Masses Mass Genesis Theorem Statement Stable Closed Iff Eight Tick Rhat Stable O

Mass genesis statement

A light pattern is a finite collection of eight-component complex windows, each attached to a position in a finite lattice, together with a topology that records quantum numbers. The framework's mass-genesis module defines what it means for such a pattern to be a stable, closed, massive object. The central definition, stable closed light pattern, requires three things: the pattern has localized support, it carries a nontrivial neutral load, and its windows return to themselves after some number of cyclic shifts that divides eight. The last condition is the eight-tick orbit: after eight shifts, every window is exactly what it started as.

The theorem stableClosed_iff_eightTickRHatStableOrbit states that this stable closed condition is equivalent to a simpler one. A pattern is stable and closed exactly when it has localized support, a nontrivial neutral load, and every window is fixed by the eightfold cyclic shift. In plain language, the eight-tick orbit is not an extra assumption; it is the whole content of closure. The equivalence is proved in the machine-checked library of formal theorems, so the two descriptions are interchangeable by construction.

This equivalence matters because it fixes the target for mass genesis before any proof work begins. The module defines a rest mass for a pattern: if the pattern is stable and closed, the rest mass equals the integrated meaning load, a sum of squared norms over the support; otherwise the rest mass is zero. The theorem restMass_eq_integratedMeaningLoad_of_stable proves that identity for stable patterns, and restMass_eq_zero_of_not_stable proves the zero case. Together they make rest mass a sharp function of the stability predicate, not a separate quantity.

What the declaration does not claim is just as important. The mass-genesis module explicitly says the bridge from these definitions to actual particle masses is not closed. The central statement remains a certificate surface whose hard fields must be proved bottom-up from the cost function, stability, topology, eight-tick closure, and the golden-ratio forcing. Reverse reconstruction from known masses is deliberately absent from the canonical statement. The theorem gives a clean equivalence, but it does not yet show that any physical pattern satisfies it, nor that the predicted masses match measurement.

/-- Stable closed light pattern: localized, nontrivial, and closed under
the eight-tick Rhat orbit. -/
def StableClosedLightPattern (ψ : LightPattern Λ) : Prop :=
  LocalizedSupport ψ ∧ NontrivialNeutralLoad ψ ∧ ClosedRHatOrbit ψ

theorem restMass_eq_integratedMeaningLoad_of_stable
    (ψ : LightPattern Λ) (hψ : StableClosedLightPattern ψ) :
    restMass ψ = integratedMeaningLoad ψ := by
  classical
  simp [restMass, hψ]

theorem restMass_eq_zero_of_not_stable
    (ψ : LightPattern Λ) (hψ : ¬ StableClosedLightPattern ψ) :
    restMass ψ = 0 := by
  classical
  simp [restMass, hψ]

What this page does not claim

The mass-genesis bridge from definitions to measured masses is closed. Any physical light pattern is known to satisfy the stable closed condition. Reverse reconstruction from known masses is part of the canonical statement.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Masses/MassGenesis/TheoremStatement.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: