Kill Switches

AP03 is falsified if any of the following are demonstrated. Each kill switch targets a specific claim. If any claim falls, the dependent claims fall with it, but independent claims survive.

Here is how to break it. The argument does not hide. It shows you exactly where to strike.

KS-R.1 — Independent variability of c and G

Claim. The two fundamental speed limits c and G are not independent. Both are determined by the single breaking amplitude ε. Originally published as conjecture E-G; upgraded to a theorem by AP20’s forcing proof that Axiom B admits exactly one free parameter.

Test. Demonstrate that the dimensionless gravitational coupling α_G(m) at a fixed reference mass varies independently of the electromagnetic fine-structure constant α — that α_G and α can be tuned independently with no common ancestor parameter. Quasar absorption spectra constrain cosmological variation of α; lunar laser ranging and Big Bang nucleosynthesis constrain α_G. AP03 predicts these variations are correlated. Uncorrelated variation falsifies the conjugacy.

Status. LIVE — EMPIRICAL.

Recovery. If KS-R.1 fires, both the conjugacy claim and AP20’s forcing proof on Axiom B are in conflict with measurement. Either the forcing proof is wrong (Axiom B admits more than one free parameter) or AP03’s identification of the parameter with ε is wrong (the parameter is something else). The 420 Code retreats by reopening Axiom B’s formal status and acknowledging that the constants are independent within the architecture as currently stated. Section 4 collapses; sections 5 and 6 inherit the collapse.

KS-R.2 — Non-binary origin

Claim. The symmetry-breaking event produces exactly two fundamental sectors because the symmetry group of the pre-state is ℤ₂, whose representation theory admits exactly two irreducible representations. Mode 1 carries propagation (c); Mode 0 carries resistance (G). Claim E2.

Test. Demonstrate that the early universe requires more than two fundamental mode sectors at the moment of symmetry breaking — not merely more than two particle species, but more than two irreducible sectors of the symmetry decomposition. Detection of a third fundamental sector that is neither gravitationally coupled (Mode 0) nor electromagnetically coupled (Mode 1) triggers this kill switch.

Status. LIVE — EMPIRICAL.

Recovery. If KS-R.2 fires, the ℤ₂ postulate (E0) fails and the pre-state must have a richer symmetry. The structural claim that exactly two speed limits emerge collapses. The 420 Code retreats by upgrading the pre-state symmetry to whatever the data forces — ℤ₃, U(1), SU(2), or richer — and re-deriving the sector content under the new representation theory. Sections 3 and 8 are reworked; section 4 retains the structure but expands to N sectors.

KS-R.3 — Dark ratio independence

Claim. The dark-to-visible energy density ratio (∼95:5) is determined by ε. Small ε implies most content remains in Mode 0. Conjecture E5.

Test. Demonstrate that the dark-to-visible energy density ratio is set by a mechanism entirely independent of the c/G relationship and of the breaking amplitude ε — for example, by a hidden gauge sector with its own coupling structure unrelated to the ℤ₂ break.

Status. LIVE — EMPIRICAL.

Recovery. If KS-R.3 fires, the qualitative link between ε and the dark-sector partition collapses. Conjecture E5 is falsified. The 420 Code retreats by treating the dark-sector partition as a separate open problem independent of AP03, possibly involving additional fields or sectors not captured by the minimal ℤ₂ architecture. Section 6 is removed; sections 1–5 and 7–8 are unaffected.

KS-R.4 — Horizon inequivalence

Claim. The cosmological origin and the black hole event horizon are structurally identical — both are the marginal surface ε = 0 of the ℤ₂ break, traversed in opposite temporal directions. Claim E-Identity. Originally LIVE — HARD; inherits the structural-forcing upgrade from KS-R.1.

Test. Demonstrate that the singularity theorems have fundamentally different character for cosmological versus black-hole singularities in a way incompatible with the ε = 0 interpretation — for example, by showing that the cosmological singularity has a structural property (handedness, dimension, residual entropy) that the black hole singularity provably cannot have within the AP03 architecture.

Status. LIVE — HARD.

Recovery. If KS-R.4 fires, the structural identification of the two surfaces fails. Section 5 collapses. The 420 Code retreats to the position that cosmological and black-hole boundaries are distinct structural surfaces — each marginal in its own way but not the same surface. AP03’s claim that the beginning and the end are the same door is withdrawn. Sections 1–4, 6–8 are unaffected.

