Conditionality Footer

Dependencies

AP20 (the canonical axioms: formal statement section 3.3; completeness and minimality stated at section 4, fenced at KS-P.1/KS-P.2) — the floor of section 1.

The Lorentzian signature (AP10 section 4, fenced at KS-D.4) — Lorentz invariance in section 4.1; general covariance in section 8.1; special relativity as a theorem.

AP20 (EH and QRA proven) — EH underwrites the entire embedding into the smooth manifold; QRA underwrites the second-order curvature constraint in sections 4 and 8.

AP10 (The Dimension) — N = 3 derived from the four independent axioms. CLOSED contingent on AP10’s KS-D.3 (one axiom, one face / dimension-minimal embedding) remaining unfired. If KS-D.3 fires, KS-I.6 reopens.

AP06 Theorem 3.1 (ε > 0 whenever c is finite) — the leakage premise for the Hawking-temperature derivation in section 6.2.

The Lock, Edition 04 (ε = electron) — the identification underwriting the coefficient identification in section 5 and the electron-at-horizon result in section 6.3.

Lovelock 1971 / Lovelock 1972 (external mathematical theorems) — the tensor-uniqueness result in 3+1 dimensions invoked in section 8.2.

Dependents

Predictions Ø — the unconditional Einstein’s field equations and the cosmological constant existence prediction feed the 420 Code’s cosmological programme.

Dissolutions Ø — the philosophical-register chapter on gravity inherits the condensate framing, the eye topology, and the Newton-Einstein relationship.

Resolutions Ø — the philosophical-register chapter on pre-state inaccessibility inherits the κ-circularity disclosure of section 5.

AP09 (The Break — QM) — the Mode 0 / Mode 1 distinction at section 2.1 reads against AP09’s quantum-mechanics derivation.

AP24 (The Residual) — m_e identification is upstream of AP08; AP24 also inherits the horizon-leakage result of section 6.

Kill switches closed by this paper

KS-I.6. N = 3. CLOSED by AP10 — contingent on AP10’s KS-D.3 (one axiom, one face / dimension-minimal embedding) remaining unfired. With N = 3 derived in AP10 under that contingency, the dimensional precondition for Lovelock’s 3+1 uniqueness is met. Einstein’s field equations are an unconditional theorem of the record algebra in the dimensional sense — unconditional relative to the dimensional precondition, with the standing contingency on AP10’s KS-D.3 named explicitly throughout.

Kill switches that remain live

KS-I.1 (Axiom-to-Poisson chain, LIVE — HARD). See section 9.

KS-I.2 (Lovelock chain, LIVE — HARD). See section 9.

KS-I.3 (Coefficient identification, LIVE — HARD). See section 9.

KS-I.4 (κ inaccessibility, LIVE — HARD). See section 9.

KS-I.5 (Curvature-record identity, LIVE — EMPIRICAL). See section 9.

KS-I.7 (Cosmological constant value, LIVE — EMPIRICAL). See section 9.

KS-I.8 (R → conservation bridge, LIVE — HARD). See section 9.

Structural debts owed

Two structural-class items are tied to AP08’s argument as the 420 Code debts. Named here so the structural exposure is visible at the door.

The Lock identification (ε = electron) — load-bearing for sections 3.2, 5, and 6.3. Tracked by KS-I.3.

The R → ∇^μ T_μν = 0 bridge — Constraint 3 of section 8.1 acknowledged as a bridge step, not a completed derivation. Tracked by KS-I.8.

External mathematical dependencies

Separately from the 420 Code structural debts, AP08 invokes the following external mathematical results as established theorems. Listed for transparency; tracked at structural-test level.

Lovelock 1971 / Lovelock 1972 — tensor uniqueness in general N and 3+1 specifically. Tracked by KS-I.2.

Potential theory in the Helmholtz-family identification — the most general second-order linear scalar operator form. Tracked by KS-I.1.

The Schwarzschild solution and Hawking 1975 — the standard surface-gravity formula and Hawking temperature. Used in section 6 as recovery, not derivation.

Items held open without claiming debt status

The cosmological constant value (KS-I.7). Existence predicted by Lovelock; value is downstream cosmological work.

Constraint 2 of section 4 (linearity in the weak-field limit). Motivated by Axiom R but best understood as a consistency requirement between sections 4 and 8 rather than an independent derivation from R alone.