Masses Anchor

Masses anchor

Masses anchor is the Recognition Science module that centralises the parameter-free constants used to build particle mass yardsticks. It defines four sector constants, one per sector: lepton, up quark, down quark, and electroweak. Each sector gets two integers, B_pow and r0, which later enter a formula for a mass scale. The module also fixes the bridge coherence energy E_coh as phi to the power minus five, in electronvolts, and defines integer rung maps for charged fermions and bosons. All of this lives in the Model layer; no proof in the module claims experimental agreement.

The constants are not arbitrary numbers. They are written as arithmetic combinations of three cube-geometry quantities: the number of edges of a three-dimensional cube (12), the passive edges left after removing one (11), and the number of wallpaper groups (17). For example, the lepton B_pow is minus two times 11, giving -22, and the lepton r0 is four times 17 minus 6, giving 62. The module proves these arithmetic equalities as theorems, but it does not force which expression belongs to which sector. The sector assignment is explicitly not forced.

The yardstick formula itself is a definition: yardstick(s) equals two to the B_pow power, times E_coh, times phi to the r0 power. This is a model choice, not a derived law. The module also defines integer maps for particle species. Leptons have rung values 2, 13, and 19 for electron, muon, and tau. Up-type quarks have 4, 15, and 21 for up, charm, and top. Down-type quarks have 4, 15, and 21 for down, strange, and bottom. Bosons W, Z, and H all have rung 1. These rung values are definitions, not theorems.

What the module establishes in plain language is a clean, central repository of the constants that downstream mass modules import. It fixes the values and proves the arithmetic identities that connect them to cube geometry and the wallpaper constant. What it does not do is force the sector assignment or claim any match to measured masses. That separation is deliberate: the values are fixed, the sector assignment remains open.

MODEL Sector · IndisputableMonolith/Masses/Anchor.lean

THEOREM B_pow_Lepton_eq · r0_Lepton_eq · IndisputableMonolith/Masses/Anchor.lean

THEOREM B_pow_UpQuark_eq · r0_UpQuark_eq · IndisputableMonolith/Masses/Anchor.lean

THEOREM B_pow_DownQuark_eq · r0_DownQuark_eq · IndisputableMonolith/Masses/Anchor.lean

THEOREM B_pow_Electroweak_eq · r0_Electroweak_eq · IndisputableMonolith/Masses/Anchor.lean

MODEL yardstick · IndisputableMonolith/Masses/Anchor.lean

What this page does not claim

This answer does not claim that the sector assignment is forced by any theorem. This answer does not claim any experimental agreement for the mass constants. This answer does not claim that the rung integers are derived from the anchor constants.

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/Anchor.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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