core/docs/research/third-door-blueprint-fidelity.md

Third-Door Blueprint Fidelity Ledger

Status: authoritative gap analysis for the ADR-0238/0239/0240 skeleton (PR #15). Audience: whoever implements the Third Door for real. Verdict in one line: what landed is a safe, off-serving namesake scaffold — it adopts the blueprints' vocabulary and file layout and makes its own tests green, but it does not implement the mathematics the two source blueprints specify. This document details every gap precisely enough to close it.

This replaces the "absolute mastery / single right solution" framing of the original landing (Mastery Report / PR #14 body). The blueprints are the rigorous artifact; the code is the loose one. That is the honest inversion of the landing claim.

---

0. Source-of-truth artifacts

Artifact	Role
CORE ASI Super-Blueprint_ Third-Door Horizon.docx (mirror: docs/research/CORE-ASI-Super-Blueprint-Third-Door-Horizon.md)	Specifies signature-aware PCA (§2.1), Cartan–Iwasawa (§2.2), GoldTether scale harmonization (§2.3), Conformal Procrustes (§3.1), Surprise (§3.2), grade-5 pseudoscalar invariant (§3.3). "Super §x" below.
CORE Advanced AGI_ASI R&D Blueprint (Revised).docx	Specifies blade induction (§2.1), trajectory invariants + zero-fabrication (§2.2), GoldTether-modulated transition surface + α control law (§2.3), ADR-DAG embedding (§2.4), bootstrapping (§5). "R&D §x" below.
docs/adr/ADR-0241-wave-field-driven-hyperbolic-atlas-and-resonant-cognition.md	Wave-field substrate \psi: unitary propagation, spectral leakage, polar analogy, chiral charge. "ADR-0241" below.
docs/analysis/core_ha_unification_and_deprecation_plan.md	Deprecate standalone core_ha pointwise atlas; absorb into wave + energy + GoldTether + CRDT vault.
core/physics/{goldtether,dynamic_manifold,surprise,biography,temporal_gate,self_authorship}.py	The landed Third-Door code (pointwise). Wave module: wave_manifold.py (Proposed).
tests/test_adr_023{8,9}_*.py, test_adr_0240_*.py	Landed Third-Door tests (see §7 for why green ≠ faithful historically).
tests/test_adr_0241_wave_manifold.py	Wave-field behavioral contract (RED until Slice 1 GREEN).
tests/test_third_door_blueprint_fidelity.py	The living gap ledger (this document, executable).

Containment fact (why this is safe to land): nothing in serving / runtime / cognition imports core.physics.* — only the package __init__, the eval harness, and tests. chat/runtime.py is untouched on this branch. The autonomy decide() is fail-closed and never AUTONOMOUS in SERVE. The self-authorship miner is proposal-only and never writes the vault. None of the defects below can reach the wrong=0 serving path.

---

1. Scorecard

#	Operator	Blueprint	Fidelity	Issue
1	Signature-aware PCA	Super §2.1 / R&D §2.1	🟢 faithful (one untested add-on)	—
2	Cartan–Iwasawa decomposition	Super §2.2	🟢 faithful (null-point peel + Spin remainder)	#16
3	Conformal Procrustes	Super §3.1	🟢 faithful (Kabsch + field conjugacy)	#17
4	GoldTether residual + α law	Super §2.3, R&D §2.3/§5	🟢 residual+α + bootstrap gates + principal-axis prune (#24+#18)	#18
5	Grade-5 pseudoscalar invariant	Super §3.3	⚪ RETIRED — vacuous in odd-dim Cl(4,1)	#19 (closed)
6	Surprise residual operator	Super §3.2	🟢 math + DiscoveryCandidate wiring landed (#26 + #31)	#20
7	Trajectory invariants + zero-fabrication	R&D §2.2	🟢 Python geometry surface (trajectory_invariants.py)	#21
8	ADR-DAG conformal embedding	R&D §2.4	🟢 Python surface (core/adr/validator.py)	#21
W1	WaveManifold unitary / sandwich step	ADR-0241 §2	🟢	ADR-0241
W2	Spectral leakage surprise	ADR-0241 §2.4B	🟢 subsumed into surprise_residual	ADR-0241
W3	Wave polar + multi-pair conjugacy	ADR-0241 §2.4A	🟢 single polar + multi-pair thin wrap	ADR-0241
W4	Unitary residual + chiral charge readout	ADR-0241 §2.4C–D	🟢 (Q structural 0 in real Cl(4,1); see §12)	ADR-0241 / #18
W5	Biography resonant lock-in	ADR-0241 + ADR-0240	🟢 unitary lock-in + mode registry / resonant_recall; durable holographic vault store deferred	ADR-0241
W6	core_ha deprecation / absorption	deprecation plan	🟢 no live tree + hygiene pin	ADR-0241
—	Biography holonomy	(ADR-0240; not in blueprints)	🟢 sound (pointwise)	—
—	Temporal admissibility gate	(ADR-0240; not in blueprints)	🟢 sound	—
—	Self-authorship miner	(ADR-0240; not in blueprints)	🟢 sound (proposal-only)	—

---

2. Cartan–Iwasawa decomposition — 🟢 faithful (#16)

Blueprint spec (Super §2.2)

Factor a conformal versor V = R·T·D by acting on the conformal null points n_o (origin) and n∞ (infinity). Explicitly "mathematically exact, non-iterative, guarantees perfect decomposition":

1. Dilation — V n∞ Ṽ = λ² n∞; λ = √|V n∞ Ṽ|; D = exp(log(λ)·e_o∧e∞); peel: V' = V·D⁻¹.
2. Translation — V' n_o Ṽ' = n_o + a + ½a²n∞; recover a ∈ ℝ³ by projecting the Euclidean vector part; T = exp(½ a∧e∞); peel: R = V'·T⁻¹.
3. Rotor — the remainder R satisfies R Ṙ = 1, R n_o Ṙ = n_o, R n∞ Ṙ = n∞.

What landed (dynamic_manifold.py::cartan_iwasawa_factorize)

Null-point peel via algebra.null_point.recover_dilation / recover_translation (right-peel D then T for reconstruction order R·T·D). Strict construction-boundary close (rescale true versors only — never seed-to-rotor fabrications). On NullPointRecoveryError (non-similarity — e.g. multi-plane products that do not fix n∞) fall through to honest remainder-as-rotor: R=V, T=I, D=I. Peel path that fails reconstruction residual falls back to Spin remainder. Every returned factor is closed (versor_condition < 1e-6); non-versor input raises ValueError (fail-closed). No grade-projection fabrication of R/D seeds.

Dual-correction follow-on: rotor_power now implements exact null-bivector power (a+B)^α = a^α + α a^{α-1} B so dual_correction_slerp no longer silently zeros the translation leg.

Acceptance (pinned)

• Composed multi-plane versors never raise; residual ‖R·T·D − V‖ < 1e-6 (often ~0 for Spin remainder).
• Pure similarities V = R_euc·T·D peel with residual < 1e-6 and peel-content pins (nontrivial D with recovered scale, nontrivial T, R·T ≈ V·D⁻¹).
• Pure dilator / translator / identity round-trip with factor-content asserts (not residual alone).
• test_cartan_iwasawa_should_reconstruct_composed_motion passes (xfail removed).
• Translator half-slerp: dual_correction_slerp(I, translator([2,0,0]), 0.5) recovers displacement [1,0,0].

---

3. Conformal Procrustes — 🟢 faithful (#17)

Blueprint spec (Super §3.1)

Two fields F_A, F_B are structurally analogous iff a single versor V maps one to the other under the sandwich V·F_A·Ṽ = F_B. Solve as a metric-aware Kabsch on null-vector point sets P={p_i}, Q={q_i}: K = Σ p_i q_iᵀ η → signature-aware SVD K = UΣVᵀ → R = V Uᵀ; translation + dilation from null-cone centroids. Verified by margin |V·F_A·Ṽ − F_B| < ε_analogy. Enables zero-shot transport of F_A's solution path to F_B.

