Physics Proton Magnetic Moment3 From Jcost

Proton magnetic moment from cost

The proton's magnetic moment is a measure of how strongly the particle responds to a magnetic field. In nuclear magnetons, a standard unit for nuclear-scale magnetism, the measured value is about 2.793. The module named Proton_Magnetic_Moment3_FromJCost in the Recognition Science library appears to aim at deriving that number from the framework's cost function, but its formal content is far narrower.

The module defines a function called domainCost, a discrete record of the cost of recognizing a ratio of two quantities, as the framework's cost J applied to m divided by e. The three proved facts about this function are: it equals zero when m equals e, it is never negative for positive inputs, and a constant phi minus 3/2 is positive. These are general properties of the cost function itself, not specific to protons or magnetic moments. The module contains no definition of m or e in terms of proton mass, charge, or any other physical quantity.

The docstring records a research intention: that mu_p might equal phi^(1/3) nuclear magnetons, or alternatively e/(2m_p) times J(phi)^(-1), which would be about 8.47 nuclear magnetons. Neither expression is proved in the module. The formal theorems establish only the three general facts listed above, universally quantified over real numbers. The structure ProtonMuMoment3Cert packages these three facts, and the certificate is inhabited, meaning the facts are consistent and proven.

In plain language: the module proves that the cost function has certain basic properties, but it does not establish any value for the proton's magnetic moment. The connection to the proton remains a stated goal, not a result. A reader who wants the measured value 2.793 must go to experimental data; a reader who wants a derivation from RS must wait for a definition of m and e in proton terms.

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

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]

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

What this page does not claim

The module does not prove any numerical value for the proton's magnetic moment. The module does not establish that phi^(1/3) or 8.47 nuclear magnetons is the correct value. The module does not define m and e in physical terms.

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/Proton_Magnetic_Moment3_FromJCost.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: