Physics Charmonium Mass3 From Phi Ladder

The J/psi mass estimate

The J/psi is a subatomic particle, a meson made of a charm quark and its antiquark, first discovered in 1974. Its measured mass is about 3097 MeV (million electron volts), a standard value from particle physics. In the Recognition Science framework, a research note records an estimate: phi^18 times a coherence energy times a dimensionless factor gives roughly 3094 MeV, within about 0.1 percent of the measured value. This estimate is a research aspiration, not a proved result.

The module named Charmonium_Mass3_FromPhiLadder contains formal statements in a machine-checked library of formal theorems. The library proves three general facts about a cost function, which the framework models as a measure of recognition effort. The cost function vanishes when its two inputs are equal, it is never negative for positive inputs, and a threshold value phi minus 3/2 is positive. These facts are universally quantified and apply to any positive real numbers, not specifically to the J/psi particle.

The central definition sets the domain cost as Jcost of the ratio m over e, where m and e are placeholders for mass and energy. Because the definition never specifies what m and e mean for charmonium, the module proves nothing about the J/psi itself. The docstring states this plainly: the paragraph above is a research note recording where the idea was meant to go, not a result. The same body is shared verbatim with 2383 sibling modules.

What the module does establish is a template. It shows that if one defines a cost in terms of a ratio, the cost is zero at equality, nonnegative for positive inputs, and has a positive canonical threshold. To make this a theorem about the J/psi, one would need a definition of m and e in the particle's own terms. That definition does not appear in the module, so the physical claim remains a hypothesis, not a derivation.

In Recognition Science, the framework models recognition cost as forced, and the golden ratio phi appears throughout its structure. Here phi appears in the threshold value and in the research note's estimate. The estimate's near-agreement with the measured J/psi mass is an empirical curiosity, but without a derivation of the coherence energy and the dimensionless factor, it does not rise to a proved prediction. The library's formal content stops at the general cost properties.

structure JPsiMass3Cert 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 cert_inhabited : Nonempty JPsiMass3Cert := ⟨cert⟩

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 proves the J/psi mass is 3094 MeV. The module derives the coherence energy or the dimensionless factor from first principles. The near-match with the measured J/psi mass is a proved prediction.

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/Charmonium_Mass3_FromPhiLadder.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

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