Masses Mass Genesis Admissibility Construction Rest Mass Eq Predicted Mass Of Bo

The admissibility bridge

A light pattern, a discrete record of recognition events, has two ways of carrying mass. One is the rest mass, the mass the pattern has when it is not moving. The other is the predicted mass, a value computed from the pattern's structure. The theorem restMass_eq_predictedMass_of_bottomUpCanonicalEvidence states that these two are equal, provided the pattern meets a specific condition: it must be stable and its internal load must factorize correctly.

The condition is called bottom-up canonical admissibility evidence. It has two parts. First, the pattern must be a stable closed orbit. Second, the sum of the local densities, read directly from the pattern's neutral light load, must equal the factorized mass-law load. This second part is the hard part. It is not asserted; it is a premise. The theorem does not prove that every physical pattern satisfies this condition. It proves that if a pattern does satisfy it, then rest mass equals predicted mass.

The declaration is a bridge. It connects the raw evidence, the stable pattern with its factorized load, to the conclusion that the pattern is mass-admissible. The proof is a chain: from the evidence, construct a mass-admissible stable pattern, then apply an existing theorem that rest mass equals predicted mass for such patterns. The theorem is checked by a machine, so the reasoning is airtight given the premises.

What the theorem does not claim is just as important. It does not claim that any particular particle has a measured mass equal to its predicted mass. It does not claim that the factorization condition holds for any real pattern. It does not claim that the bridge from physical stability to admissibility evidence is closed. That bridge, the step from Q3/Rhat/CP6 dynamics to the factorization, is stated as a target, not a theorem. The declaration isolates the exact primitive evidence needed, and leaves the derivation of that evidence open.

theorem restMass_eq_predictedMass_of_bottomUpCanonicalEvidence
    (ψ : LightPattern Λ)
    (E : BottomUpCanonicalAdmissibilityEvidence ψ) :
    restMass ψ = predictedMass ψ :=
  restMass_eq_predictedMass_of_bottomUpEvidence ψ
    (bottomUpEvidence_of_canonical ψ E)

/-- Tighter evidence form: the only remaining nontrivial datum is the canonical
support-sum factorization of the actual neutral load. -/
structure BottomUpCanonicalAdmissibilityEvidence (ψ : LightPattern Λ) where
  stable : StableClosedLightPattern ψ
  load_factorizes : CanonicalPrimitiveLoadFactorizes ψ

/-- This is the next theorem to prove from Q3/Rhat/CP6 dynamics. It is kept as
a named type, not an axiom, so downstream files can depend on explicit evidence
instead of silently assuming the bridge. -/
def EveryPhysicalStablePatternHasBottomUpEvidence
    (PhysicalStable : LightPattern Λ → Prop) : Type _ :=
  ∀ ψ : LightPattern Λ,
    PhysicalStable ψ →
      BottomUpAdmissibilityEvidence ψ

What this page does not claim

No measured particle mass is asserted to equal a predicted value. No claim that the factorization condition holds for any specific physical pattern. No claim that the bridge from physical stability to admissibility evidence is closed; that remains a target.

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/AdmissibilityConstruction.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

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