Kill Switches

AP05 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-B.0 — Universal: independent specifications

Claim. The axiom 1:1 + 1×ε @ AS is a structural generator: the expanding-side initial conditions are derivable from the collapsing-side terminal conditions through the junction at Σ. The two readings are two descriptions of one structure. They do not require independent, unrelated specifications.

Test. Demonstrate that the expanding universe requires initial conditions that are not derivable from the terminal conditions of a collapsing description — that the two readings need separate, unrelated specifications. The operational handle becomes available once Open Problem B-JP is solved and a derivation rule from collapsing-side terminal data to expanding-side initial data has been exhibited. Until then, KS-B.0 functions as a theoretical consistency check on the structural-generator claim of the axiom.

Status. LIVE — HARD (pending B-JP; migrates to LIVE — EMPIRICAL once B-JP is solved).

Recovery. If KS-B.0 fires, the axiom fails as a generator. It is no longer a single structure with two readings; it is a coincidence with two parts. The 420 Code retreats by reopening the axiom’s structural-generator claim and acknowledging that the two cosmological patches are independently posed. The entire architecture inherits the demotion: Claim B1 (Scope) collapses; the chain still runs but its premise is no longer structural in the strong sense; AP04’s cosmological identity becomes a coincidence rather than a structural fact. Targets: the axiom, Claim B1, the entire architecture.

KS-B.1 — Bounce superior

Claim. The cosmological identity is best described by the junction formulation of section 3 — boundary data on Σ, not dynamical evolution through it. The post-expansion perturbation spectrum is determined by [K] on Σ, not by smooth continuation across t₀.

Test. Demonstrate that the CMB power spectrum is best explained by smooth dynamical evolution through a bounce — continuous correlations across the transition, memory of pre-bounce perturbations carried dynamically, parameter fits that prefer the bounce interpretation over the junction interpretation. Empirical handles: detailed shape of the CMB temperature and polarisation spectra, structure of correlations on super-horizon scales, signatures of pre-bounce phase memory.

Status. LIVE — EMPIRICAL.

Recovery. If KS-B.1 fires, the junction formulation is falsified. The cosmological identity may survive under the bounce interpretation — AP04’s global pullback may still hold dynamically rather than as boundary data — but AP05 section 3’s reformulation does not. The 420 Code retreats by re-coupling the cosmological identity to dynamical bounce machinery and acknowledging that the junction reformulation, however structurally elegant, was empirically wrong. Targets: Conditions J1, J2, section 3 in its entirety.

KS-B.2 — Spectrum mismatch (staged)

Claim. A completed junction solution (Open Problem B-JP), together with a derived mapping from the boundary mismatch [K] on Σ to the post-expansion curvature perturbation spectrum P_ℛ(k), predicts a spectrum consistent with observations: near scale invariance, measured tilt n_s ≈ 0.965, no significant running, tensor-to-scalar ratio within bounds.

Test. Demonstrate that the predicted spectrum is inconsistent with observations. The test becomes operational once two things are in place: a solution to Open Problem B-JP, and a derived mapping from boundary data on Σ to the perturbation spectrum P_ℛ(k). Until both are in place, KS-B.2 is staged — a future operational kill switch.

Status. LIVE — STAGED (pending B-JP and the spectrum-mapping derivation).

Recovery. If KS-B.2 fires, the junction formulation makes wrong predictions about the post-expansion spectrum. The 420 Code retreats by reformulating Condition J2 — the extrinsic curvature mismatch on Σ cannot be the source of the observed spectrum in the way the staged mapping would have it. The structural identity (J1) may survive in a degraded form; the empirical content of J2 fails. Targets: Condition J2, Open Problem B-JP, the empirical mapping.

KS-B.3 — No junction solution

Claim. The Einstein-Cartan-Sciama-Kibble field equations on the Kantowski-Sachs interior admit a completion across Σ with [γ_ab] = 0 and controlled [K_ab] = (ε/ℓ_Σ) · h_ab.

Test. Demonstrate that no such completion exists — that the boundary-value problem has no solution with the required conditions, or that the only solutions have uncontrolled (divergent or otherwise pathological) [K]. The test is sharp because it is mathematical: existence or non-existence of solutions to a well-posed boundary-value problem is decidable.

Status. LIVE — HARD.

Recovery. If KS-B.3 fires, the junction formulation does not exist as a mathematical object. The structural identity introduced in AP04 — the geometric relation between collapsing and expanding descriptions — cannot be carried by the junction formulation. The cosmological component of AP05 fails entirely. The 420 Code retreats by accepting that the cosmological identity, if it exists, must be carried by another formulation — possibly the global pullback of AP04 directly, or a different formal device not yet identified. Targets: Conditions J1, J2, the structural identity, the entirety of section 3.

KS-B.4 — Chain break

Claim. Every step in the derivation chain B-0 through B-6 depends only on the previous step and on the axiom, the four declared bridges B1–B4, and the declared empirical premise P. No undeclared assumption enters at any step.

Test. Demonstrate that some step in the chain requires an assumption not contained in {axiom, B1, B2, B3, B4, P}. The test is operational: pick any of the seven steps, examine its formal block, and identify the load-bearing imports. If any of those imports cannot be discharged into the axiom, the four bridges, or the declared empirical premise P, the chain has a break at that step.

Status. LIVE — HARD.

Recovery. If KS-B.4 fires at step B-k, the scope claim B1 (all structure follows from axiom + B1–B4 + P) is falsified. The chain still runs through step B-(k−1), but the link at step B-k requires either a new bridge declaration or a new empirical premise declaration or a re-derivation that closes the gap. The 420 Code retreats by either declaring the missing input (as a fifth bridge B5 with explicit cost, or as a second empirical premise P′, depending on its kind), or by withdrawing the chain at step B-k and acknowledging that the architecture’s reach falls short of the previously claimed scope. Targets: Claim B1, the chain at step B-k, the dependency declarations of all subsequent steps.

Why these five and not more

The five kill switches above cover the load-bearing claims of the paper. Each closure would force a different kind of retreat.

KS-B.0 closes the universal generator claim of the axiom — the deepest structural test. KS-B.1 closes the junction formulation against the bounce alternative — the empirical comparison test. KS-B.2 closes the specific spectrum predicted by the junction formulation — the parameter-level test, staged on B-JP. KS-B.3 closes the existence of the junction solution itself — the mathematical test. KS-B.4 closes the structural integrity of the chain — the architectural test.

Two further structural claims that some readings would expect to carry their own formal kill switch — Bridge B4’s status as a declared cost rather than a theorem, and the seven-step count of the chain rather than fewer or more — are absorbed into the kill switches above. B4’s declared-cost status is named in the front matter (section 1.4) and again at step B-6; any falsification of B4’s legitimacy as a bridge is a falsification of step B-6 and is therefore tested by KS-B.4 at that step. Similarly, the empirical premise P (observer plurality) is named in the front matter (section 1.4) and discharged at step B-4; any challenge to P’s legitimacy as a declared input is a challenge to step B-4 and is tested by KS-B.4 there. The seven-step count is forced by the dependency structure: each step is the minimum needed to introduce one new structural fact, and any restructuring that produced fewer steps would have to discharge multiple bridges (or P) at once — a violation also tested by KS-B.4. All three claims are thus held to formal kill-switch standard without adding entries to the master register.

Smaller claims throughout the paper — the specific named geometric objects (Kantowski-Sachs interior, ECSK extension), the identification of the structural triad in section 2.6 (hierarchy, cooperation, deterrence) as exhaustive, the choice of “obligation” as the right English word for the perspectival recognition at step B-6 — are illustrative or terminological rather than load-bearing. If they turn out to be poor choices, the paper still stands. If KS-B.0 through KS-B.4 hold, the structural argument of AP05 holds.