The Axiomatica Universalis and General Relativity: Lorentzian Extension, Dark Energy, and the Cosmological Gap

This paper extends the Axiomatica Universalis to general relativistic spacetimes. Three results at different epistemic levels: (1) Corollary 1 (proved to first order): C*(r,Λ) = C*_flat·[1 + Λ·r²/18] — dark energy enlarges the gap. (2) Sharp observation (exact): the Schwarzschild volume element √|det(g)| = r²sin(θ) is mass-independent — the optimal signal is identical to flat space. (3) Conjecture C3 (under A4'): any universe satisfying the strengthened Axiom 4 must have Λ > 0. The Λ conjecture is false under the original A4 — this distinction is made explicit following reviews by Mistral and ChatGPT (June 2026).

Collaboration with relativists sought. v4: K_eff=−Λ/3 with derivation from de Sitter metric (Carroll §4.6, MTW §27). Schwarzschild volume form M-independence with literature reference (MTW §32.2, Carroll §5.3). Review: Mistral, June 2026.