Masses Mass Genesis T10 Run Cascade Quadratic Scale Boundary Canonical Exact Oct

The exact-octave filter

In the Recognition Science account of mass generation, a ledger is a discrete record of recognition events, and a filter is a rule that accepts or rejects a proposed carrier, a package of pattern and amplitude that would carry a mass. The declaration canonicalExactOctaveFilter_violates_r4 proves that one particular filter, which accepts a carrier only if its settled octave record equals a fixed canonical record, cannot satisfy the four-witness interface RunPatternScaleCouplingInterface. The proof shows this filter is run-only: it depends only on the settled octave, not on any other feature of the carrier.

Why does that matter? The four-witness interface is a set of conditions that any viable scale-coupling must meet, and a run-only filter fails them all. The theorem states that no filter in this class can meet the interface, and the exact-octave filter is a concrete, non-vacuous instance: it accepts the intended carrier, so the failure is real, not an artifact of an empty class. The proof is a membership theorem, not a second wall: every predicate excluded here was already excluded by the earlier run-only obstruction T10RunHistoryScaleCouplingBoundary.

The theorem does not claim that no filter can ever satisfy the interface. It does not classify the complement: filters keyed to pattern.support or pattern.topology lie outside both the run-only class and the quadratic family, and amplitude-pinning filters with an octave-varying level already meet all four witnesses. The theorem only establishes that this natural, maximally free candidate family sits inside the run-only class, and therefore cannot serve as a scale coupling.

/-- Fully concrete specialization to the constructed Gray-settled octave. -/
theorem canonicalExactOctaveFilter_violates_r4 :
    ¬ RecognitionGroundStateSelection
      (CarrierRealized
        (ExactOctaveFilter canonicalQ3SettledLedgerOctave)) :=
  exactOctaveFilter_violates_r4
    canonicalQ3SettledLedgerOctave

/-- Exact-octave equality is run-only. -/
theorem exactOctaveFilter_isRunOnly
    (octave : Q3SettledLedgerOctave) :
    IsRunOnly (ExactOctaveFilter octave) := by
  intro c d hcd
  unfold ExactOctaveFilter
  rw [hcd]

/-- The filter accepts the actual intended carrier over that octave. -/
theorem exactOctaveFilter_accepts_intended
    (octave : Q3SettledLedgerOctave) :
    ExactOctaveFilter octave
      (intendedGapOneFactorCarrier octave) :=
  rfl

What this page does not claim

The theorem does not classify all filters that fail the interface; it only covers the run-only and quadratic families. The theorem does not construct or assume any surviving coupling with an independently derived nonzero reference level. The theorem does not claim that no filter can ever satisfy the interface.

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/T10RunCascadeQuadraticScaleBoundary.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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