Kill Switches

Each kill switch in Claim / Test / Status / Recovery form. KS-25, KS-26, KS-27 are new; KS-21 is affected and untriggered. Identifiers per the Master Kill Switch Registry.

KS-25 — One-loop amplitude and coefficient finiteness

Claim. The one-loop correction depends on bounded amplitude contributions a(k) for virtual records and a finite dimensionless coefficient γ in δG/G = γℓ_P²/L².

Test. Compute the explicit monoid matrix elements at one loop. If they are ill-defined, unbounded, or produce a divergent γ, the formula fails.

Status. LIVE — EMPIRICAL. The dimensional-uniqueness theorem (§3.4) fixes the form independently of the matrix elements; bounded matrix elements of unitary evolution bound a(k). The exact coefficient requires Gap 1.

Recovery. If γ = 0, the correction vanishes at one loop — a smaller correction, which strengthens rather than invalidates the architecture. If γ diverges, see KS-26.

KS-26 — Monoid combinatorics at one loop

Claim. The dimensionless constant γ depends on the number of distinct ways a virtual record at cell k couples to the geometry at neighbouring cells, and is finite (of order unity).

Test. Construct the explicit monoid coupling structure and compute γ. If γ diverges with system size, finiteness fails.

Status. LIVE — HARD. The scaling argument gives γ ~ O(1), but rigorous computation remains open. The principal remaining gap.

Recovery. If γ diverges, the one-loop finiteness claim fails and the correction formula must be re-derived. The path-sum architecture (§2) survives; the finiteness conclusion does not.

KS-27 — Higher-loop finiteness

Claim. The one-loop scaling extends structurally to higher loop orders within the same monoid/Hilbert construction — each additional loop adds one factor of ℓ_P²/L² and generates no new operator type.

Test. Perform a two-loop calculation. If it produces a divergence or a new operator type (a higher-derivative counterterm), the all-orders claim is falsified. Here is the weapon: find the two-loop divergence.

Status. LIVE — EMPIRICAL. Each higher loop is conjectured to add one ℓ_P²/L² factor and the geometric construction (§4.5) is argued to exclude new operators, but the combinatorics grow at each order and the formal inheritance is outstanding (D7).

Recovery. If KS-27 fires, the one-loop result stands but the all-orders extension fails. The corpus is unaffected beyond AP14’s all-orders claim.

KS-21 — Commutation corrections at the Planck scale

Claim. The canonical commutator [x̂, p̂] = iℏ (AP12 §4.2) may receive corrections of order γℓ_P²/L².

Test. Measure or derive the commutator at scales approaching ℓ_P. A deviation from iℏ at the predicted order tests the claim.

Status. LIVE — EMPIRICAL. This paper confirms corrections are of order unity at L ~ ℓ_P (δG/G ~ γ). Affected but untriggered.

Recovery. If the commutator correction is shown to differ in form from γℓ_P²/L², the link between the one-loop correction and the uncertainty principle requires revision; the G_eff result itself is independent.