Masses Mass Genesis T10 Run History Scale Coupling Boundary Run Only Accepts Dou

The run-only boundary

The declaration runOnly_accepts_doubled_phi_inversePhi concerns a proposed rule for sorting emitted signals. The framework models each signal as a carrier holding two kinds of data: an exact settled ledger octave (a discrete record of eight posting events) and a freely chosen positive amplitude with a pattern read at that amplitude. A filter is run-only when its verdict depends only on the ledger octave and ignores the amplitude and pattern entirely. The theorem states that if such a run-only filter accepts the intended gap-one carrier, it must also accept the same carrier after its amplitude is doubled, scaled by the golden ratio phi, or scaled by inverse phi. All three rescaled carriers share the identical ledger run, so a filter that reads only the run cannot distinguish them.

The consequence is a boundary result. The induced realization class from such a run-only filter violates RecognitionGroundStateSelection already at the doubled carrier, meaning the filter's blindness to scale breaks a required ground-state rule. The declaration also records an exact interface: any surviving coupling must accept the intended carrier while rejecting the doubled, phi-scaled, and inverse-phi-scaled patterns. A filter meeting that four-witness interface is proved not run-only. The interface is a precise specification of what a lawful coupling must do, not a construction of one.

What the declaration does not claim is equally sharp. No run-pattern coupling satisfying the interface is constructed or assumed. The module does not derive R4, does not assume a selector, and does not identify a lawful order-sensitive posting observable. It closes only the proposal to filter the present free-amplitude readout by a property of the ledger run alone. The interface records witness behavior only; it does not certify that the filter has independent physical ancestry or that its definition avoids factor posting or a zero loadRecognitionCost. 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, assume a selector, or identify a lawful order-sensitive unnormalized posting observable. The interface does not certify independent physical ancestry or avoidance of factor posting or zero loadRecognitionCost.

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.

Derived articles

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