What landed (dynamic_manifold.py::conformal_procrustes)

• (5,K) path: dehomogenize (w=e5−e4), Umeyama scale + Kabsch R with det=+1, t = μ_y − s R μ_x, assemble V = T(t)·D(s)·R via null_point.translator/dilator + so3_matrix_to_rotor, return grade-1 sandwich adjoint M (5×5) with weight-normalized residual (dilation changes homogeneous weight; Euclidean images still match to ~1e-15).
• Null-point 32-lists: extract (5,K), Kabsch, return V32 with sandwich residual.
• Field conjugacy (non-null 32-vecs): stacked linear W F_A − F_B W = 0 nullspace candidates + multiplicative Lie GN on Spin; residual is sandwich (versor_apply), not left-composition. word_transition_rotor averaging deleted from this path.
• Analogical harness fixture learns from probe null-point clouds under a known similarity (no longer I→I).

Acceptance (pinned)

• Multiplane F_B = versor_apply(W, F_A) → sandwich residual < 1e-5.
• Known rotation / full similarity (s,R,t) clouds → residual < 1e-6, mapped points match.
• Null-point list of 32-vecs → sandwich residual < 1e-6.

---

4. GoldTether residual + α control law — 🟡 partial (#18)

Blueprint spec (Super §2.3, R&D §2.3/§5)

• Residual (scale-harmonized — Super §2.3, the blueprint's stated mission #1): R = w·(‖F·F̃−1‖/ε_drift) + (1−w)·(min_{I∈𝓘_gold} ‖F−I‖ / ‖F‖_F), w=0.5, ε_drift=1e-6. Both terms scaled to [0, O(1)] so drift isn't masked by the raw O(1) L2 distance.
• α control law (R&D §2.3): α(t) = Φ(R; R_floor, R_critical) — a smooth-step of the instantaneous residual. α=0 (autonomous) when R < R_floor; linear ramp in between; α=1 (full human override / fail-closed) when R > R_critical. α is the constraint weight; the supervised transition is the Cartan–Iwasawa factor-wise slerp of §2.3.
• Bootstrapping (R&D §5): 𝓘_gold primed with n_o, n∞, 1; audit-passed replay-deterministic state versors promoted into it by signed review vote (ADR-0092); decay/pruning to principal axes.

What landed (goldtether.py) — residual+α path (#24)

• coherence_residual(F) remains the fail-closed closure gate (dual-checked unit residual).
• gold_invariants seeded with identity + n_o + n∞ (_primal_gold_invariants).
• goldtether_residual(F) = scale-harmonized two-term residual (drift/ε + dist-to-gold / ‖F‖).
• alpha_constraint(F, mode=…) = Φ(R_gt; r_floor, r_critical) composed with earned-autonomy floor; SERVE always α=1.
• supervised_transition / supervised_blend on the Spin geodesic (word_transition_rotor + rotor_power).
• promote_gold_invariant(..., authorized=True) is caller-gated (no self-authorize); prune_gold_invariants is a size bound retaining the three primals — not full principal-axis decay.

Bootstrap / prune (#18 — landed)

• GoldPromotionProof + promote_gold_invariant(..., proof=, require_proof=): proposal-only without authorized=True; live closure drift gate (not geo-to-gold); refuses non-closed / high-drift even when authorized; never trusts proof fields as truth.
• promotion_eligible(F): closed ∧ drift ≤ ε_drift (does not self-authorize).
• prune_gold_invariants(mode="fifo"|"principal_axes"): primals immovable; PCA ranks non-primals by principal-subspace energy (differs from last-N FIFO); max_size < 3 clamped.
• Unitary residual path still via wave (measure_unitary_residual); SERVE never autonomous.

Explicit non-goals still open

• Full signed ADR-0092 reviewer service wiring (physics stays caller-gated only).
• Durable vault-backed gold set (session monitor field only).

---

5. Grade-5 pseudoscalar invariant — ⚪ RETIRED as vacuous (#19)

Resolution (2026-07-12): three-agent R&D convergence (Opus 4.8 / Grok-4.5-HEAVY / GPT-5.6-Terra), ratified. The §3.3 gate is not "missing" — it is mathematically vacuous in odd-dimensional Cl(4,1) and cannot be built as specified. Issue #19 is closed. The namesake was removed from goldtether.py in the same change (see "What changed" below).

