docs(brief): ADR-0241 P7 true cross-spectral polar handoff for Gemini
Stop-point brief for algebra-native C_AB + Clifford polar mastery; thin-wrap honesty gate and RED test contract for PR #37 takeoff.
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docs/briefs/ADR-0241-cross-spectral-polar-brief.md
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# Brief: ADR-0241 True Cross-Spectral \(\mathcal{C}_{AB}\) + Clifford Polar (P7)
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**For:** Antigravity / Gemini design + TDD implementation
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**From:** CORE ADR-0241 mastery (PR #37, `feat/adr-0241-0242-implementation`)
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**Status:** STOP POINT — largest remaining namesake-green gap on wave polar
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---
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## Takeoff
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- Forgejo: `core-labs/core` — **not** GitHub
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- Branch: `feat/adr-0241-0242-implementation`
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- Pull latest (includes ADR-0242 packing/Fibonacci):
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`git fetch forgejo && git checkout feat/adr-0241-0242-implementation && git pull forgejo feat/adr-0241-0242-implementation`
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- PR: https://core-gitquarters.acbcontent.org/core-labs/core/pulls/37
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### Read first (order)
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1. `AGENTS.md`
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2. `docs/adr/ADR-0241-wave-field-driven-hyperbolic-atlas-and-resonant-cognition.md` § Decision table (Procrustes → cross-spectral polar)
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3. `docs/research/third-door-blueprint-fidelity.md` §12 (W3 marked 🟡 thin wrap)
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4. `core/physics/wave_manifold.py` — `wave_analogical_polar`, `wave_field_conjugacy`
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5. `core/physics/dynamic_manifold.py` — `_field_conjugacy_versor` (current engine under the thin wrap)
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6. Existing green pins: `tests/test_adr_0241_wave_manifold.py` polar / multi-pair tests
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### Already GREEN (do not redesign)
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| Surface | Status |
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|---------|--------|
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| Sandwich / left-spinor / Schrödinger step | GREEN |
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| Spectral leakage → surprise | GREEN |
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| Unitary residual → GoldTether | GREEN |
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| `resonant_reconstruct`, `phase_correlation` | GREEN |
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| Holographic vault + public `get_versor` | GREEN |
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| Atlas packing + Fibonacci (ADR-0242) | GREEN |
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| Serve quarantine | GREEN |
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---
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## Problem (why this is not green mastery yet)
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ADR-0241 claims:
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> Cross-spectral correlation \(\mathcal{C}_{AB}\) → Clifford polar decomposition for analogy rotor
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**Current code:** `wave_analogical_polar` / `wave_field_conjugacy` are a **lazy thin wrap** over `_field_conjugacy_versor` (SVD nullspace + multiplicative Gauss–Newton residual minimizer). That is pre-ADR pointwise conjugacy, **not** a spectral correlation matrix + polar factor.
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Goal: make polar **algebraically faithful** so at least one RED test fails on thin wrap alone and passes on true polar.
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---
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## Hard constraints
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| Rule | Detail |
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|------|--------|
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| Algebra-native only | `algebra/*` only — **no scipy as algebraic truth** |
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| Transport pin | Multivector field path = sandwich \(R\psi\widetilde{R}\); do not silently mix left-spinor |
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| Closure | Construction-boundary close only; `versor_condition < 1e-6`; no hot-path unitize |
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| No dual permanent path | `conformal_procrustes` field path must keep calling wave polar (no parallel residual engine) |
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| Determinism | No random; fixed fixtures |
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| Off-serve | Do not wire into `chat/runtime.py` |
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| Exact recall | No cosine/ANN |
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---
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## Design deliverables (do these first if math is non-obvious)
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Write a short design note (can live in PR body or `docs/briefs/` update) covering:
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1. **Definition of \(\mathcal{C}_{AB}\)** on multivector fields in Cl(4,1) 32-vectors (not Euclidean feature matrices).
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2. **Polar decomposition path** that yields sandwich rotor \(R\) with \(\psi_B \approx R\psi_A\widetilde{R}\).
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3. **Multi-pair aggregation**: how N pairs become one \(R\) (spectral aggregate then polar vs joint residual).
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4. **Relation to `_field_conjugacy_versor`**: replace, fallback, or residual-check only.
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5. **Global sign ambiguity** of rotors (tests already allow ±R).
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If design requires multi-model debate, return the design note for human/Grok review **before** large GREEN implementation. If design is clear and RED tests fail thin wrap, proceed TDD.
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---
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## Implementation targets
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| API | Expected change |
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|-----|-----------------|
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| `WaveManifold.wave_analogical_polar(ψ_A, ψ_B) -> R` | True polar / \(\mathcal{C}_{AB}\) path |
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| `WaveManifold.wave_field_conjugacy(sources, targets) -> (R, residual)` | Multi-pair true path |
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| `dynamic_manifold.conformal_procrustes` field path | Remains wave delegate |
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| Kabsch null-point / (5,K) clouds | **Unchanged** compatibility path |
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---
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## RED tests that must not pass for free on thin wrap
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Add / extend `tests/test_adr_0241_wave_manifold.py` (or `tests/test_adr_0241_wave_polar.py`):
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```text
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test_wave_polar_recovers_known_sandwich_rotor # already green — keep
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test_wave_polar_multi_grade_packet_beats_thin_wrap # NEW: case where residual-minimizer
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# conjugacy diverges from true polar
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test_wave_field_conjugacy_multi_pair_true_polar # multi-pair fidelity pin
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test_conformal_procrustes_still_delegates_to_wave # no dual path regression
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test_polar_construction_closed_versor_condition # versor_condition < 1e-6
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test_no_scipy_as_algebraic_truth_in_wave_polar_module # AST/import pin optional
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```
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**Critical:** invent at least one multi-grade or multi-pair fixture where current `_field_conjugacy_versor` residual is acceptable under loose tol but **true polar** is required by ADR math. If no such fixture exists after honest design, document why thin wrap **is** the polar for Cl(4,1) sandwich conjugacy and demote ADR language instead of shipping namesake-green — **honesty over theater**.
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---
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## Out of scope (this task)
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- Non-vacuous chiral / pair-spinor (P8 — separate brief)
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- Contemplation Trace A wiring (P9)
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- True \(H^2\) geodesic packing refinement (ADR-0242 packing already green with CGA null-point \(d\))
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- Rust/MLX acceleration
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- Serve-path wiring
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- CLAIMS.md / ADR Accepted flip
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---
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## Validation
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```bash
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python3 -m pytest tests/test_adr_0241_wave_manifold.py tests/test_adr_0242_*.py tests/test_third_door_cohesion.py tests/test_adr_0241_holographic_vault.py -q
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# plus any new polar tests
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# Third-Door Procrustes / surprise / goldtether must stay green
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python3 -m pytest tests/test_adr_0239*.py tests/test_adr_0238*.py -q
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```
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## Success
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1. Polar path is either **algebraically true \(\mathcal{C}_{AB}\)+polar** with thin-wrap-failing RED tests, **or** ADR/fidelity language demoted with proof that conjugacy **is** the polar in this algebra.
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2. No dual permanent residual path.
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3. Serve quarantine + versor_condition held.
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4. Fidelity W3 flipped only under the honest criterion above.
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5. Commit on `feat/adr-0241-0242-implementation` and push Forgejo (updates PR #37) — or open stacked PR if preferred.
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