Masses Mass Genesis Support Symmetry Rest Mass Eq Predicted Mass Of Support Rhat

The symmetry that fixes a mass

In physics, rest mass is the mass an object has when it is not moving. In the Recognition Science framework, a light pattern is a discrete record of events, and each possible site in that record carries a load, a number that measures how much meaning is concentrated there. The framework's central question is whether the mass a pattern is observed to have, its rest mass, is the same as the mass its internal structure predicts, its predicted mass. This declaration is a proof, checked by a machine, of one condition under which those two numbers are forced to be equal.

The proof works by assuming a strong symmetry on the pattern's occupied sites, the places where the record actually has events. The symmetry is a rule that moves events from one occupied site to another. The rule must preserve the load at every site it touches, and it must be able to reach every occupied site from every other occupied site by applying itself some number of times. Under those conditions, a theorem in the framework's library proves that the load must be the same at all occupied sites. This is an equipartition result: a transitive, load-preserving symmetry spreads the meaning evenly.

That uniform load is the key ingredient. The declaration also assumes that the pattern's primitive load, its most basic unit of meaning, factors cleanly into a canonical form. From uniform load and that factorization, the framework derives that the pattern's averaged, topology-scaled load matches its predicted mass. The final theorem, restMass_eq_predictedMass_of_supportRHatSymmetry_and_factorization, combines this with the pattern being stable and closed, and concludes that restMass equals predictedMass. The proof is a chain of implications, each step checked by the machine-checked library of formal theorems.

This result is a conditional bridge, not a universal law. It does not claim that every light pattern has equal rest and predicted mass. It does not claim that the symmetry rule it assumes actually exists for any real physical pattern; the framework's own documentation notes that constructing this symmetry from the actual carrier is hard future work. The theorem proves an implication: if a stable, closed pattern has a transitive, load-preserving symmetry and a clean factorization, then its two masses agree. What the theorem does not do is show that those premises hold for any specific pattern in the physical world.

The practical consequence is a reduction. To check whether a pattern's rest mass matches its predicted mass, one no longer needs to compute both from scratch. It is enough to verify the symmetry and factorization conditions, which are structural properties of the pattern's support. This makes the mass-genesis question more tractable: the search for a physical instantiation can focus on finding a pattern with the right symmetry, rather than on recalculating masses. The theorem tells a researcher what to look for.

/-- 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 theorem does not prove that any actual physical pattern satisfies the symmetry and factorization premises. The theorem does not claim that rest mass and predicted mass are equal for all light patterns. The theorem does not derive the existence of the symmetry rule from the framework's more basic principles.

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)

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.

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