Physics Electroweak Zero Param Score Card

The electroweak scorecard

The Standard Model of particle physics describes the weak nuclear force and electromagnetism with four free parameters: the two gauge couplings g and g', the Higgs vacuum expectation value v, and the Higgs self-coupling λ. These numbers are not predicted by the theory; they are measured and inserted by hand. The electroweak zero-parameter scorecard is a machine-checked statement, within the Recognition Science framework, that these four inputs can instead be derived from a single forcing chain, reducing the count to zero.

The framework's library of formal theorems proves that each of the four Standard Model inputs traces back to a proved theorem in its own construction. The inverse fine-structure constant α⁻¹ is placed in the interval (137.030, 137.039). The weak mixing angle satisfies sin²θ_W · cos²θ_W = (8 − φ)/36, where φ is the golden ratio. The Z boson mass is set by a φ-power ladder, and the Higgs vacuum expectation value follows from a tree-level relation. The scorecard formalizes this as a certificate: a structure that holds the four derivations, the four source theorems, and the parameter counts, all checked by the machine.

The scorecard's honesty is part of its content. The α⁻¹ band is about 429,000 times wider than the CODATA 2022 measurement 137.035999177(21), and the framework's own library proves the construction value is excluded by that measurement at more than 30,000 standard deviations. The band holds the construction and the measurement at the same time, but that is not agreement; no measurement could have contradicted it. The scorecard does not import that external data, preserving the forward construction clean, but it does not hide the verdict.

In Recognition Science, the electroweak sector is not a set of measured inputs but a consequence of the forcing chain that starts from the cost function J(x) = (x + 1/x)/2 − 1. The scorecard's four source theorems are the uniqueness of that cost function, the forcing of the golden ratio, the eight-tick cycle, and the cube gauge embedding. The framework models these as the only inputs needed, and it proves the reduction from four parameters to zero. The plain statement is that the framework derives the electroweak sector's shape from its own axioms, with nothing fitted.

What a reader can take away is a precise claim with its limits attached. The zero-parameter claim is a theorem about the framework's construction, not a prediction that matches the measured world. The one numerical anchor is a window, not a match. The scorecard is a proof of internal consistency, and its own documentation says so.

/-- The SM electroweak parameter count. -/
def sm_ew_param_count : ℕ := 4

/-- RS free parameters. -/
theorem rs_zero : rs_ew_param_count = 0 := rfl

/-- α⁻¹ ∈ (137.030, 137.039). -/
theorem alpha_in_band : (137.030 : ℝ) < alphaInv ∧ alphaInv < 137.039 :=
  ⟨Numerics.alphaInv_gt, Numerics.alphaInv_lt⟩

/-- sin²θ_W · cos²θ_W = (8-φ)/36. -/
theorem sc_product : sin2_theta_W_rs * cos2_theta_W_rs = (8 - phi) / 36 :=
  sin2_cos2_product

/-- The RS forcing chain inputs that determine the EW sector. -/
inductive EWForcingInput
  | alpha_em
  | weinberg_angle
  | z_mass_rung
  | vev_from_tree
  deriving DecidableEq, Fintype

/-- Each forcing input traces to a proved theorem. -/
inductive EWSourceTheorem
  | t5_jcost_uniqueness
  | t6_phi_forcing
  | t7_eight_tick
  | cube_gauge_embedding
  deriving DecidableEq, Fintype

What this page does not claim

The scorecard does not claim the α⁻¹ band matches the measured fine-structure constant. The scorecard does not claim the electroweak derivations are physically validated by experiment. The scorecard does not claim the four source theorems are the only possible inputs to the electroweak sector.

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/ElectroweakZeroParamScoreCard.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: