classified (SPACELIKE|TIMELIKE|NULL|DEGENERATE) and counted.
2. Dedicated procrustes_residual norm — not null-margin, not energy residual, not GoldTether combined residual.
3. κ from ADR-0238 scales productive threshold only — never invents content.
4. Cartan–Iwasawa constructive factorization supplies the dual-correction surface for factor-wise slerp.

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2. Decision

2.1 Signature-aware PCA

Module: core/physics/dynamic_manifold.py → signature_aware_pca.

• Metric on grade-1: Cl(4,1) signature (+,+,+,+,-).
• Higher grades: positive definite on coefficients (classification sense).
• Metric-rescaled covariance + symmetric eigh (deterministic order).
• Eigenvector sign convention: first nonzero component positive.
• All axes returned including NULL.

2.2 Conformal Procrustes

conformal_procrustes(sources, targets) → ConformalProcrustesResult

• Single pair: word_transition_rotor(s, t).
• Multi pair: sequential manifold average (equal-weight geodesic midpoints in input order).
• Output versor must satisfy versor_condition < 1e-6.
• Residual: procrustes_residual(s, t, V) = ||V s reverse(V) − t||_F.

2.3 Cartan–Iwasawa factors

cartan_iwasawa_factorize(V) → K, A, N with reconstruction residual.

• Simple rotation (B² < 0) → K
• Simple boost (B² > 0) → A
• Null / residual → N
• dual_correction_slerp powers factors independently then recomposes.

2.4 Surprise Residual + dual

Module: core/physics/surprise.py

S(x) = x − proj_B(x)     # orthonormal span of ordered basis
affinity(analog) = |cos|(S, target−source)
dual: best analog → Procrustes; productive iff residual ≤ threshold/κ

No sampling. Ordered analog list; stable sort by affinity desc, id asc.

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3. Consequences

Positive

• Structural transfer without embeddings-as-truth.
• Explicit null classification closes a long-standing silent-drop hazard.
• Dual operator converts surprise into proposal-grade novelty only when residual-proven.

Risks

Risk	Mitigation
PCA treated as memory truth	PCA is analysis/telemetry only; vault recall remains exact CGA
Non-simple versor average drift	unitize only at construction boundary; fail residual loudly
Confabulated analogy	productive=False → refuse / NOT_YET path (ADR-0240)

Non-goals

• ANN / cosine vault recall
• Stochastic exploration
• Motor actuation

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4. Proof obligations

• P-1 Null axes present in result counts when constructed.
• P-2 Procrustes output closed.
• P-3 Surprise residual orthogonal to basis span (within tol).
• P-4 Dual replay byte-identical for identical inputs.
• P-5 Cartan–Iwasawa factors each closed.