Standard Model Higgs Coupling Rs

Higgs coupling in RS

The Standard Model of particle physics describes how the Higgs field gives mass to other particles. The strength of that interaction with the top quark, the heaviest known particle, is called the top Yukawa coupling. Measured at the Large Hadron Collider, its value is about 0.994, strikingly close to 1. In Recognition Science (RS), this near-equality is not a coincidence but a target: the framework predicts that at a special unification scale, the coupling is exactly 1.

The classical entry point is the formula y_t = sqrt(2) * m_t / v, where m_t is the top quark mass (about 173 GeV) and v is the Higgs vacuum expectation value (about 246 GeV). Plugging in numbers gives y_t ≈ 0.994. The closeness to 1 has long intrigued physicists, but the Standard Model offers no reason for it. RS supplies a reason: it places the top Yukawa coupling at the phi^6 rung of its recognition cycle, where phi is the golden ratio, and derives that the coupling equals 1 at the Planck scale. This is a prediction, not a measurement, and it has a named falsifier: a precise measurement of the top Yukawa at unification that deviates from 1 by more than the framework's tolerance would refute the claim.

In Recognition Science, the framework models physical structure from a single starting point: reality keeps a ledger, a discrete record of recognition events, and the cost of recognition is forced by a proved cost function J(x) = (x + 1/x)/2 - 1. The module Higgs_Coupling_RS applies this cost function to the ratio of two masses, m/e, defining a domain cost. The machine-checked library of formal theorems proves three general facts about this cost: it vanishes when m equals e, it is nonnegative for positive inputs, and the threshold phi - 3/2 is positive. These are universal properties of the cost function, not specific to the Higgs boson. The module does not prove that the top Yukawa is 1; that remains a research note and a prediction.

The distinction matters. The formal theorems establish the mathematical behavior of the cost function, but they do not connect it to the physical top quark. That connection requires a definition of m and e in the particle's own terms, which the module does not provide. So the honest summary is: the framework's cost function has the right shape to describe a coupling that tends to 1, and the prediction is stated, but the physical bridge is open.

What a reader can take away: RS offers a concrete, falsifiable reason for a number that the Standard Model leaves unexplained. The prediction is testable in principle, and the formal part is limited to general cost properties. The gap between the two is exactly where future work must go.

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

theorem cert_inhabited : Nonempty HiggsCouplingCert := ⟨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]

What this page does not claim

The module proves the top Yukawa equals 1; it only proves general cost properties. The prediction of y_t = 1 at unification has not been experimentally verified. The framework derives the fine-structure constant alpha; that is a separate open target.

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/StandardModel/Higgs_Coupling_RS.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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