Kill Switches

Four kill switches engage in AP15. One existing corpus kill switch (KS-4) is affected. Each is testable. Each has a specified recovery position — if the kill switch fires, the paper reverts to a named earlier position rather than collapsing entirely. Identifiers follow the Master Kill Switch Registry.

KS-28 — Phase-group uniqueness (U(1))

Claim. The argument derives U(1) as the gauge group from the phase freedom of ℋ. No larger group acts on the phase of a single complex amplitude.

Test. Demonstrate that the complex Hilbert space admits a gauge symmetry larger than U(1) from the phase alone (before considering spin or colour). Failure: the derivation is overconstrained.

Status. CLOSED — MATHEMATICAL. The symmetry of a circle is U(1).

Recovery. CLOSED. No recovery needed: the symmetry group of a circle is U(1) as a mathematical fact.

KS-29 — Maxwell uniqueness

Claim. The Maxwell action S = −(1/4) ∫ FμνF^{μν} is the unique dimension-4 gauge-invariant local action (up to total derivatives) consistent with U(1) + conservation + D = 4, with the action principle derived from the path sum (Theorem 3).

Test. Demonstrate another dimension-4 gauge-invariant local action with these properties that produces different field equations. Failure: the derivation is ambiguous.

Status. CLOSED — MATHEMATICAL. Standard classification of gauge-invariant operators by mass dimension.

Recovery. CLOSED. The Maxwell action is uniquely selected at leading derivative order by the mathematical classification.

KS-30 — Phase globality

Claim. The derivation assumes the pre-state’s phase is globally coherent. The pre-state is the 1:1 — it has no internal structure across which the phase could vary.

Test. Demonstrate that the pre-state can have phase discontinuities — that the white space can be internally divided. Failure: the connection is not forced to exist by the global-phase argument.

Status. LIVE — STRUCTURAL. The pre-state is the 1:1. Division of the pre-state would be a second break, violating Axiom B (one element, minimum).

Recovery. If KS-30 fires, the global-phase-on-local-manifold argument of sections 2–3 falls. The connection would have to be derived by an alternative route (perhaps by the standard gauge promotion argument). Theorems 1, 5 remain (they do not depend on global phase coherence). Theorem 4 (Phase Coherence Partition) falls because its premise (pre-state pure, S = 0) requires global coherence.

KS-31 — Entanglement–connection identification

Claim. Section 5 identifies the gauge connection and entanglement as two expressions of pre-state unity. They are not two separate structures; they are two columns in one ledger. The structural reading is: the purity of the pre-state (S = 0) entails a conservation relation between the two columns. The formal conserved-balance theorem — exhibiting a single quantity whose connection-curvature and entanglement-entropy components are commensurable and sum to a constant — is held open as the path to closure for this claim.

Test. Theorem 4 (Phase Coherence Partition) proves the identification: the pre-state’s phase coherence partitions exhaustively into connection curvature (field) and entanglement (correlation), with ε as the sole transfer mechanism. Failure: identify a phase-coherent structure that is neither connection curvature nor entanglement.

Status. LIVE — STRUCTURAL. Theorem 4 (Phase Coherence Partition) establishes the exhaustive bivalent partition and identifies ε as sole transfer mechanism, but does not exhibit a conserved quantity with connection-curvature (a field action) and entanglement (a von Neumann entropy) shown to be commensurable and to sum to a constant. The partition is a structural reading of strong correspondence; the conserved-balance theorem the ledger language asserts is not exhibited. Gap D: structurally addressed, formal balance theorem held open.

Recovery. If KS-31 fires — if a phase-coherent structure can be exhibited that is neither connection curvature nor entanglement, or if connection-curvature and entanglement-entropy cannot be made commensurable in a conserved-balance form — the structural reading remains (the partition is exhaustive by Axiom R’s bivalence; ε is the transfer mechanism between field and correlation accounts), but the ledger framing is downgraded from a balance theorem to a structural metaphor. The derivations of Theorems 1, 2, 3, 5 are independent of Theorem 4 and survive. The path to closure: exhibit a single quantity — connection-curvature action plus an entanglement-entropy measure on the same footing — that is conserved under the dynamics induced by ε-record events.

KS-4 — α ≈ 1/137 (existing corpus kill switch, affected)

Claim. AP15 identifies the fine-structure constant α_em ≈ 1/137 as the coupling strength of ε to the connection (section 4.3). AP15 derives that this coupling exists; it does not derive the numerical value.

Test. Derive the numerical value of α_em from {S, B, R, C} alone. Failure of the broader corpus to do so leaves KS-4 LIVE.

Status. LIVE — HARD. Carried forward to AP24 (the six-faces formalisation of ε’s multi-projection structure and the leakage-tolerance reframe on α) and AP28 (channel-counting derivation of G).

Recovery. If KS-4 is closed by AP24/AP28, no recovery needed (the result becomes derived). If KS-4 remains permanently LIVE, AP15’s derivation of the structure of electromagnetism stands; only the numerical coupling strength remains empirical input. The structural results of AP15 are independent of α_em’s value.

Why these four and not more

The four kill switches cover the load-bearing claims of AP15. KS-28 and KS-29 close mathematically (the symmetry of a circle is U(1); the Maxwell action is uniquely selected). KS-30 carries the structural assumption that the pre-state is undivided; this is the one remaining live falsification surface for the global-phase argument. KS-31 is held LIVE — STRUCTURAL on Theorem 4 (the partition is a structural reading; the conserved-balance theorem the ledger framing asserts is held open). KS-4 is the existing corpus kill switch affected by AP15’s identification of α_em as the coupling strength. Smaller claims throughout the paper — the specific Lovelock-type uniqueness language, the doorknob illustration, the “debit/credit/receipt” ledger metaphor, the “dictionary” framing of the connection — are illustrative rather than load-bearing. If any single illustration turned out to be poorly chosen, the paper would still stand. The kill switches engage the load-bearing structural claims, not the illustrative material.