KS-R.5 — Planck scale mismatch

Claim. The propagation speed c emerges from the broken vacuum as c = √(β/α) (Result A.1, equation 7.8), and the Planck mass scales as mₚ ∝ √ε (equation 4.7). The Planck scale is the scale of the break itself.

Test. Demonstrate that the propagation speed of perturbations on the broken vacuum is parametrically different from √(β/α), or that the Planck-scale onset is shown incompatible with mₚ ∝ √ε. The empirical handles are precision tests of Lorentz invariance at high energy (deviation from c at the Planck scale) and high-energy cosmic-ray observations of the effective UV cutoff.

Status. LIVE — EMPIRICAL.

Recovery. If KS-R.5 fires, the action principle of section 7 fails. c is not derived as √(β/α); the kinetic term needs revision, or the broken-phase analysis is incomplete. Result A.1 collapses; the conjugacy claims that depend on it weaken to qualitative form. Sections 1–3, 5–6, 8 stand.

KS-R.6 — Dimensionless scaling violation

Claim. The dimensionless conjugacy holds: at fixed reference mass m and fixed cutoff Λ, the product α · α_G(m) is independent of ε, and the ratio α/α_G(m) scales as ε² (equations 4.4 and 4.5). The dimensionful gravitational hierarchy ke²/(G·m_e²) ≈ 10⁴²–10⁴³ is the SI illustration of the same fact; the unit-independent statement is the dimensionless one. Originally registered with the dimensionful form c/G ∝ ε² in the AP03 conjecture; the dimensionless statement is the corrected scaling actually produced by the derivation.

Test. Demonstrate that the product α · α_G(m) varies measurably with ε — either across cosmological epochs (where α may vary, per the AP06 identification of ε with α) or at fixed-mass laboratory comparisons — or that the hierarchy α/α_G(electron) is not consistent with ε² scaling once the (Λ/m_e)² factor is fixed via AP24. The empirical handles are precision tests of cosmological variation of the electromagnetic fine-structure constant (quasar absorption spectra) and laboratory tests of the gravitational fine-structure constant at fixed reference masses (lunar laser ranging, Big Bang nucleosynthesis). Scope: the ε² scaling tested here is the substrate-level statement at fixed κ and Λ (κ, Λ free, debt D-AP03.1); the physical response of the hierarchy to a measured variation of α is carried by AP28’s canonical form (G ∝ ε²¹, hierarchy ∝ ε⁻²⁰) and is tested there.

Status. LIVE — HARD. Superseded as the statement of G’s value by AP28 (registry status: SUPERSEDED AS VALUE — see AP28); the switch’s live content is the substrate-level statement at fixed κ and Λ.

Recovery. If KS-R.6 fires, the form of G’s dependence on ε derived in section 7 is wrong. The 420 Code retreats by treating G’s specific dependence on ε as governed by a more complex relationship — possibly involving additional structural quantities beyond ε. Section 4.2 and section 7.5 are reworked; section 4.5 (mₚ ∝ √ε) inherits the change. Section 5 may survive in modified form; section 6 unaffected.

Why these six and not more

The six kill switches above cover the load-bearing claims of the paper as registered in the master kill switch register. Each closure would force a different kind of retreat.

KS-R.1 closes the conjugacy of c and G — the central structural claim of the paper. KS-R.2 closes the binary decomposition by undermining ℤ₂. KS-R.3 closes the dark-sector connection. KS-R.4 closes the origin-horizon identity. KS-R.5 closes the action-principle derivation of c. KS-R.6 closes the specific dimensionless scaling.

Two structural claims that some readings would expect to carry their own formal kill switch — the ℤ₂ minimality postulate (E0) and the Hawking-radiation structural interpretation (E-Hawking) — are absorbed into the kill switches above. E0’s minimality is tested by KS-R.2: any falsification of the binary decomposition (more than two fundamental sectors) is also a falsification of ℤ₂ as the minimal symmetry, since a richer pre-state symmetry would produce more than two irreducible representations. E-Hawking’s structural interpretation is tested by KS-R.4: the origin-horizon identity is what makes Hawking radiation a structural consequence of global asymmetry; if KS-R.4 fires (cosmological origin and black-hole horizon are not the same marginal surface), the structural account of Hawking radiation falls with it. Both claims are thus held to formal kill-switch standard without adding entries to the master register.

Smaller claims throughout the paper — the specific values of α_G(e), the Schwarzschild interpretation as Mode 0 dominance — are illustrative rather than load-bearing. If they turn out to be poor illustrations, the paper still stands. If KS-R.1 through KS-R.6 hold, the structural argument of AP03 holds.