Masses Mass Genesis T10 Run Reference Provenance Boundary

Provenance boundary

The T10 run-reference provenance boundary is a machine-checked record in the Recognition Science library that settles a specific accounting question. The question concerns a continuum target value, phi^42/8, which appears in the mass-genesis campaign. The numeral 42 is not a rung of the seed pattern; a theorem proves the gap-one worldline seed has rung 0. Instead, 42 equals 55 minus 13, the Electroweak anchor offset, so the number carries anchor and topology ancestry, not settlement-integer ancestry.

The module also proves the target value already lies in the permitted field Q(phi), and that it is exactly the intended gap-one factor amplitude squared. A posting-reference law accepts the intended amplitude if and only if the law's function returns the continuum target. These are all kernel-checked theorems.

The key structural result is a counterexample. A constant functional that always returns the target factors through every run summary and is Q(phi)-valued. Therefore, no theorem of the form "every functional factoring through a killed summary and landing in Q(phi) misses the target" is true. The underivability floor is not expressible by these extensional properties.

In Recognition Science, this boundary record clarifies what is and is not claimed. No derivation of a run-reference functional is given, and no proof that one is impossible. A function returning the target exists trivially, so only the ancestry of a candidate can decide the campaign. The remaining question is provenance, not extension.

/-- The manager's proposed "rung 42" is not the seed rung. -/
theorem gapOne_seed_rung_eq_zero :
    rungOf (worldlinePattern gapOneTwoPhaseMode) = 0 := by
  simp [rungOf, rungFromTopology, worldlinePattern]

/-- The numeral 42 is the Electroweak anchor offset 55 - 13. -/
theorem electroweak_anchor_phi_offset_eq_fortyTwo :
    Anchor.r0 Anchor.Sector.Electroweak - 13 = (42 : ℤ) := by
  rw [YardstickPremiseFreeCert.r0_ew_certified_eq_55]
  norm_num

/-- The squared continuum target already belongs to the permitted φ-field. -/
theorem continuumReferenceLoad_inQPhi :
    InQPhi continuumReferenceLoad := by
  unfold continuumReferenceLoad
  exact (inQPhi_phi_pow 42).div
    ⟨(8 : ℚ), (0 : ℚ), by norm_num⟩
    (by norm_num)

/-- Consequently, factorization through any killed run summary plus φ-field
valuedness cannot prove the requested W6 value exclusion. -/
theorem factorization_and_phiField_do_not_exclude_target
    {α : Type*}
    (summary : Q3SettledLedgerOctave → α) :
    ¬ (∀ f : ExactRunFunctional,
      FactorsThrough summary f →
      PhiFieldValued f →
      ∀ octave, f octave ≠ continuumReferenceLoad) := by
  intro h
  have hfac : FactorsThrough summary constantContinuumReference :=
    ⟨fun _ => continuumReferenceLoad, fun _ => rfl⟩
  have hfield : PhiFieldValued constantContinuumReference := by
    intro octave
    simpa [constantContinuumReference] using
      continuumReferenceLoad_inQPhi
  exact
    (h constantContinuumReference hfac hfield
      canonicalQ3SettledLedgerOctave) rfl

What this page does not claim

No derivation of a run-reference functional is given. No proof that a run-reference functional is impossible is given. The numeral 42 is not the rung of the seed pattern.

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/T10RunReferenceProvenanceBoundary.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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