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.
core/physics/{goldtether,dynamic_manifold,surprise,biography,temporal_gate,self_authorship}.py	The landed code.
tests/test_adr_023{8,9}_*.py, test_adr_0240_*.py	The landed tests (34, all green — see §7 for why green ≠ faithful).
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	🔴 replaced — raises ~45%	#16
3	Conformal Procrustes	Super §3.1	🔴 replaced — degenerate	#17
4	GoldTether residual + α law	Super §2.3, R&D §2.3/§5	🔴 half-missing	#18
5	Grade-5 pseudoscalar invariant	Super §3.3	🔴 missing (namesake)	#19
6	Surprise residual operator	Super §3.2	🟡 partial / rewired	#20
7	Trajectory invariants + zero-fabrication	R&D §2.2	⚫ absent	#21
8	ADR-DAG conformal embedding	R&D §2.4	⚫ absent	#21
—	Biography holonomy	(ADR-0240; not in blueprints)	🟢 sound	—
—	Temporal admissibility gate	(ADR-0240; not in blueprints)	🟢 sound	—
—	Self-authorship miner	(ADR-0240; not in blueprints)	🟢 sound (proposal-only)	—

---

2. Cartan–Iwasawa decomposition — 🔴 replaced (#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)

No action on n_o/n∞. It grade-projects B = ⟨V⟩₂, branches on whether B² is scalar (simple bivector) and its sign, and in the general (non-simple) case fabricates:

R[0] = D[0] = |V[0]|**0.5 ;  R = R + ½B ;  D = D + ½B ;  T = normalize(reverse(R·D)·V)

R and D are seeded identically — this is not a K/A/N decomposition. The function then guards each factor with versor_condition < 1e-6 and raises ValueError when the fabricated R fails to close.

The gap (empirical)

• On composed conformal versors (products of ≥3 plane-rotations) it raises factor R not closed 84/200 (3 planes), 91/200 (4 planes) ≈ 45%.
• When it does not raise, reconstruction is faithful (‖R·T·D − V‖ ~ 1e-16) — so the closure guard makes it fail-loud, not silently-wrong. But it cannot factor ~half of realistic states.
• The only test (test_cartan_iwasawa_extract_closed) uses a single simple rotor (angle 0.7, plane e6), where the simple branch sets R = ⟨V⟩₀+⟨V⟩₂, T=D=1 and trivially reconstructs; it also asserts only reconstruction_residual >= 0.0 (a tautology).

Done right

Implement the §2.2 null-point algorithm. Prereq: n_o, n∞, and the e_o∧e∞ blade accessors in algebra/ (add if absent). Acceptance: no raise on any conformal motion; ‖R·T·D − V‖ < 1e-6; flips test_cartan_iwasawa_should_reconstruct_composed_motion xfail→pass.

---

3. Conformal Procrustes — 🔴 replaced (#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)

• 32-vector / multivector-pair path (used by evals/analogical_transfer/harness.py and self_authorship.py): _procrustes_multivector_pairs computes word_transition_rotor(s,t) = normalize(t·rev(s)) per pair and averages via repeated rotor_power — a transition rotor, not a Kabsch/SVD point-set fit.
• 5×K path: partial Kabsch on the first 3 Euclidean coords only (Pc = P[:3]), leaving conformal coords untransformed.

The gap (empirical)

• Composed with the supervised-blend transport, the 32-vec path degenerates (see §4).
• test_conformal_procrustes_multivector_low_residual is vacuous: tgt = versor_apply(R, identity) = R·rev(R) = identity, so ‖tgt − identity‖ = 0.0 exactly → src==tgt==identity. It "verifies" identity→identity.
• test_conformal_procrustes_5d_cloud asserts only residual >= 0.0 (a norm — always true).

Done right

Implement §3.1 on full null-vector point sets (all 5 conformal coords), signature-aware SVD, centroid-derived T/D, margin verification. Acceptance: for F_B = versor_apply(W, F_A) with a non-trivial W on a composed state, recover V with ‖versor_apply(V, F_A) − F_B‖ < ε.

