IndisputableMonolith.Physics.ElectroweakZeroParamScoreCard
Scorecard module comparing Standard Model electroweak free-parameter count to Recognition Science, which claims zero free EW parameters. It packages four forcing inputs, four source theorems, an alpha-band check, and a product score that is positive under SM reduction and zero for RS. Phenomenologists auditing RS vs SM electroweak economy would cite the certificate. The module is mostly definitions and assembled certificates over imported mass, VEV, Fermi, and alpha results.
claimAn electroweak zero-parameter scorecard: $N_{\mathrm{SM}}^{\mathrm{EW}}$ free SM electroweak parameters versus $N_{\mathrm{RS}}^{\mathrm{EW}}=0$ RS parameters, built from four forcing inputs and four source theorems (including $\alpha^{-1}$ in its RS band), with score product positive under SM reduction and vanishing for RS.
background
Recognition Science aims to replace free electroweak inputs by quantities forced from the phi-ladder and related identities. Upstream, electroweak boson masses place the Z at a fixed rung ($m_Z = 2\varphi^{51}/10^6$ MeV in the stated units). VEV consistency (P5a partial) shows the Higgs VEV is not independent: tree-level EW relations give $v^2$ from $m_Z$, $\sin^2\theta_W$, and $\alpha^{-1}/\pi$. Fermi-from-RS then sends that VEV into $G_F = 1/(\sqrt{2},v^2)$.
Alpha bounds supply a rigorous interval for $\alpha^{-1}$ from the symbolic RS derivation. Constants supply the RS-native tick and related units. This module sits above those imports and does not re-derive masses; it tallies how many independent EW knobs remain once those chains are granted.
Sibling objects name SM vs RS parameter counts, an EW forcing-input bundle, four source theorems, an alpha-in-band predicate, score product/positivity, RS-zero and SM-reduction flags, and a final certificate.
proof idea
Definition and certificate module rather than a single deep proof. It fixes numeric SM and RS EW parameter counts, packages four forcing inputs and four named source theorems drawn from the mass/VEV/Fermi/alpha imports, checks alpha lies in the RS band, and forms a score product. Positivity of the score under SM reduction and vanishing for RS are recorded as simple algebraic or boolean facts over those counts. The certificate aggregates the flags. Heavy lifting lives upstream in ElectroweakMasses, VEVConsistency, FermiFromRSInputs, and AlphaBounds.
why it matters in Recognition Science
In the RS program the electroweak sector is supposed to be parameter-free once the forcing chain and ladder assignments are fixed. This module is the audit surface for that claim: it makes the SM count explicit, asserts RS count zero, and ties the claim to concrete upstream results (Z mass rung, VEV from $m_Z$ and weak mixing and alpha, $G_F$ from the VEV, alpha interval). No downstream used_by edges are listed, so it functions as a leaf scorecard for physics review rather than an intermediate lemma. It touches the broader zero-free-parameter narrative next to T5–T8 landmarks and the alpha band $(137.030, 137.039)$, without itself proving mass formulae or the fine-structure derivation.
scope and limits
- Does not re-prove Z, W, or Higgs mass formulae; imports them.
- Does not derive alpha from first principles; only consumes interval bounds.
- Does not establish full VEV or Fermi theorems beyond cited partial chains.
- Does not count QCD, Yukawa, or cosmological free parameters.
- Does not claim experimental fits beyond the assembled certificate flags.
depends on (5)
declarations in this module (13)
-
def
sm_ew_param_count -
def
rs_ew_param_count -
inductive
EWForcingInput -
theorem
four_forcing_inputs -
inductive
EWSourceTheorem -
theorem
four_source_theorems -
theorem
alpha_in_band -
theorem
sc_product -
theorem
sc_positive -
theorem
rs_zero -
theorem
sm_reduction -
structure
ElectroweakZeroParamScoreCardCert -
theorem
electroweakZeroParamScoreCardCert_holds