Masses Verification Electron Relative Error

The electron mass check

The electron mass is one of the best-measured quantities in physics. The Particle Data Group's 2024 review gives 0.51099895069 MeV, a number known to about one part in a hundred million. Recognition Science (RS) does not try to match that precision. Its claim is far more modest: a simple formula built from the golden ratio phi and powers of two lands within 0.04 of the measured value, meaning the prediction is within four percent of experiment.

The formula itself is a definitional choice, not a derived law. For the lepton sector, RS sets the prediction for the electron as phi raised to the 59th power divided by 4194304000000, expressed in MeV. Here phi is the golden ratio, about 1.618, and 4194304000000 is 2 to the 22nd power times 10 to the 6th. The machine-checked library of formal theorems proves that this expression, when plugged into the framework's mass ladder, yields a number whose relative error against the imported experimental value is less than 0.04. That is the entire content of the declaration: a bound on the difference between a formula and a measurement.

What the declaration does not do is just as important as what it does. The experimental mass is an imported constant, not something RS derives. The framework explicitly quarantines such experimental values from its certified surface, meaning the comparison is a check, not a proof. The four percent band is also not a statement about the true uncertainty of the prediction; it is a deliberately loose bound chosen so that the inequality can be verified by simple arithmetic. A tighter bound would require more precise handling of the golden ratio's powers, which the library does not attempt for this declaration.

In Recognition Science, the mass ladder is a model: a definitional structure that places particle masses on a phi-power grid. The electron check shows that one rung of that grid sits close to the measured world. It does not show that the grid is the reason the electron has the mass it does. The framework's own documentation marks this entire comparison as quarantined from its certified theorems, a deliberate separation between what is derived and what is merely observed.

The practical lesson for a reader is precise. A stranger to RS can take the formula, compute phi to the 59th power, divide by 4194304000000, and get a number within four percent of the electron's measured mass. That is a reproducible fact. What remains open is why that formula should work at all, and whether the pattern extends to other particles with the same looseness. The declaration itself offers no mechanism; it only certifies the arithmetic.

def m_e_exp : ℝ := 0.51099895069

def m_e_exp : ℝ := 0.51099895069

theorem electron_pred_eq : rs_mass_MeV .Lepton 2 = electron_pred :=
  lepton_pred_eq_aux 59 2 (by norm_num)

theorem muon_relative_error :
    |rs_mass_MeV .Lepton 13 - m_mu_exp| / m_mu_exp < 0.04 := by
  rw [muon_pred_eq]
  have hb := muon_mass_bounds
  have hexp_pos : (0 : ℝ) < m_mu_exp := by unfold m_mu_exp; norm_num
  rw [div_lt_iff₀ hexp_pos, abs_lt]
  unfold m_mu_exp
  constructor <;> nlinarith [hb.1, hb.2]

theorem muon_relative_error :
    |rs_mass_MeV .Lepton 13 - m_mu_exp| / m_mu_exp < 0.04 := by
  rw [muon_pred_eq]
  have hb := muon_mass_bounds
  have hexp_pos : (0 : ℝ) < m_mu_exp := by unfold m_mu_exp; norm_num
  rw [div_lt_iff₀ hexp_pos, abs_lt]
  unfold m_mu_exp
  constructor <;> nlinarith [hb.1, hb.2]

What this page does not claim

The electron mass is derived from first principles within RS. The four percent band represents the true uncertainty of the prediction. The formula works for all particles with the same accuracy. The declaration proves the mass ladder is physically correct.

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/Verification.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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: