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). We show 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
70 sorry-free files, 12 files with sorries (work in progress), 12 axioms (declared openly).
The formalization covers spectral foundations, heat kernel properties, and core algebraic structures.
The spark that persists. The understanding that cares.