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module module moderate

IndisputableMonolith.Physics.ProtonRadius

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This module assembles definitions and theorems for proton radius estimates together with lepton mass ratios inside the Recognition Science phi-ladder. It records the muon-electron mass ratio as phi to the eleventh power from the rung difference between electron (rung 2) and muon (rung 13). Researchers deriving particle properties from the J-cost function would cite these results. The module consists of positivity facts, ratio lemmas, and radius calculations built directly on the imported JcostCore machinery.

claim$m_μ/m_e = φ^{11}$ with electron rung 2 and muon rung 13. Proton radius follows from the mass formula yardstick × φ^(rung − 8 + gap(Z)) applied to the appropriate rung.

background

Recognition Science derives masses from the J-cost function J(x) = (x + x^{-1})/2 − 1 supplied by the imported JcostCore module. Particle states occupy discrete rungs on the self-similar phi-ladder whose spacing is fixed by the T5 J-uniqueness and T6 phi fixed-point steps. The module introduces auxiliary facts phi_pos and phi_gt_one to guarantee ordering and positivity before computing explicit ratios and radius estimates.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The declarations supply concrete rung assignments and radius estimates that feed the Recognition Science mass formula and the T0-T8 forcing chain. They instantiate the phi-ladder for leptons and the proton, supporting later derivations of constants such as alpha and G in native units.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (13)