Kill Switches

Seven kill switches engage in AP27. 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 (global numbering).

KS-61 — Internal state space existence

Claim. Lemma 1 derives the internal electroweak state space ℋ_EW ≅ ℂ² from Axiom S’s two-sector structure.

Test. Show that no well-defined internal ε-state space can be constructed from Axiom S. Failure: Lemma 1 fails and AP27 collapses.

Status. LIVE — STRUCTURAL. The construction follows the same pattern as AP15 and AP19.

Recovery. If KS-61 fires, no internal state space can be constructed from Axiom S. The electroweak sector requires an alternative structural ground. Lemma 2, Proposition 1, Proposition 2 all fall (they depend on Lemma 1). AP15 (U(1)_EM) and AP19 (SU(3)) are unaffected.

KS-62 — Gauge group overcounting

Claim. Lemma 2 identifies the structure group of the local basis freedom as U(2). Proposition 1 decomposes U(2) into SU(2) × U(1)_Y.

Test. Show that the local basis freedom generates a group other than U(2) — larger or smaller. Failure: Lemma 2 and Proposition 1 fail.

Status. LIVE — STRUCTURAL. The argument from inner-product preservation gives U(2) as the standard gauge-theory construction.

Recovery. If KS-62 fires, the gauge structure has to be re-derived. Lemma 1 (state space exists) survives. Section 5 (chiral coupling) would need rewriting if the gauge group differs.

KS-63 — Chiral coupling derivation (principal debt)

Claim. Proposition 2 identifies the chiral coupling pattern — left-chiral fields as doublets, right-chiral fields as singlets — through Axiom R’s arrow of time and the CPT identification (AP22). The coupling theorem is STRUCTURAL: physically motivated, consistent with all data, but not yet formally proved.

Test. (a) Demonstrate that the chiral coupling pattern cannot be formally derived from Axiom R, the Lorentz structure, and the CPT identification — in which case the paper derives the gauge group but not the representation content. (b) Independently: if experiment showed parity conservation in the weak interaction (contradicting Wu 1957 and all subsequent data), the chiral pattern itself would fail.

Status. LIVE — STRUCTURAL. Principal open problem of AP27.

Recovery. If KS-63 fires on path (a) — if the chiral coupling cannot be derived from the structural inputs — the paper still derives SU(2) × U(1)_Y as the electroweak gauge group. The doublet/singlet split reverts to empirical input rather than structural prediction. If KS-63 fires on path (b) — experimental parity conservation — the chiral pattern as currently identified is wrong, and a deeper rethinking is required.

KS-64 — SU(2)_weak ≠ SU(2)_spin conflation

Claim. Lemma 1 explicitly constructs ℋ_EW as an internal space distinct from spin space. The SU(2) derived in AP27 acts on ℋ_EW and is the weak isospin group, separate from the Lorentz spin SU(2) of AP11.

Test. Demonstrate that the derived SU(2) on ℋ_EW is identical to the Lorentz spin SU(2) of AP11. Failure: the paper has derived the wrong group.

Status. LIVE — STRUCTURAL. Lemma 1 explicitly distinguishes the internal sector-relationship space from spin space.

Recovery. If KS-64 fires, the weak isospin group is identical to the spin group, and the standard separation of internal and spacetime symmetries (Coleman–Mandula) is violated within the corpus. A deep rework would be required.

KS-65 — Hypercharge assignments

Claim. Proposition 1 identifies U(1)_Y as hypercharge but does not derive specific hypercharge values for each fermion species.

Test. Derive the specific Y values for each fermion species from {S, B, R, C} and the AP27 structure. Until done, KS-65 stands.

Status. OPEN DEBT. Named item; not addressed by AP27.

Recovery. The closure of KS-65 requires the detailed representation content of ε’s internal structure plus anomaly cancellation. This is held for the matter sector (Notebook V) and subsequent NB IV chapters.

KS-66 — Generations

Claim. The Standard Model has three generations of fermions. AP27 does not derive why.

Test. Derive the three-generation structure from {S, B, R, C}. Until done, KS-66 stands.

Status. OPEN DEBT. Named item; not addressed by AP27.

Recovery. Held for the matter sector (Notebook V). AP27 derives the gauge structure; the matter content that fills representations of that structure is a separate question.

KS-67 — AP15/AP27 EWSB consistency

Claim. AP15’s U(1)_EM and AP27’s U(1)_Y are structurally distinct (post-breaking remnant vs pre-breaking hypercharge). Their relationship requires electroweak symmetry breaking: Q = T³ + Y/2.

Test. Derive the EWSB mechanism that takes SU(2)_L × U(1)_Y to U(1)_EM from {S, B, R, C} and the AP27 structure. Until done, KS-67 stands.

Status. OPEN DEBT. Held for AP16 (Electroweak Break).

Recovery. KS-67 is structurally addressed once AP16 derives the EWSB mechanism. AP27’s claim that U(1)_Y ≠ U(1)_EM is consistent with the Standard Model’s structure; the structural ground for the breaking is the work of AP16.

Why these seven and how they relate

The seven kill switches partition cleanly. KS-61 and KS-62 carry Lemmas 1 and 2 — the existence and structure of the electroweak gauge connection. If either fires, the entire derivation falls. KS-64 carries the distinctness of weak SU(2) from spin SU(2) — a corpus-internal consistency check. KS-63 carries the chiral coupling pattern — the paper’s principal debt. KS-65, KS-66, KS-67 are OPEN DEBTS — named items the paper does not attempt and that belong to subsequent chapters (AP16 for KS-67, the matter sector for KS-65 and KS-66). Smaller claims throughout the paper — the “three notes of a chord” framing, the “harmonics” title, the specific Lie-algebra notation choices — are illustrative rather than load-bearing. If any illustration turned out poorly chosen, the structural results would still stand.