Masses Mass Law Gap Zero Neutral

The neutral baseline

The recognition gap is a correction term inside the framework's master mass formula, a discrete record of how a particle's charge shifts its position on a ladder of allowed masses. The formula assigns each stable state a mass proportional to a sector yardstick times the golden ratio raised to a power: rung minus 8 plus the gap. The gap itself is defined as log_phi(1 + Z/phi), where Z is a charge-based integer shift. The theorem gap_zero_neutral proves that when Z is zero, the gap is exactly zero: log_phi(1 + 0) = 0. That is the entire content of the declaration.

What this establishes is a baseline. The neutral case, no charge shift, sits at the reference point of the ladder. The formula's other terms, the rung integer and the sector yardstick, carry the species and sector information; the gap only corrects for charge skew. With Z = 0, the correction vanishes, and the mass formula reduces to yardstick times phi^(r - 8). The theorem is a lemma about the logarithm, not a physical measurement. It states a fact about the framework's own definition, verified by the machine-checked library of formal theorems.

The declaration does not claim that any real particle has zero charge shift, nor that the neutral baseline matches any measured mass. It does not assert that the gap formula is correct physics; that is a modeling choice, not a proved result. The theorem only cleans the arithmetic at one point of the definition. Its value is organizational: it fixes the origin from which the ladder's rungs are counted, so that later comparisons against measured particle masses have a well-defined reference.

/-- The "gap" term corrects for the charge-based shift.
    When Z=0 (neutral sector baseline), gap(0) = 0. -/
theorem gap_zero_neutral : gap_correction 0 = 0 := by
  unfold gap_correction
  simp only [Int.cast_zero, zero_div, add_zero, Real.log_one, zero_div]

/-- The recognition gap correction term: gap(Z) = log_φ(1 + Z/φ).
    This term corrects the rung position based on the charge-induced skew. -/
noncomputable def gap_correction (Z_val : ℤ) : ℝ :=
  Real.log (1 + (Z_val : ℝ) / phi) / Real.log phi

What this page does not claim

The declaration does not claim any real particle has zero charge shift. It does not assert the gap formula is correct physics, only that it is a definition. It does not compare the neutral baseline to any measured mass.

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

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