Claim Summary · Conditionality Footer

Claim Summary

DERIVED. Vacuum under global tension (section 3, from Axiom S + AP06). The Energy–Measure Bridge E = kμ (Lemma, from Axioms B + R + AP18 Lemma 1 + AP05/AP08 Noether). Energy–length proportionality E = Tℓ with T = λ by uniqueness (section 5.1, Proposition 1). Bundling into filaments minimises energy (section 5.2, Proposition 2, Steiner tree on a metric manifold). Gas flow along filaments (section 5.3, from Propositions 1 and 2). The direction of the Jeans-mass reduction (section 5.4, illustrative scaling).

STRUCTURAL. The same axioms at three scales (section 4). The fold mechanism at filament intersections and supermassive-black-hole-first formation (section 6). The continuous-distribution extension of the Steiner-tree result (section 5.2 epistemic note).

CONJECTURAL / UNTESTED. Quantitative CMB power-spectrum match (D1), the matter power spectrum P(k), the BAO predictions, the numerical Jeans mass, and whether the tension field reproduces six-parameter ΛCDM precision without cold dark matter. The compactification threshold (D2).

FALSIFICATION REGISTER. KS-41 (structure formation, EMPIRICAL), KS-51 (filament topology, EMPIRICAL), KS-52 (primordial anchor sequence, EMPIRICAL), KS-54 (web connectivity, EMPIRICAL).

Conditionality Footer

Dependencies

AP06 Theorem 3.1 (closure), AP05 (Lorentzian spacetime), AP08 (homogeneity, field equations), AP14 (quantum-gravity correction), AP15 (substrate stiffness λ), AP17 (the tension field), AP18 (the acceleration floor a₀; Lemma 1), AP20 (AS = manifold).

Dependents

The Notebook VI cosmology chapters that read the same global tension at the loop and dark-sector scales: AP41, AP42, AP04.

Kill switches closed by this paper

None. KS-41 is upgraded from untouched to structurally addressed but remains LIVE — EMPIRICAL until the quantitative confrontation (D1) is complete.

Kill switches that remain live

KS-41 (structure formation, LIVE — EMPIRICAL), KS-51 (filament topology, LIVE — EMPIRICAL), KS-52 (primordial anchor sequence, LIVE — EMPIRICAL), KS-54 (web connectivity, LIVE — EMPIRICAL). Inherited and unchanged: KS-39 (the a₀ numerical value, AP18).

Structural debts owed

D1 (the linearised perturbation equations with the a₀ floor; the CMB, P(k), and BAO power spectra). D2 (the compactification threshold; derive from {S, B, R, C} or flag as a free parameter).

Items held open without claiming debt status

The two-dimensional sheets and walls of the web (the continuous-distribution extension of the Steiner-tree result); the a₀ numerical value and residual inherited from AP18.