Nuclear Proton Electric Dipole V3

The proton's electric dipole

The proton's electric dipole moment (EDM) is a number that would tell you whether the proton's positive charge is distributed symmetrically. If the charge were slightly more concentrated toward one side, the proton would act like a tiny bar magnet, but with electric charge instead of magnetic poles. Physicists have measured this asymmetry and found it extraordinarily small: the current experimental bound is |d_p| < 2.1 × 10⁻²⁵ e·cm. That is less than a billionth of a billionth of a billionth of a centimeter times the elementary charge.

In the standard model of particle physics, the proton's EDM is not exactly zero. It receives tiny contributions from processes that violate a symmetry called CP, and those contributions are predicted to be far below the current experimental reach. The puzzle is that the strong nuclear force, which binds quarks into protons, has a term in its Lagrangian that could naturally produce an EDM about ten billion times larger than the experimental bound. The fact that no such large EDM is seen is known as the strong CP problem.

Recognition Science approaches this from a different starting point. The framework models reality as a ledger, a discrete record of recognition events, and derives a forced cost function J(x) = (x + 1/x)/2 − 1. The framework's library proves general facts about this cost: it vanishes when its two inputs are equal, it is nonnegative for positive inputs, and the threshold φ − 3/2 is positive. These three facts are formal theorems, checked by machine.

The module named Proton_Electric_Dipole_v3 applies this cost to the ratio of a mass m to a charge e, defining domainCost(m, e) = J(m/e). It proves the three general facts for this specific definition. But the module itself does not define what m and e mean for the proton. Its docstring says plainly: "It proves nothing specific to this subject." The research note attached to the module records the intended direction: from the framework's eight-tick uniqueness, the strong CP angle θ_QCD is forced to zero, and therefore the proton's EDM is exactly zero to all orders.

That prediction, if it holds, would resolve the strong CP problem by eliminating the offending term entirely. It is a hypothesis, not a theorem: the framework's library has not yet derived θ_QCD = 0 from its axioms. The falsifier is clear: any measurement of a nonzero proton EDM above the current bound would refute the prediction. Until then, the experimental bound remains the tightest constraint, and the framework's exact-zero claim remains an unproved consequence of its internal logic.

structure ProtonEDM_v3Cert where
  cost_at_eq : ∀ r : ℝ, r ≠ 0 → domainCost r r = 0
  cost_nonneg : ∀ m e : ℝ, 0 < m → 0 < e → 0 ≤ domainCost m e
  threshold_pos : 0 < canonicalThreshold

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)

noncomputable def cert : ProtonEDM_v3Cert where
  cost_at_eq := domainCost_at_eq
  cost_nonneg := domainCost_nonneg
  threshold_pos := canonicalThreshold_pos

What this page does not claim

The framework has not proved that the proton's electric dipole moment is zero; that remains a hypothesis. The module does not provide a physical definition of mass or charge for the proton. The framework's prediction does not explain why the experimental bound is so small; it claims the value is exactly zero instead.

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/Nuclear/Proton_Electric_Dipole_v3.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.

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