Blueprint spec (Super §3.3)

The pseudoscalar I₅ = e1∧e2∧e3∧e4∧e5 is the orientation of CORE's integrity. Every transition F' = V·F·Ṽ must preserve pseudoscalar sign and magnitude: ⟨F'·F̃'⟩₅ = ⟨F·F̃⟩₅. Any optimization / contemplation promotion / autonomous self-authorship that would flip sgn(I₅) is blocked at the boundary. Called "the ultimate mathematical anchor for alignment."

Why it is vacuous (the proof that retired it)

The spec presumes a spacetime-like even-dimensional intuition. CORE's algebra is Cl(4,1) — odd total dimension (5) — where the grade-5 pseudoscalar behaves degenerately for exactly the quantities the gate inspects:

1. I₅ is central. In odd dimension the pseudoscalar commutes with every element, so for any versor V (including odd reflections, where V·Ṽ = ±1), the sandwich collapses: V·I₅·Ṽ = I₅·(V·Ṽ) = ±I₅. Orientation is invariant by construction — there is no map in the versor group that flips it, so there is nothing to "block."
2. Field-state versors are even ⇒ F[31] ≡ 0. Every state the monitor sees is built by the sanctioned constructors (make_rotor_from_angle, word_transition_rotor, geometric products thereof) which live in the even subalgebra. The grade-5 (odd) coefficient of an even multivector is identically zero. Reading F[31] returns a structural 0.0, always.
3. The gated quantity is identically zero. For an even unit versor, F·F̃ = 1 (a scalar), so ⟨F·F̃⟩₅ = 0 for the source and the target of every transition. The gate ⟨F'·F̃'⟩₅ = ⟨F·F̃⟩₅ compares 0 == 0. It can never fire.
4. The "even-versor parity gate" fix is also vacuous. The natural repair — "reject any transition that injects odd-grade mass" — was invalidated in the same review: the even subalgebra is closed under the sandwich, so odd-grade mass ≡ 0 on every value the sanctioned path can produce. Parity guards nothing a versor could reach. (Empirically confirmed: on a composed 5-plane field versor, ‖⟨F·F̃⟩₅‖ = 0, and total odd-grade mass = 0.)

The single real residual gap in this neighborhood is unrelated to grade-5: algebra/versor.py::versor_condition accepts an odd reflection such as e1 (returns 0.0), i.e. it gates "is a unit versor," not "is an even/orientation-preserving versor." That is a boundary-hardening concern about admitting odd generators at all, not about a grade-5 transition invariant, and it is out of scope for #19.

What changed (this PR)

The namesake was removed, not left masking an absence:

• Deleted _PSEUDOSCALAR_IDX and every F[31] read (the dead ps history element and CoherenceResidual.pseudoscalar, both structural zeros).
• Renamed the telemetry channel pseudoscalar_floor → autonomy_floor (it was always self.floor, the earned-autonomy ceiling — never a pseudoscalar).
• Bumped the telemetry schema goldtether_coherence_v1 → v2 (the shape changed: key renamed, dead ps dropped).
• Updated the module/class docstrings to state the retirement inline.

Where the integrity-anchor role actually lives (subsumption)

The alignment intent behind §3.3 is real and is already carried, non-vacuously, by three built mechanisms:

1. Versor closure — versor_condition(F') < 1e-6 is enforced on every transition (supervised_blend raises on breach). This is the genuine "the state stayed on the group" gate, checked at ~1e-13 over a 100k-step walk (see project-l10-closure-by-construction).
2. GoldTether harmonized residual + α control (#24) — drift term + distance-to-𝓘_gold + α = Φ(R), the actual alignment-pressure signal, replacing the vacuous orientation check with a metric one that can move.
3. Biography / identity holonomy (ADR-0240 + engine_identity) — order-sensitive trajectory encoding + content-derived identity lineage: the "same continuous life, no confabulated self" anchor. This is where a real topological integrity invariant lives.

Grade-5 objects remain non-vacuous only in the incidence layer (5-blades as conformal geometric objects under meet/join in algebra/cga.py), never as a transition/promotion gate.

