IndisputableMonolith.Verification.AnchorNonCircularityCert
Verification module certifying that single-anchor RS mass phenomenology is non-circular: SM beta coefficients depend only on gauge representations, not fermion masses. Phenomenologists cite NonCircularityCert, stationarity bounds, and dispersion-minimum certificates when defending the anchor scale. The argument is structural packaging of group-only beta data, mass-independence lemmas, and bound certificates rather than a deep analytic derivation.
claimThe module certifies that SM one-loop beta coefficients $\beta_0$ (QCD: $\beta_0=(11/3)C_A-(4/3)n_f T_F$ with $C_A=3$, $T_F=1/2$; QED: $\beta_0=-(4/3)\sum_i Q_i^2$) depend only on gauge data, not fermion masses; that stationarity and dispersion-minimum bounds hold at the anchor $\mu_\star$; and packages these into a non-circularity certificate for single-anchor RG transport of mass residues.
background
Recognition Science reads fermion masses at a single anchor scale $\mu_\star$ through the bridge data of RSBridge.Anchor: species, the charge index $Z$, the gap display $F(Z)=\ln(1+Z/\varphi)/\ln\varphi$, and mass-at-anchor. Empirical residues are defined by RG transport between scales (Physics.RGTransport). AnchorPolicy exposes that single-anchor interface and isolates stability and flavor hypotheses so downstream code can audit them.
A standard circularity objection is that beta functions used in the running might themselves depend on the masses being predicted. The SM one-loop structure blocks that route: QCD and QED $\beta_0$ are fixed by Casimirs, Dynkin indices, active flavor count, and electric charges alone. This module records that group-only dependence and turns it into verification certificates.
proof idea
Certificate and definition layer, not one deep theorem. It encodes the group-only SM beta data (SMBetaStructure, canonicalSMBeta), proves structural mass-independence (beta_is_mass_independent, is_mass_independent), supplies anchor positivity and $\varphi$-tied couplings (muStar_positive, lambda_from_phi), then builds StationarityCert / certified_stationarity_bounds and DispersionMinCert / certified_dispersion_minimum, and aggregates them as NonCircularityCert.
why it matters in Recognition Science
Answers the non-circularity half of the colleague concerns named in AnchorPolicy (radiative stability and flavor compatibility): RG kernels must not smuggle predicted masses back into the anchor. Graph used_by is empty, so the module is a terminal verification surface for the mass framework rather than an intermediate lemma. It underwrites audit of the RS bridge (Z-map, gap, mass-at-anchor) and of residue transport, sitting strictly downstream of Constants, Anchor, RGTransport, and AnchorPolicy. Without these certificates, single-anchor phenomenology would remain open to the charge that $\mu_\star$ running is tuned by the masses it claims to explain.
scope and limits
- Does not derive SM beta functions from Recognition first principles; imports group structure.
- Does not treat multi-loop betas, thresholds, or scheme conversions.
- Does not certify numerical mass fits, only structural mass-independence of beta.
- Does not discharge all AnchorPolicy stability hypotheses beyond packaged certs.
- Does not cover beyond-SM gauge factors or scalar self-couplings.
- Does not prove uniqueness of the anchor scale from dynamics alone.
depends on (4)
declarations in this module (18)
-
structure
SMBetaStructure -
def
canonicalSMBeta -
theorem
stationarity_structural -
theorem
beta_is_mass_independent -
theorem
lambda_from_phi -
theorem
muStar_positive -
structure
StationarityCert -
def
certified_stationarity_bounds -
structure
DispersionMinCert -
def
certified_dispersion_minimum -
structure
NonCircularityCert -
def
is_mass_independent -
def
is_parameter_free -
def
canonical_anchor_cert -
theorem
anchor_mass_independent -
theorem
anchor_parameter_free -
theorem
anchor_value -
theorem
anchor_scale_certified