Claim Summary · Conditionality Footer

Claim Summary

Section-by-section structural enumeration with epistemic-status labels.

1 (Hawking channel). FALSIFICATION REGISTER. Claim C1 (Established): gravitational absorbers exhibit six structural features; η > 0 by Hawking radiation; c is the constraining constant.

2 (Retinal channel). FALSIFICATION REGISTER. Claim C2 (Established): electromagnetic absorbers exhibit the same six features; η ≈ 10⁻⁶ to 10⁻⁵; c constrains η via α.

3 (Leakage Theorem). DERIVATION. Theorem 3.1 (Derived — scoped): η > 0 in the analysed channels when c and coupling are finite. Result C3 (Derived — scoped): perfect absorption not achieved in the two analysed channels.

4 (Landauer synthesis). SYNTHESIS. Claim C4 (Synthesis): leakage cost per bit = k_B T × O(1) in all three domains; same form, different magnitudes.

5 (CMB channel). FALSIFICATION REGISTER. Claim C5 (Established): CMB exhibits all six structural features; anisotropy ∼10⁻⁵; boundary = last scattering surface.

6 (Cosmological Corollary). STRUCTURAL CONNECTION. Claim C6a (Structural Corollary): the cosmological channel of section 5 and AP43 D5’s cosmological 1×ε integration are one structural process read at two boundaries.

7 (Epsilon Identification). INTERPRETATION. Identification 6.1 (Claim C6) [INTERPRETATION]: ε ≡ η. The axiom’s ε is the measured leakage ratio at every analysed boundary.

8 (Planck constraint). CONJECTURE (non-load-bearing). Section 8.1: G = κ/(εΛ²), G depends on c through ε. Section 8.4: Conjecture C7 (multidimensional residual). All constants as faces of one residual.

Conditionality Footer

Dependencies

Established physics: Hawking 1975; Bekenstein 1973; Hammer et al. 2022; Mordant et al. 2011; Penzias & Wilson 1965; Planck 2020; Landauer 1961; Bérut et al. 2012; Smoot et al. 1992; Tolman 1934.

Framework: Axiom B (the break) from AP01; AP03 (the conjugacy c² = β/α and the scaling form G = κ/(εΛ²)); AP05 (structural derivation of the break); AP20 (the forcing proof: Axiom B → one parameter, constraining KS-L.6); AP43 D5 (the cosmological 1×ε integration carried as corollary in Section 6).

Dependents

AP15 (Connection — U(1) electromagnetism on the boundary AP06 establishes). AP24 (Residual — formalising the multidimensional residual conjecture of section 8.4). AP28 (Constant — deriving G via channel-counting using ε = α_em from the chemical-biological scale AP06 grounds). AP14 (Correction — Planck-scale corrections at the high-energy end of the same leakage process). Notebook VI APs (cosmology line opened by section 6’s Cosmological Corollary).

Kill switches closed by this paper

None. AP06 opens kill switches; it does not close prior corpus kill switches. The pre-AP06 status of ε as postulate is upgraded to an interpretive identification with a measured quantity; this is a grounding, not a closure of a prior kill switch.

Kill switches that remain live

KS-L.1 (Perfect absorber): LIVE — EMPIRICAL. Load-bearing for Theorem 3.1.

KS-L.2 (Sufficiency failure): LIVE — EMPIRICAL. Load-bearing for Theorem 3.1 (scoped form).

KS-L.3 (Dependent): LIVE — DEPENDENT. Falls if KS-L.1 or KS-L.2 fires.

KS-L.4 (Landauer violation): LIVE — EMPIRICAL. Targets section 4.

KS-L.5 (No shared parameterisation): LIVE — HARD. Non-load-bearing.

KS-L.6 (G independent of c): LIVE — HARD. Structurally constrained by AP20.

KS-L.7 (Poisson derivation): LIVE — HARD. Partially reduced by AP43 section 7.

Structural debts owed

D1 (Broader class). The Leakage Theorem holds in two analysed channels; extension to all physical near-perfect absorbers is advanced but not proven. [AP06-specific]

D2 (Numerical factor). The eye’s leakage ratio (∼10⁻⁵) and the CMB anisotropy (∼10⁻⁵) are numerically similar; honestly stated as likely coincidental (section 5.4). [AP06-specific, non-load-bearing]

D3 (Poisson derivation). The Poisson equation derivation with G depending on c through the leakage (KS-L.7) has not been completed. [Shared with AP03 D1; partially reduced by AP43 section 7]

Items held open without claiming debt status

The cosmological 1×ε integration corollary of section 6 at the level of formal mathematical detail (full account lives in AP43 D5).

The relationship between domain-dependent ε values (ε_gravity, ε_eye, ε_cosmo) and the canonical corpus-wide value ε = α_em ≈ 1/137 (chemical-biological scale identification via The Lock, Edition 04).