This layer is easiest to read when it is broken into the same stable sequence every time: axioms, definitions, theorems, lemmas, extended framework, and closure. The detailed pages already exist. This page gives the clean map.
This framework does not treat science and theology as separate vocabularies, and it does not lean on loose analogy. It asks whether theological doctrines can be mapped onto strict mathematical, physical, informational, and logical constraints: not metaphor, but shared structure under variable substitution.
Works-based salvation becomes a linear-algebra question. If a moral sign sigma is trapped under self-preserving operations, the system cannot flip itself. Reversal requires an external, non-unitary operator: grace.
The Von Neumann chain cannot regress forever through finite observers. The framework names the structural endpoint as a terminal infinite observer, then asks whether theology has already named that observer.
Claims pass through death conditions: self-refutation, infinite regress, empirical contradiction, logical incoherence, and explanatory failure. The Why-Penalty keeps useful-but-unexplained claims from pretending to be complete.
Coherence chi is treated as an integrated product across entropy, time, quantum state, relational coherence, grace, and the other load-bearing variables. Closed systems decay; positive coherence requires external input.
Lean 4 can verify the structure of the mathematics, not independently prove Christianity's historical claims. The socket is mathematics. The plug is theology. The page keeps that boundary visible.
If distinction, information, thermodynamics, observation, and coherence are real constraints, the framework argues that their shared grammar mirrors the Fall, the persistence of the soul, and the necessity of external grace.
Detailed pages: axioms-layer-0-core.html, axioms-layer-2-derived.html, axioms-layer-3-extended.html, axioms-closure.html.