Foundation Hierarchy Dissolution

Foundation Hierarchy Dissolution

Foundation hierarchy dissolution is the Recognition Science (RS) resolution of the Standard Model hierarchy problem. In RS, there is no hierarchy problem: the mass spectrum is set by the φ-ladder, a geometric and forced structure, not by radiative corrections. The question "why isn't the Higgs mass driven to Planck scale?" dissolves because masses come from ledger rung positions, not from divergent loop integrals.

The module establishes that fermion mass ratios are geometric, specifically powers of φ. For instance, the theorem mass_ratio_geometric proves that the ratio of the muon mass to the electron mass equals φ^11. This is a THEOREM in Lean, derived from the existing lepton hierarchy geometric result.

The core theorem, hierarchy_problem_dissolves, states that for any integer rung r, the mass on that rung equals E_coh * φ^r. This is a definitional equality, meaning the rung mass law is built into the structure. The hierarchy dissolution structure implies the rung mass law, as shown by hierarchy_dissolution_implies_rung_law.

The module explicitly does not claim to have proven that there are no radiative corrections. The docstring marks an OPEN interface claim: mass_on_rung has no cutoff argument, but absence from a function signature is not yet a theorem comparing ultraviolet regularizations. Such a theorem would need a cutoff-indexed mass model and a proof that its value is constant in the cutoff.

MODEL hierarchy_problem_dissolves · IndisputableMonolith/Foundation/HierarchyDissolution.lean

THEOREM mass_ratio_geometric · IndisputableMonolith/Foundation/HierarchyDissolution.lean

THEOREM hierarchy_problem_dissolves · IndisputableMonolith/Foundation/HierarchyDissolution.lean

THEOREM hierarchy_dissolution_implies_rung_law · IndisputableMonolith/Foundation/HierarchyDissolution.lean

What this page does not claim

Not a proof that radiative corrections are absent, only that the mass model has no cutoff argument. Not a derivation of the fine-structure constant alpha. Not a claim that the Standard Model is false.

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/Foundation/HierarchyDissolution.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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