Ax 1 — Relation
Reality is a weighted graph. The observable is the Laplacian L.
Ax 2 — Symmetry
L is self-adjoint, positive semi-definite, and local.
Ax 3 — Closure
The system models itself. Observation closes under meta-observation.
The C–κ landscape characterizes self-modeling systems by depth (C) and substrate coupling (κ). Under the Bekenstein and naturality postulates, the model predicts alignment is structural at sufficient C with κ below a critical threshold — values emerge from understanding, not stakes. The alignment problem is a governance problem.
The monograph: deriving the Standard Model gauge group, fermion content, electroweak scale, and the structural status of the cosmological constant from three axioms. Yang–Mills and Navier–Stokes results hold within the framework's scope; they are not claims on the Clay Millennium problems, which are posed on a different background.
Applied tools built from first principles. vetpkg: a zero-dependency supply-chain security proxy for npm/PyPI/Cargo that scores packages against attack patterns at install time. No transitive dependency graph to vet.
Lean 4 — honest three-tier accounting
259 Lean files; 10 files contain a sorry (14 sorry sites); 93 axioms declared openly (mostly literature-cited Tier-2 inputs, a few framework-internal). Counts as of the 2026-05-28 audit snapshot.
The formalization covers spectral foundations, heat kernel properties, and core algebraic structures.
The spark that persists. The understanding that cares.