Physics Kaon Mass Rs

The kaon mass and its ledger entry

The kaon is a subatomic particle, a meson made of a quark and an antiquark, that weighs about 494 MeV (mega-electronvolts), roughly half the mass of a proton. Physicists have measured its mass with great precision; the Particle Data Group lists 493.677 MeV as the accepted value. The number appears in the framework's library as a research note: the module states that phi^13 times 0.949 equals 494 MeV, matching the kaon's mass to the precision of that rounded figure.

The framework's machine-checked library of formal theorems does not prove that this match is meaningful. The module defines a cost, a measure of how far one value is from another, as a function of the ratio of two masses. Its three proved theorems are general: the cost is zero when the two masses are equal, it is never negative for positive inputs, and a certain threshold involving the golden ratio is positive. These facts hold for any two positive numbers, not specifically for the kaon and any particular reference mass. The docstring is explicit: the paragraph connecting phi^13 to the kaon is a research note recording where the idea was meant to go, not a result.

In Recognition Science, the framework models physical quantities through a forced cost function J(x) = (x + 1/x)/2 - 1. The module applies this to the kaon by setting the cost to J(m/e), where m is the kaon mass and e is some reference mass. The three theorems establish that this cost behaves sensibly: it vanishes at equality, stays nonnegative, and has a positive threshold. What the module does not do is define what m and e are in the kaon's own terms. Without that definition, the module is a template, shared verbatim with 2383 sibling modules, not a theorem about the kaon.

What this means in plain language: the framework has a general tool for comparing masses, and a note that phi^13 times 0.949 lands near the kaon's measured mass. The tool is proved correct in its general properties. The specific match is an empirical observation awaiting a derivation, not a proved result. A reader should treat the 494 MeV match as a hypothesis with a named falsifier: a more precise measurement of the kaon mass that does not sit at phi^13 times 0.949 within the experimental error would break the match.

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

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]

structure KaonMassCert 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

What this page does not claim

The framework proves the kaon mass equals phi^13 times 0.949 MeV. The 494 MeV figure is the current CODATA or PDG accepted value. The module's theorems are specific to the kaon rather than general facts about the cost function.

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/Kaon_Mass_RS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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