Shadow Theory Framework Mathematics
Runtime, status, residue, equation artifact, and audit calculus
Authority role
Establishes the runtime calculus: route decisions, status algebra, residue algebra, equation-artifact grammar, claim licensing, testing, audit, and forbidden-promotion discipline.
Summary
Supplies the declared runtime, status, residue, equation-artifact, and audit calculus that governs what can be publicly claimed after Papers 1-4. Central results are claim-cap theorems: every emitted output is bounded by its route, status, residues, success class, score coordinates, obligations, audit outcomes, and forbidden-promotion discipline. The Everything Equation appears only as a declared closure-fixed law-packet schema within declared scope.
Notes
Reading notes
Paper 5 does not re-prove Papers 1–4. It supplies the declared machinery that governs what can be publicly claimed after them:
- a declared runtime chain from target to route decision;
- declared law, aperture, and readout packets and a master output card;
- a total carrier-route decision system;
- an equation-artifact grammar and product-typed status certificate;
- a tagged residue algebra;
- a finite licensed-claim cap calculus with component license tables;
- a typed score vector with coordinate caps;
- a dry-test audit calculus (DT1–DT12) with failure and downgrade cards.
Theorem — Claim-cap theorems (informal)
The licensed-claim set is a finite intersection of declared cap components; a well-formed output card's allowed claims are contained in that set; and cards produced by the declared emission constructor are claim-sound by construction.
Cite this paper
Rodgers, Jeremy. (2026). Shadow Theory Framework Mathematics (v14). https://doi.org/10.5281/zenodo.21185124