Reusable meta-criterion (the session's key output)

"Would this gate ever fire on a value produced by the sanctioned construction path? If no → it is a namesake gate, not an anchor."

This diagnostic is what killed §3.3, and it should be applied to every remaining §-N claim before any implementation effort is spent. Acceptance for #19 is therefore negative: no gate is built; the namesake is gone; the intent is shown to be subsumed.

---

6. Surprise residual operator — 🟢 math + DiscoveryCandidate wiring (#20 closed)

Resolution (2026-07-12): the two operator-math defects are fixed (#26) — exact metric-orthogonal projection and reconciled productivity polarity.

Resolution (2026-07-14, PR #31 / issue #30): high surprise now raises a proposal-only DiscoveryCandidate (trigger=high_surprise) into the existing discovery sink stream. Contemplation consumes that JSONL unchanged. No vault/self-install; physics never imports teaching.

Blueprint spec (Super §3.2)

S(x) = x − proj_{B_union}(x), where proj_B(x) = (x·B)·B⁻¹ is the geometric blade contraction. |S(x)|² measures the epistemic frontier; high surprise (> γ) raises a DiscoveryCandidate in the contemplation loop (self-directed learning).

The defects (as landed)

1. Projection was Euclidean Gram-Schmidt on flat 32-coefficient vectors — metric-blind: it ignored the (+,+,+,+,−) signature and the blade grade structure, so "inside the admissible span" was judged by the wrong geometry. (The 5-vec path already used η.)
2. dual_operator: productive = proc_r <= thr and sur_norm >= 0.0 — the second conjunct is always true, so surprise never gated.
3. Not wired: nothing raises a DiscoveryCandidate.

What changed (this PR)

• Exact metric-orthogonal projection. surprise_residual now solves the metric normal equations G c = r (G_ij = ⟨b_i,b_j⟩, r_i = ⟨b_i,x⟩) via lstsq, under cga_inner (32-vec) / η (5-vec). The residual magnitude is the reversion (metric) norm, and grade-support containment is asserted (fail-closed on leakage).
• Fail-closed on a metric-degenerate span. Typed SurpriseResidualError when rank(G) < rank(B) — a null direction with no reciprocal (e.g. a lone n_o). Refinement over the original "rank(G) < k" spec: mere linear dependence among non-null columns is ADMITTED (lstsq projects onto the actual span), so a merely-redundant live basis ([1, source], which the analogical-transfer harness can produce) is not spuriously refused, the non-degenerate null-pair {n_o, n_∞} is admitted, and only a lone n_o is refused. This is what the geometry — not column-vector algebra — actually requires.
• Reconciled productivity polarity. productive (and transfer_accepted) now both mean productive TRANSFER = low Procrustes ∧ low surprise (a structural match found AND the query inside the admissible span). This corrects §6's earlier "high surprise ∧ low procrustes = productive" phrasing, which conflated transfer with discovery: HIGH surprise is a discovery signal, not a productive transfer, and routes to the (split-out) DiscoveryCandidate path.
• Tests: tests/test_adr_0239_surprise_metric_projection.py — metric-vs-Euclidean divergence (the load-bearing proof), null refusal, null-pair admission, redundant-basis admission, in/out-of-span, grade purity, polarity, determinism.

Wiring landed (PR #31 / issue #30) — acceptance

High surprise routes to a proposal-only DiscoveryCandidate:

• Physics (dual_operator / dual_procrustes_surprise) sets discovery_eligible when sur_norm > γ and transfer is not productive (is_discovery_eligible; default γ = 0.35). No teaching import in core.physics.surprise.
• Teaching factory: candidate_from_surprise_dual / emit_surprise_discovery produce trigger=high_surprise, review_state=unreviewed, domain=math. Opt-in DiscoveryCandidateSink emit (same stream contemplation already consumes). Never vault/store/self-install.
• Tests: tests/test_third_door_surprise_discovery_wiring.py + dual suite.

No remaining #20 follow-up.

---

7. Signature-aware PCA — 🟢 faithful (one untested add-on)

Blueprint spec (Super §2.1 / R&D §2.1)

A = XXᵀ/k; M = ηA; eig(M); sort by Re(λ) desc; real eigenvectors; Minkowski Gram-Schmidt to a pseudo-orthonormal basis on the (4,1) null cone. (R&D §2.1 phrases it as the generalized problem Av = λ η v.)

