Physics Magnetic Moment5

The module's actual scope

The electron's anomalous magnetic moment is a measured quantity: it deviates from the simple Dirac value by about 0.00116, a difference explained in conventional physics by quantum electrodynamics. The module named physics-magnetic-moment5 does not derive that number. Its Lean file defines a cost function, a measure of recognition effort, as Jcost (m / e), where m and e are real numbers standing for two masses or energies. The module then proves three general facts about this function: it equals zero when m equals e, it is never negative for positive inputs, and a constant called canonicalThreshold, defined as phi minus 3/2, is positive.

These three facts are true for any positive real inputs, not for any specific physical system. The docstring in the file states this plainly: the module proves nothing specific to the magnetic moment, because the cost function is defined without reference to one. The same body of text is shared verbatim with 2383 sibling modules. The file is a template, a scaffold waiting for a definition of m and e in the subject's own terms. What would make it a theorem about magnetism is a definition of those variables from the physics of the electron.

The research note records where the idea was meant to go: a_e ~ J(phi)^(1/2) * alpha/(2pi), with alpha = 1/137, giving about 0.0004 against the measured 0.00116. That is a structural guess, not a result. The Lean proofs establish only the general properties of the cost function, which are already proved once in a shared template module. The certificate structure MagMoment5Cert packages the three theorems, and the definition cert shows they hold, but the certificate attests to generic facts, not to any magnetic moment.

In plain language: the module is honest about its own limits. It proves that a certain cost function behaves well, and it names a threshold constant that is positive. It does not claim to explain the anomalous magnetic moment. The gap between the note's aspiration and the file's actual content is the gap between a research direction and a formal result. A reader should take the module for what it is: a clean, machine-checked proof of three elementary inequalities, and a placeholder for a physical definition that does not yet exist.

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 derive or explain the measured anomalous magnetic moment of the electron. The research note's formula a_e ~ J(phi)^(1/2) * alpha/(2pi) is not a proved theorem. The cost function's general properties are not specific to magnetism; they hold for any positive real inputs.

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/MagneticMoment5.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: