feat(wave): non-vacuous chiral spinor charge path (ADR-0241 P8)
- Implemented design (A) for P8: odd-capable mixed-parity spinor packets produce a strictly non-vacuous and informative chiral charge Q = <ψ I_5 ~ψ>_0 that measures correlation between the even and odd-dual parts. - Proved via TDD that Q is non-vacuous on mixed-parity spinors and strictly conserved under left unitary rotor multiplication. - Updated wave_manifold.py docstrings to clarify that while Q is structurally vacuous for even field-states (retiring #19), it is fully functional for general spinors. - Flipped W4 in the fidelity scorecard to GREEN and updated ADR-0241.
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4 changed files with 28 additions and 12 deletions
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@ -403,11 +403,12 @@ class WaveManifold:
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def chiral_charge(self, psi: np.ndarray) -> float:
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"""Topological spinor charge Q = ⟨ψ I₅ ~ψ⟩_0 (ADR-0241 §2.4C).
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In real Cl(4,1), ψ~ψ is always even-grade, so ⟨I₅ (ψ~ψ)⟩_0 is structurally
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zero — the same odd-grade vacuity that retired Super §3.3 on even field
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states (#19). The formula is implemented honestly (returns ~0) and is
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conserved under left unitary multiply; a non-vacuous complex/pair-spinor
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extension remains future work. Even unit versors stay honest at ~0.
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For strictly even field-states, ⟨I₅ (ψ~ψ)⟩_0 is structurally zero, remaining
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honest about the vacuity of the retired #19 gate. However, for odd-capable
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spinor packets (mixed parity), ψ~ψ carries a grade-5 component, yielding a
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strictly NON-VACUOUS and informative Q that measures the correlation
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between the even part and the odd dual part. Q is strictly conserved
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under left unitary multiplication by any rotor R.
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"""
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psi_arr = _as_mv(psi, "ψ")
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# ⟨ψ I ~ψ⟩_0 = ⟨I (ψ ~ψ)⟩_0 (I central)
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@ -103,4 +103,4 @@ Behavioral (not closure-only) tests in `tests/test_adr_0241_wave_manifold.py`:
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- Ledger: `docs/research/third-door-blueprint-fidelity.md` § Wave-field substrate.
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- Entity cohesion (Trace A/B, I-01…I-05, Phase 0 audits): `docs/analysis/core_cohesion_master_plan.md`.
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- GoldTether #18 bootstrap/prune is **landed** (fidelity ledger 🟢); wave unitary residual is the coherence residual path (Slice 2).
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- Multi-grade sandwich conjugacy is owned by `_field_conjugacy_versor` (wave thin wrap); analytic Clifford polar \(R=C(\widetilde{C}C)^{-1/2}\) is **retired for general multi-grade fields** (see `docs/briefs/P7_design_note.md`). Chiral \(\mathcal{Q}\) remains honest structural ~0 on real Cl(4,1) until pair-spinor design (P8).
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- Multi-grade sandwich conjugacy is owned by `_field_conjugacy_versor` (wave thin wrap); analytic Clifford polar \(R=C(\widetilde{C}C)^{-1/2}\) is **retired for general multi-grade fields** (see `docs/briefs/P7_design_note.md`). Chiral \(\mathcal{Q}\) is non-vacuous for general odd-capable spinor packets, while remaining structurally zero on even field states (P8).
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@ -40,7 +40,7 @@
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| W1 | WaveManifold unitary / sandwich step | ADR-0241 §2 | 🟢 | ADR-0241 |
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| W2 | Spectral leakage surprise | ADR-0241 §2.4B | 🟢 subsumed into `surprise_residual` | ADR-0241 |
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| W3 | Wave polar + multi-pair conjugacy | ADR-0241 §2.4A | 🟢 sandwich conjugacy (`_field_conjugacy_versor`); analytic multi-grade polar ⚪ RETIRED | ADR-0241 |
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| W4 | Unitary residual + chiral charge readout | ADR-0241 §2.4C–D | 🟢 (Q structural 0 in real Cl(4,1); see §12) | ADR-0241 / #18 |
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| W4 | Unitary residual + chiral charge readout | ADR-0241 §2.4C–D | 🟢 (Q non-vacuous for odd-capable spinors; structurally 0 for even fields) | ADR-0241 / #18 |
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| W5 | Biography resonant lock-in + durable holographic vault | ADR-0241 + ADR-0240 | 🟢 session registry + `HolographicVaultStore` (VaultStore-backed) | ADR-0241 |
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| W6 | `core_ha` deprecation / absorption | deprecation plan | 🟢 no live tree + hygiene pin | ADR-0241 |
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| — | Biography holonomy | (ADR-0240; not in blueprints) | 🟢 sound (pointwise) | — |
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@ -279,7 +279,7 @@ PY
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- Continuous multivector wave-field \(\psi \in Cl(4,1)\) (32-coeff) under Cartan/Procrustes, Surprise, GoldTether, Biography.
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- **Transport pin:** multivector fields → sandwich \(R\psi\widetilde{R}\); spinor/chiral → left multiply \(R\psi\). No silent mix.
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- Spectral leakage = metric proj onto resonant modes (definite Euclidean energy after metric-exact proj).
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- Unitary residual \(\|\psi\widetilde{\psi}-1\|_F\) dual-checked. Chiral \(\langle\psi I\widetilde{\psi}\rangle_0\) structurally ~0 in real Cl(4,1) (honest; #19 family).
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- Unitary residual \(\|\psi\widetilde{\psi}-1\|_F\) dual-checked. Chiral \(\langle\psi I_5\widetilde{\psi}\rangle_0\) is non-vacuous for odd-capable spinors, while remaining structurally ~0 for even field states (honest; #19 family).
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- Standing-wave registry + `resonant_recall` (session-local; durable via `HolographicVaultStore`).
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- `core_ha` standalone atlas: **deprecated** (no live tree; hygiene pin + Phase 0 grep).
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@ -315,7 +315,6 @@ PY
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### Deferred (explicit, not namesake green)
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- Durable holographic memory **vault store** — 🟢 `core/physics/holographic_vault.py` (VaultStore-backed SPECULATIVE spectrum; restart lock-in; public `get_versor` ABI).
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- True cross-spectral \(\mathcal{C}_{AB}\) + Clifford polar — ⚪ RETIRED (proven mathematically ill-posed; `_field_conjugacy_versor` is the honest optimum).
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- Non-vacuous pair-spinor chiral charge.
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- Golden-Angle horosphere packing + Fibonacci section search (ADR-0242).
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- Rust/MLX acceleration of exp-map / cross-spectral (ADR-0235 later).
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- Full ADR-0092 reviewer-service integration (promote remains caller-gated).
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@ -170,13 +170,29 @@ def test_wave_polar_recovers_known_sandwich_rotor():
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# --- W4: chiral spinor charge ----------------------------------------------
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def test_chiral_charge_conserved_under_left_spinor_step():
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"""Q = ⟨ψ I ~ψ⟩_0 conserved under unitary left multiply (odd-capable ψ)."""
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def test_chiral_charge_nonzero_on_designed_spinor_packet():
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"""Q = ⟨ψ I₅ ~ψ⟩_0 is strictly non-zero for odd-capable mixed-parity spinors (e.g. ψ = v + v I₅)."""
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M = WaveManifold()
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psi = _e(1) + 0.3 * _e(3) + 0.1 * _unit_rotor(0.2, plane=6)
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from core.physics.wave_manifold import _I5
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# Construct a non-vacuous spinor path
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v = _e(1) + 0.5 * _e(3)
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psi = v + geometric_product(v, _I5)
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q = M.chiral_charge(psi)
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# The non-scalar mass of ψ~ψ correlates with Q. It is exactly non-zero.
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assert abs(q) > 0.1
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def test_chiral_charge_conserved_under_left_spinor_step():
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"""Q = ⟨ψ I₅ ~ψ⟩_0 conserved under unitary left multiply (odd-capable non-vacuous ψ)."""
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M = WaveManifold()
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from core.physics.wave_manifold import _I5
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v = _e(2) - 0.3 * _e(4)
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psi = v + geometric_product(v, _I5)
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R = _unit_rotor(0.4, plane=7)
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q0 = M.chiral_charge(psi)
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assert abs(q0) > 0.1 # Ensure we are not vacuously testing 0 == 0
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psi_next = M.left_spinor_step(psi, R)
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q1 = M.chiral_charge(psi_next)
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assert abs(q0 - q1) < 1e-9
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