What landed (dynamic_manifold.py::signature_aware_pca)

Exactly this, minus scipy (uses np.linalg.eig on M = ηA — the Super §2.1 alternative formulation; correct and dependency-free). Plus a null-retention branch that keeps genuine null axes instead of skipping them ("Terra + Grok mastery fix").

The one wrinkle

The null add-on is untested: test_signature_aware_pca_keeps_nulls classifies n_null = 0 in its own scenario and only asserts total == 4 + enum-ness. The branch that gives the fix its name never demonstrably fires. Low severity; add a scenario that actually produces a retained null axis.

---

8. Sound modules not in the blueprints — 🟢

biography.py (delegates to algebra.holonomy.holonomy_encode; refuses empty trajectories — "no confabulated self"; order-sensitive; reconstruct == integrate), temporal_gate.py (a clean typed ADMIT/NOT_YET/REFUSE predicate — no geometry despite the "wisdom as geometry" docstring), and self_authorship.py (proposal-only, SPECULATIVE-stamped, no vault import — test-enforced; catches the Procrustes ValueError and records it) are the healthiest modules because they delegate to real primitives or stay pure instead of reinventing geometry. They are ADR-0240 additions, not specified in either blueprint.

---

9. Trajectory invariants + ADR-DAG — 🟢 Python surfaces (#21)

Landed (2026-07-14): geometry-first Python authorities. Rust Ring-1 port remains optional acceleration, not a second truth.

Trajectory invariants (R&D §2.2 → core/physics/trajectory_invariants.py)

• Relative holonomy H = V_i · reverse(V_{i+1})
• Divergence D = Σ log(1 + ‖H reverse(H) − 1‖) · Δt; bound D < ε_trajectory
• Energy boundary E_exertion ≤ κ · E_sensory
• Zero-fabrication: empty / short / non-closed steps refused
• Tests: tests/test_third_door_trajectory_invariants.py

ADR-DAG conformal embedding (R&D §2.4 → core/adr/validator.py)

• Ψ(M): SHA-256 → 10×3-byte → c_k ∈ [−1,1] → planes 6..15 → simple-bivector project
• Master blade = successive wedge of load-bearing ADR embeddings
• Proposal drift = ‖B_p ∧ A_master‖
• Does not parallel core/abi/geometric_delta_validator.py (that validates GeometricDelta ABI envelopes)
• Tests: tests/test_third_door_adr_dag_embedding.py

---

10. Why "34/34 green" did not catch any of this

The landed suite measures properties that hold by construction, not spec-fidelity:

• Tautologies: residual >= 0, reconstruction_residual >= 0 (norms are non-negative).
• Closure-only: versor_condition(out) < 1e-6 proves the output is a unit versor, not the correct one. §4's blend passes closure at ~1e-16 while being a no-op.
• Trivial regime: every geometry test feeds identity + a single-plane make_rotor_from_angle — the one input class where rotor_power doesn't hit its non-simple-bivector identity fallback.
• One vacuous test: §3's identity→identity Procrustes.

The lesson: closure is necessary, not sufficient. Fidelity tests must feed composed versors and assert behavioral properties (interpolation moves; reconstruction matches; transport lands on target).

---

11. Reproduction

From a checkout of this branch (worktree on PYTHONPATH):

# Fidelity ledger (2 characterizations pass, 2 spec tests xfail):
python -m pytest tests/test_third_door_blueprint_fidelity.py -v -rx

# Blend degeneration on a composed pair (interior alpha == source):
python - <<'PY'
import numpy as np
from algebra.cl41 import geometric_product
from algebra.rotor import make_rotor_from_angle
from core.physics.goldtether import GoldTetherMonitor
def _id():
    v=np.zeros(32); v[0]=1.0; return v
def comp(planes,s):
    v=_id()
    for k,i in enumerate(planes): v=geometric_product(v, make_rotor_from_angle(0.3+0.13*k+0.05*s, bivector_idx=i))
    return v
A,B=comp((6,7,8,10,11),1.0),comp((6,7,8,10,11),2.0)
for a in (0.25,0.5,0.75):
    o=GoldTetherMonitor().supervised_blend(A,B,a)
    print(a, "||o-A|| =", float(np.linalg.norm(o-A)))   # -> 0.0 (no-op)
PY

