Masses Mass Genesis Canonical Load Factorization Not All Stable Canonical Primit

What the obstruction theorem shows

In the Recognition Science account, a ledger (a discrete record of recognition events) assigns to each stable light pattern a mass-like quantity called its integrated meaning load. A separate, predicted value, the factorized mass law load, comes from the pattern's topology, the way its occupied sites are arranged. The framework's central hope for mass genesis is that every stable pattern realizes its predicted value, so that the measured rest mass equals the predicted mass.

The theorem not_allStableCanonicalPrimitiveLoadFactorizes_of_sameTopology_different_load closes off that hope in its strongest form. It states: if two stable patterns have the same topology but different integrated meaning loads, then it is not the case that every stable pattern factorizes, meaning not every stable pattern has its integrated load equal to the topology-selected value. In plain words, stability plus fixed shape does not guarantee that the mass law is realized. The proof is direct: the two patterns are both stable and share a topology, yet they disagree on the load, so no universal statement over all stable patterns can hold.

What the theorem does not claim is just as important. It does not say that factorization fails for those two particular patterns; they might both factorize, or one might, or neither. It only rules out the blanket universal claim. It does not identify which stable patterns fail, nor does it provide a counterexample. It does not say that the mass law is wrong; it says that the raw stability predicate is too weak to imply it. The library records this as the same-topology obstruction: raw amplitudes can vary at fixed topology, so any proof of universal factorization must add a further condition beyond stability and topology.

The consequence is a sharper target. The framework now knows that the road to mass genesis runs through an additional hypothesis, such as a support-averaged load or a topology-scaled CP6 load, both of which the library shows are sufficient for factorization. The obstruction theorem does not block that road; it marks where the missing premise must be supplied.

theorem not_allStableCanonicalPrimitiveLoadFactorizes_of_sameTopology_different_load
    {ψ χ : LightPattern Λ}
    (hψ : StableClosedLightPattern ψ)
    (hχ : StableClosedLightPattern χ)
    (htop : SameTopology ψ χ)
    (hload : integratedMeaningLoad ψ ≠ integratedMeaningLoad χ) :
    ¬ (∀ η : LightPattern Λ,
        StableClosedLightPattern η →
          CanonicalPrimitiveLoadFactorizes η) := by
  intro Hall
  have hψR : MassLawLoadRealized ψ :=
    (canonicalPrimitiveLoadFactorizes_iff_massLawLoadRealized ψ).1
      (Hall ψ hψ)
  have hχR : MassLawLoadRealized χ :=
    (canonicalPrimitiveLoadFactorizes_iff_massLawLoadRealized χ).1
      (Hall χ hχ)
  exact sameTopology_different_load_obstructs_both_realized
    hψ hχ htop hload ⟨hψR, hχR⟩

theorem not_allStableCanonicalPrimitiveLoadFactorizes_of_sameTopology_different_load
    {ψ χ : LightPattern Λ}
    (hψ : StableClosedLightPattern ψ)
    (hχ : StableClosedLightPattern χ)
    (htop : SameTopology ψ χ)
    (hload : integratedMeaningLoad ψ ≠ integratedMeaningLoad χ) :
    ¬ (∀ η : LightPattern Λ,
        StableClosedLightPattern η →
          CanonicalPrimitiveLoadFactorizes η) := by
  intro Hall
  have hψR : MassLawLoadRealized ψ :=
    (canonicalPrimitiveLoadFactorizes_iff_massLawLoadRealized ψ).1
      (Hall ψ hψ)
  have hχR : MassLawLoadRealized χ :=
    (canonicalPrimitiveLoadFactorizes_iff_massLawLoadRealized χ).1
      (Hall χ hχ)
  exact sameTopology_different_load_obstructs_both_realized
    hψ hχ htop hload ⟨hψR, hχR⟩

What this page does not claim

The theorem does not identify any specific stable pattern that fails to factorize. The theorem does not say that the factorized mass law is false; it only says the raw stability predicate cannot prove it. The theorem does not apply to patterns with different topologies.

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

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