vev_electron_rung_27_order
plain-language theorem explainer
The ratio of the electroweak vacuum expectation value to the electron mass lies between 300000 and 600000, placing it near rung 27 on the phi-ladder where phi^27 approximates 514229 within 7 percent. Researchers deriving mass hierarchies from ledger rung structure in Recognition Science cite this bound to support the structural assignment of the VEV scale. The proof is a direct numerical verification that splits the conjunction and evaluates the arithmetic.
Claim. $300000 < 246000 / 0.511 < 600000$, with the electroweak VEV taken as 246000 MeV and the electron mass as 0.511 MeV.
background
Recognition Science assigns particle masses via the phi-ladder: each rung multiplies a yardstick by a power of phi, with the electron placed near rung 27. The electroweak VEV v is compared to the electron mass m_e to locate the scale on this ladder. Module C-020 formalizes the structural framework for v approximately 246 GeV, showing that RS dissolves naturalness as a tuning problem because mass scales emerge from ledger rung structure rather than free parameters. The upstream Constants structure from LawOfExistence bundles abstract CPM constants such as Knet and Cproj but supplies no numerical content here.
proof idea
The proof is a one-line term-mode wrapper. Constructor splits the conjunction into two inequalities; norm_num then evaluates the concrete arithmetic 246000 divided by 0.511 against the bounds 300000 and 600000.
why it matters
This theorem supplies the numerical anchor for the phi^27 assignment inside C-020, confirming the VEV/electron ratio brackets the self-similar fixed point phi. It feeds the hierarchy problem dissolution by replacing parameter tuning with rung structure from the forcing chain (T5 J-uniqueness through T8 D equals 3). The result remains open on full numeric extraction of v from the Recognition Composition Law, as noted in the module registry.
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