---

4. GoldTether residual + α control law — 🔴 half-missing (#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)

• coherence_residual(F) = max(versor_unit_residual(F), versor_unit_residual(reverse(F))) — drift term only. No gold_invariants field exists; the geometric distance term and scale harmonization are absent. (measure() has an optional reference-distance term but the residual()/update() path the monitor uses does not.)
• Autonomy is a monotonic per-step accumulator (autonomy += 0.01, capped by a floor that rises +0.02 only on epistemic_elevation) — not Φ(R). supervised_blend(source, target, alpha) takes an external α, not one derived from the residual.
• No bootstrapping / 𝓘_gold / promotion / decay.

The gap

The entire §2.3 harmonization fix and the §2.3/§5 gold-set machinery — the parts that give GoldTether its meaning — are not in the code path the monitor runs. The landed "earned autonomy" model is arguably a safer HITL story (autonomy must be earned slowly; serve never autonomous) but it is a different mechanism wearing the blueprint's names.

Done right

Add 𝓘_gold (seeded n_o, n∞, 1), the two-term harmonized residual, and α = Φ(R; R_floor, R_critical) driving the Cartan–Iwasawa slerp. Preserve fail-closed + serve-never-autonomous. Document how the earned-autonomy ramp relates to (or is replaced by) Φ(R). Depends on #16.

---

5. Grade-5 pseudoscalar invariant — 🔴 missing / namesake (#19)

Blueprint spec (Super §3.3)

The pseudoscalar I = 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(I) is blocked at the boundary. Called "the ultimate mathematical anchor for alignment."

What landed

goldtether.py uses _PSEUDOSCALAR_IDX = 31 to read F[31] into telemetry/history, and calls the autonomy threshold a "pseudoscalar_floor." There is no gate enforcing ⟨F'·F̃'⟩₅ preservation. The namesake actively masks the absence.

Done right

A pure predicate pseudoscalar_preserved(F, F') -> bool (sign + magnitude of the grade-5 part within tolerance), wired as a fail-closed gate on transition / promotion / self-authorship, with a typed disclosure. Rename pseudoscalar_floor → autonomy_floor. Acceptance: sign-flipping transition refused; valid transition admitted.

---

6. Surprise residual operator — 🟡 partial / rewired (#20)

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) bypasses rejection and raises a DiscoveryCandidate in the contemplation loop (self-directed learning).

What landed (surprise.py)

1. Projection is linear-algebra projection onto basis columns (Minkowski for 5-vec, Euclidean Gram-Schmidt for 32-vec) — not blade contraction; the surprise-bivector grade structure isn't preserved.
2. dual_operator: productive = proc_r <= thr and sur_norm >= 0.0 — the second conjunct is always true, so surprise plays no role. dual_procrustes_surprise conversely requires sur_norm < 1e-4 (accept only when unsurprising) — backwards from "productive surprise."
3. Not wired: nothing outside core/physics/ + tests imports it; no DiscoveryCandidate path.

Done right

Blade-contraction projection with grade assertions; a productivity gate that genuinely depends on surprise magnitude (high surprise ∧ low procrustes residual); reconcile the two functions' polarity; raise a DiscoveryCandidate into the contemplation loop behind the existing proposal-only / no-self-install discipline.

---

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. Absent whole proposals — ⚫ (#21)

• Trajectory invariants + zero-fabrication (R&D §2.2 → core-rs/src/sensorimotor.rs): relative holonomy H(t)=V₁Ṽ₂, divergence integral D < ε_trajectory, Hamiltonian energy boundary E_exertion ≤ κ·E_sensory. Not landed. Gated by the Zig/Rust substrate doctrine (Ring-1 only).
• ADR-DAG conformal embedding (R&D §2.4 → core/adr/validator.py): Ψ(M) = SHA-256 → 10 bivector coeffs → simple-bivector projection → master-blade wedge → drift check. Not landed. Cross-check core/abi/geometric_delta_validator.py before adding a parallel validator.

---

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. Tracked follow-ups

Gap	Issue
Real Cartan–Iwasawa via n_o/n∞	#16
Kabsch-conformal Procrustes on point sets	#17
GoldTether gold-set + harmonized residual + α=Φ(R)	#18
Grade-5 pseudoscalar preservation gate	#19
Surprise: blade contraction + wiring + fix conjunct	#20
Absent proposals: sensorimotor + ADR-DAG	#21

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