Masses Mass Law

The master mass law

The master mass law is the formula in Recognition Science that predicts the mass of a stable recognition state, called a particle. It is not an empirical fit. The law states that mass equals a sector yardstick times the golden ratio raised to the rung position, corrected by a charge-based gap. In symbols, m = yardstick(Sector) * phi^(r - 8 + gap(Z)). The number 8 is the fundamental cycle period tau_0, and r is the species-specific rung integer on the phi-ladder.

The module establishes three plain facts. First, the mass is always positive for any valid configuration. Second, the law exhibits phi-scaling: increasing the rung by 1 multiplies the mass by phi. Third, for a neutral baseline with Z = 0, the gap correction vanishes, so the formula reduces to the pure phi-power form. These are established in Lean, not assumed.

The gap correction itself is defined as gap(Z) = log_phi(1 + Z/phi), which adjusts the rung position for charge-induced skew. The sector yardstick is a prefactor that depends on the sector. The law is a definitional model in the framework, and its predictions against measured particle masses are an empirical check, not a theorem.

MODEL predict_mass · IndisputableMonolith/Masses/MassLaw.lean

THEOREM predict_mass_pos · IndisputableMonolith/Masses/MassLaw.lean

THEOREM mass_rung_scaling · IndisputableMonolith/Masses/MassLaw.lean

THEOREM gap_zero_neutral · IndisputableMonolith/Masses/MassLaw.lean

What this page does not claim

The master mass law is not derived from the forcing chain in this module; it is a definitional model. The numerical agreement of the law with measured particle masses is not a theorem in this module.

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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