Masses Mass Genesis T10 Double Entry Mass Quantum Two Valued Occupation Settleme

The settlement load

In the Recognition Science framework, a ledger is a discrete record of events, and a mass is assigned to a pattern of occupation on an eight-tick cycle. The declaration twoValuedOccupation_settlementLoad_eq_normSq_mul_cutCount proves a precise formula for the load of such a pattern. It states that the load equals the squared magnitude of the occupation's amplitude multiplied by the number of times the pattern changes value between consecutive ticks. This is a theorem about a model: the framework defines the load and the cut count, then proves the relationship between them.

The formula is settlementLoad occ = Complex.normSq lam * cutCount occ for a two-valued occupation with amplitude lam. The load is the squared norm of the settlement window, which is the discrete tick-derivative of the occupation. The cut count is the number of positions where the occupation changes value. The theorem shows that the load factors cleanly into an amplitude-squared term and a count of changes. This means the unit of amplitude cancels in any ratio of loads, which is a key property for comparing masses.

The result is a theorem on a model carrier. The framework defines the ledger, the occupation, and the load; the theorem proves the formula within that model. It does not claim that the amplitude lam is derived from anything more fundamental. The choice of lam is a units choice, and the theorem shows that this choice cancels in ratios. The theorem also does not claim anything about how many voxels a particle occupies; it concerns a single eight-tick voxel.

The honest wall is that the settlement window does not fix a scale. The literal value 1 in a unit commit occupation is an indicator of a decidable ledger predicate. The forced content is two-valuedness, and which two complex values appear is a units choice. The theorem establishes the relationship, not the value of the amplitude itself.

The practical consequence is that the mass of a two-valued occupation is determined by two factors: the amplitude and the number of changes. This separates the scale choice from the structural count. The framework proves that the load is always an even multiple of the unit squared amplitude for integer occupations, and for Boolean occupations it lies in the set {0, 2, 4, 6, 8}. The unit-free wall of four holds for any posting unit, making the substrate requirement harder, not easier.

theorem t10DoubleEntryUnitFreeMassWallCert :
    T10DoubleEntryUnitFreeMassWallCert where
  unit_factors_out := twoValuedOccupation_settlementLoad_eq_normSq_mul_cutCount
  cutCount_even := twoValuedOccupation_cutCount_even
  cutCount_le_eight_field := cutCount_le_eight
  load_cutCount_cancel := twoValuedOccupation_load_cutCount_cancel
  unit_free_mass_ratio_le_four := twoValuedOccupation_mass_ratio_le_four
  wall_tight_at_cuts_two_and_eight := twoValuedOccupation_mass_ratio_wall_tight
  vacuum_and_full_cycle_massless :=
    ⟨twoValuedVacuum_settlementLoad, twoValuedFull_settlementLoad⟩
  three_valued_discriminates_R9 :=
    ⟨threeValuedDiscriminatingWitness_settlementLoad,
      threeValuedDiscriminatingWitness_cutCount,
      threeValuedDiscriminatingWitness_R9_fails_at_one⟩
  scope_one_eight_tick_voxel := trivial
  scope_lepton_ratios_not_addressed := trivial
  scope_posting_unit_not_derived := trivial

theorem t10DoubleEntryUnitFreeMassWallCert :
    T10DoubleEntryUnitFreeMassWallCert where
  unit_factors_out := twoValuedOccupation_settlementLoad_eq_normSq_mul_cutCount
  cutCount_even := twoValuedOccupation_cutCount_even
  cutCount_le_eight_field := cutCount_le_eight
  load_cutCount_cancel := twoValuedOccupation_load_cutCount_cancel
  unit_free_mass_ratio_le_four := twoValuedOccupation_mass_ratio_le_four
  wall_tight_at_cuts_two_and_eight := twoValuedOccupation_mass_ratio_wall_tight
  vacuum_and_full_cycle_massless :=
    ⟨twoValuedVacuum_settlementLoad, twoValuedFull_settlementLoad⟩
  three_valued_discriminates_R9 :=
    ⟨threeValuedDiscriminatingWitness_settlementLoad,
      threeValuedDiscriminatingWitness_cutCount,
      threeValuedDiscriminatingWitness_R9_fails_at_one⟩
  scope_one_eight_tick_voxel := trivial
  scope_lepton_ratios_not_addressed := trivial
  scope_posting_unit_not_derived := trivial

What this page does not claim

The amplitude lam is not derived from anything more fundamental. The theorem does not specify how many voxels a particle occupies. The charged-lepton ratios are not addressed by this result.

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/T10DoubleEntryMassQuantum.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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