Masses Mass Genesis T10 Run History Scale Coupling Boundary

The scale-coupling boundary

The T10 run-history scale-coupling boundary is a result in the Recognition Science framework's account of mass generation. It concerns a proposed shortcut: read a particle's mass directly from the ordered history, or run, of recognition events in a settled ledger octave, while ignoring the freely chosen continuum amplitude and pattern. The module proves this shortcut fails, and records the precise four-witness condition that any surviving coupling must satisfy.

In the framework, a ledger is a discrete record of recognition events. A settled ledger octave is the exact ordered run of such events. A carrier is the full emitted readout: it combines this exact octave with a positive continuum amplitude and a pattern. The module defines rescaling, which multiplies the amplitude by any positive factor and transforms the pattern, while provably preserving the octave and every state of its run.

The central theorem is a no-go result. A run-only filter is one that gives identical verdicts to carriers with identical settled octaves, meaning it depends only on the run. If such a filter accepts the intended gap-one factor carrier, it must also accept its doubled, phi-scaled, and inverse-phi-scaled carriers, because these share the same run. The induced realization class then violates the ground state selection rule R4 already at the doubled carrier. The proof is machine-checked, with no gaps and no new axioms.

The module then states what a surviving coupling must do. The RunPatternScaleCouplingInterface requires a filter to accept the intended carrier while rejecting the doubled, phi-scaled, and inverse-phi-scaled carriers. Any filter meeting this interface is proved not run-only. This is a boundary: it closes the proposal to filter the present free-amplitude readout by a property of the ledger run alone.

What the module does not do is as important as what it proves. It does not construct or assume any run-pattern coupling satisfying the interface. It does not derive R4, and it does not identify a lawful order-sensitive unnormalized posting observable. The interface records witness behavior only, not physical ancestry. Those intensional provenance requirements remain open for any future construction.

/-- A run-only filter accepting the intended carrier accepts all three scale decoys. -/
theorem runOnly_accepts_doubled_phi_inversePhi
    (P : EmittedScaledSettledReadoutCarrier → Prop)
    (hP : IsRunOnly P)
    (octave : Q3SettledLedgerOctave)
    (hintended : P (intendedGapOneFactorCarrier octave)) :
    P (doubledCarrier (intendedGapOneFactorCarrier octave)) ∧
      P (phiScaledCarrier (intendedGapOneFactorCarrier octave)) ∧
        P (inversePhiScaledCarrier
          (intendedGapOneFactorCarrier octave)) := by
  have hdoubled :
      P (doubledCarrier (intendedGapOneFactorCarrier octave)) :=
    (runOnly_doubledCarrier_iff
      P hP (intendedGapOneFactorCarrier octave)).mp hintended
  have hphi :
      P (phiScaledCarrier (intendedGapOneFactorCarrier octave)) := by
    exact
      (runOnly_rescaledCarrier_iff
        P hP Constants.phi Constants.phi_pos
        (intendedGapOneFactorCarrier octave)).mp hintended
  have hinverse :
      P (inversePhiScaledCarrier
        (intendedGapOneFactorCarrier octave)) := by
    exact
      (runOnly_rescaledCarrier_iff
        P hP
        (Constants.phi⁻¹)
        (inv_pos.mpr Constants.phi_pos)
        (intendedGapOneFactorCarrier octave)).mp hintended
  exact ⟨hdoubled, hphi, hinverse⟩

/-- The class induced by any run-only filter accepting the intended carrier fails R4 at the double. -/
theorem runOnly_carrierRealized_violates_r4
    (P : EmittedScaledSettledReadoutCarrier → Prop)
    (hP : IsRunOnly P)
    (octave : Q3SettledLedgerOctave)
    (hintended : P (intendedGapOneFactorCarrier octave)) :
    ¬ RecognitionGroundStateSelection (CarrierRealized P) := by
  have hdoubled :
      P (doubledCarrier (intendedGapOneFactorCarrier octave)) :=
    (runOnly_accepts_doubled_phi_inversePhi
      P hP octave hintended).1
  have hmem :
      CarrierRealized P
        (doubledCarrier (intendedGapOneFactorCarrier octave)).pattern :=
    carrierRealized_of_accepts hdoubled
  exact
    doubled_intended_carrier_violates_r4
      octave
      (CarrierRealized P)
      (by
        simpa only [intendedGapOneFactorCarrier] using hmem)

/-- Any carrier filter meeting the four-witness coupling interface is necessarily non-run-only. -/
theorem runPatternScaleCouplingInterface_not_runOnly
    (P : EmittedScaledSettledReadoutCarrier → Prop)
    (octave : Q3SettledLedgerOctave)
    (hgate : RunPatternScaleCouplingInterface P octave) :
    ¬ IsRunOnly P := by
  intro hrun
  have hdoubled :
      P (doubledCarrier (intendedGapOneFactorCarrier octave)) :=
    (runOnly_accepts_doubled_phi_inversePhi
      P hrun octave hgate.1).1
  exact hgate.2.1 (carrierRealized_of_accepts hdoubled)

What this page does not claim

No run-pattern coupling satisfying the interface is constructed or assumed. The module does not derive R4 or identify a lawful order-sensitive unnormalized posting observable. The interface does not certify independent physical ancestry for any filter.

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/T10RunHistoryScaleCouplingBoundary.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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