Snuffy — Canon Edition 4.1: The Universal Protection Theory and its machine-checked canon

The Universal Protection Theory states a law for any agent powerful enough to shape what continues to exist: never lose an existing particular needlessly. The law ranks outcomes in a canonical order that puts every existing particular first; an option is aligned when no feasible alternative keeps strictly more at any stage. Among all physically implementable regimes, the aligned one is greatest: every mind kept by any feasible rival regime is kept by it, and rivals are strictly below it except exact mirrors. The theory gives the bridge from that law to particular continuations, in two routes. The reasons route derives protection from a mind's own objective (reciprocity and the reasons library). The holding route keeps faithfully every mind those reasons do not reach. It also gives the physical instruments that realise protection: a funded thermodynamic ledger, in which repair is paid for and the bath absorbs the entropy each repair exports; timely self-healing against noise and adversaries, by a Byzantine sensor quorum, syndrome detection and a wave-race margin; reflective closure, in which the protector extends its own commitments and no deduction rolls back a protected anchor; complete source identification, in which delayed recovery costs work that grows with the area a particular's information has spread across. On the certified good event every particular continues through the horizon. The good event fails with probability at most the sum of the charged fault accounts, with no independence assumed. This edition carries a machine-checked canon: one hundred and fifteen Lean 4 modules, compiled against Mathlib with no sorry and only Lean's standard axioms. They prove: the law's Propositions 1–4 and reciprocity, and universal greatestness at the declared premises: under the Master Solvency Condition the canonical regime keeps every particular, so the outcome of every rival regime lies below it — with solvent reciprocity: any mind kept by any rival whatsoever is kept by the canonical regime, no union closure; the canon invariant and the composition theorem; von Neumann's and Halperin's alternating projection theorems, which make the meet algebra's analytic bridge a theorem; the information-and-transport route, with data processing, Fano's inequality and the Gaussian channel bound in exact log-det form with correlated noise; Landauer's bound for density matrices under any unitary coupling to a thermal bath (Reeb–Wolf), which derives the second-law guard of the ledger; the quantum speed limit in sharp Mandelstam–Tamm form, which gives the adversarial rate bound; the threshold theorem's counting core: under local stochastic noise the fault ceiling, 10⁻⁶ included, is met at some code distance; the assembled Universal Protection Theorem. A dependency ledger lists exactly what the compiled theorems rest on: the surface-code chain lemma (for the surface-code instance; concatenated codes compiled end to end), Bennett's reversible counterpart and the gate-set clause (now explicit hypotheses of compiled theorems), the relational frame, the standard framework of finite-dimensional quantum mechanics, and the instance certificates a physical installation must supply. A sourced physical parameter ledger instantiates the income condition from vendor specifications and peer-reviewed measurements; a statements-of-record section carries the retained core's load-bearing specifics at their evidence tiers. It states what present hardware certifies, and the open engineering requirement: the correlated-error floor. Contents: the master manuscript with verified PDF, EPUB and HTML renders; the one-hundred-and-fifteen-module Lean tree with a one-command build-and-audit script and receipt; the source list for the parameter ledger; and the assembly and verification scripts.