Physics Electron Proton Mass Ratio V2

Mass ratio and its ledger

The electron to proton mass ratio is one of the most precisely known numbers in physics: the electron weighs about 1/1836.15 as much as the proton. That ratio, roughly 0.0005446, has been measured to extraordinary precision, and it poses a long-standing puzzle because no simple theoretical rule predicts it from first principles. The number appears in atomic spectra, chemical binding energies, and the stability of matter, so a structural explanation would reach deep into the foundations of the standard model.

In Recognition Science, the framework models this ratio through its ledger, a discrete record of recognition events, and its cost, the forced price of recording one event. The framework's central cost function, J(x) = (x + 1/x)/2 - 1, vanishes when two masses are equal and grows as they separate. For the electron and proton, the framework's golden-ratio ladder suggests a structural value: phi^15 / phi^3 = phi^12, which is about 321.9, close to 322. The measured ratio 1836.15 divided by 322 is about 5.7, a gap the framework's research note attributes to a needed rung correction. That note is a research hypothesis, not a derived result.

The machine-checked library of formal theorems proves three general facts about the cost function applied to a mass ratio. First, the cost is zero when the two masses are equal. Second, the cost is never negative for positive masses. Third, the threshold phi - 3/2 is positive. These are true for any positive inputs, not specifically for the electron and proton, because the framework defines its cost as J(m/e) without ever defining m and e in physical terms. The formal certificate bundles these three facts, and its existence is itself a theorem.

The plain-language result is narrower than the framework's name suggests. The framework proves structural properties of its cost function, and it records a numerical coincidence between phi^12 and the measured ratio's square root, but it does not derive the electron-proton mass ratio from the framework's axioms. The research note is explicit: the paragraph above the formal code is where the idea was meant to go, not a result. What the framework establishes is that the cost function behaves sensibly for any mass ratio, and that a golden-ratio threshold is positive, not that the physical ratio follows.

For a reader, the honest takeaway is that the framework's machinery is in place, but the physical bridge is missing. The gap between 322 and 1836 is a factor of about 5.7, and the framework's own note says a rung correction is needed. That correction, if it exists, remains an open target. The formal library's contribution is a clean set of cost properties, not a prediction of the measured value.

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

theorem cert_inhabited : Nonempty ElecProtonRatioV2Cert := ⟨cert⟩

What this page does not claim

The framework does not derive the measured electron-proton mass ratio from its axioms. The numerical near-match with phi^12 is a research note, not a proved structural result. The formal theorems do not depend on any physical definition of the electron or proton.

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/Physics/Electron_Proton_Mass_Ratio_v2.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: