Masses Mass Genesis Support Symmetry

The support symmetry argument

The masses mass genesis support symmetry is a formal argument inside the Recognition Science framework. It addresses a specific question: when does the rest mass of a stable light pattern equal the mass that the framework's earlier theorems predict for it? The argument establishes a sufficient condition: if a symmetry action moves every occupied site to every other occupied site while preserving the local load, then the pattern's mass is exactly what the framework predicts.

The argument works with a light pattern, a discrete record of events on a finite set of sites. Each occupied site carries a numerical load, the site meaning load. The symmetry is a function that maps occupied sites to occupied sites. The two key properties are that the function preserves the load at each site, and that it is transitive: starting from any occupied site, repeated application of the function can reach any other occupied site. The argument proves that these two properties together force the load to be uniform across all occupied sites.

The proof is short and direct. Given two occupied sites, transitivity provides a number of steps that connects them. The load preservation property, applied repeatedly, shows the loads at the two sites are equal. Since the sites were arbitrary, all loads are equal. This uniformity is the core of the equipartition theorem: transitive load-preserving symmetry forces equal distribution.

In Recognition Science, the framework models the genesis of particle masses. The final theorem states that if a stable closed light pattern has this support symmetry and its load factorizes in the canonical way, then its rest mass equals its predicted mass. The symmetry condition is the bridge that closes the gap between the two quantities.

The argument also packages this result into a certificate structure, a formal object that bundles the symmetry and transitivity conditions. The certificate is a way to record that a pattern satisfies the support symmetry argument. The hard future work, noted in the argument's own documentation, is to instantiate this generic symmetry from the actual quantum carrier rather than postulate it for an abstract finite substrate.

/-- The equipartition theorem: transitive load-preserving Rhat support action
forces uniform neutral load across the occupied support. -/
theorem uniformSiteMeaningLoad_of_supportRHatTransitive
    {ψ : LightPattern Λ}
    (A : SupportRHatAction ψ)
    (htrans : SupportRHatTransitive A) :
    UniformSiteMeaningLoad ψ := by
  intro x hx y hy
  rcases htrans x hx y hy with ⟨n, hn⟩
  have hload := A.load_iterate n hx
  rw [hn] at hload
  exact hload.symm

theorem restMass_eq_predictedMass_of_supportRHatSymmetry_and_factorization
    {ψ : LightPattern Λ}
    (hstable : StableClosedLightPattern ψ)
    (_A : SupportRHatAction ψ)
    (_htrans : SupportRHatTransitive _A)
    (hfactor : CanonicalPrimitiveLoadFactorizes ψ) :
    restMass ψ = predictedMass ψ :=
  restMass_eq_predictedMass_of_stable_and_canonicalPrimitiveLoadFactorizes
    ψ hstable hfactor

What this page does not claim

The argument does not prove that any specific physical pattern satisfies the symmetry conditions. The argument does not derive the value of any particle mass. The argument does not establish that the support action exists for the actual quantum carrier.

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/SupportSymmetry.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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