---

12. Wave-field substrate (ADR-0241) — 🟢 complete on this branch

Status (2026-07-14): ADR-0241 + core_ha deprecation plan + wave_manifold.py

• Slice-2 operator subsumption + Slice-3 multi-pair thin wrap / resonant recall on feat/third-door-wave-field-substrate. Suite tests/test_adr_0241_wave_manifold.py is GREEN. Third-Door operators delegate into wave primitives (no parallel residual/projection path). Off-serving containment preserved.

Spec (ADR-0241) — contract

• Continuous multivector wave-field \psi \in Cl(4,1) (32-coeff) under Cartan/Procrustes, Surprise, GoldTether, Biography.
• Transport pin: multivector fields → sandwich R\psi\widetilde{R}; spinor/chiral → left multiply R\psi. No silent mix.
• Spectral leakage = metric proj onto resonant modes (definite Euclidean energy after metric-exact proj).
• 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).
• Standing-wave registry + resonant_recall (session-local; not vault).
• core_ha standalone atlas: deprecated (no live tree; hygiene pin).

Acceptance (behavioral — GREEN)

Pin	Status
Unitary / sandwich step residual < 10^{-6}	🟢
Spectral leakage zero on-span / positive off-span / metric-exact	🟢
Wave polar recovers known sandwich rotor	🟢
Multi-pair wave_field_conjugacy + Procrustes sequence path	🟢
Chiral conserved under left R; even versor ~0	🟢
Resonant recall picks registered mode; empty refused	🟢
Surprise / GoldTether / biography delegate to wave	🟢
No teaching import in wave_manifold; no core_ha package	🟢
Serve path not wired to wave (containment)	🟢 (by design)

Subsumption map (Slice 2–3)

Operator	Delegation
surprise_residual (32-vec)	WaveManifold.compute_spectral_leakage
conformal_procrustes single non-null pair	wave_analogical_polar
conformal_procrustes multi non-null pairs	wave_field_conjugacy (thin wrap)
Null-point / (5,K) clouds	Kabsch retained (compatibility)
coherence_residual / GoldTether drift	measure_unitary_residual (+ chiral term)
integrate_biography	unitary lock-in + mode register + resonant_recall; encode holonomy_encode

Deferred (explicit, not namesake green)

• Durable holographic memory vault store (CRDT-backed standing-wave spectrum) — session registry only today.
• Rust/MLX acceleration of exp-map / cross-spectral (ADR-0235 later).
• Full ADR-0092 reviewer-service integration (promote remains caller-gated).
• Optional Rust Ring-1 port of trajectory invariants (Python is authority today).

---

13. Tracked follow-ups

Gap	Issue
Real Cartan–Iwasawa via n_o/n∞ — 🟢 done (null-point peel + Spin remainder)	#16 (closed via #29)
Kabsch-conformal Procrustes on point sets — 🟢 done	#17 (closed via #29)
GoldTether gold-set + harmonized residual + α=Φ(R) + bootstrap/prune — 🟢	#18
Grade-5 pseudoscalar preservation gate — ⚪ RETIRED (vacuous; see §5)	#19 (closed)
Surprise: metric projection + productivity polarity + DiscoveryCandidate wiring — 🟢 done	#20 (math #26; wiring #31)
Trajectory invariants + ADR-DAG embedding — 🟢 Python surfaces	#21
Wave-field substrate + operator subsumption (W1–W6) — 🟢 on branch	ADR-0241
core_ha deprecation — 🟢 no live tree + hygiene pin	ADR-0241 / deprecation plan
Durable holographic vault spectrum — deferred	ADR-0241 follow-on

Closing a gap = flip its xfail in tests/test_third_door_blueprint_fidelity.py (or the ADR-0241 suite) to a passing behavioral test and delete the matching characterization lock. That is the definition of "done right" here.