sm_verification_cert
The mass verification certificate definition assembles the positivity of all fermion masses, the golden ratio scaling of the mass law, and the enumeration of nine fermions into a single structure. Researchers auditing Recognition Science predictions for Standard Model particles would cite this to confirm the core mass law properties hold with zero free parameters. The construction is a direct record definition that supplies the three fields from upstream theorems on positivity, rung scaling, and finite cardinality.
claimThe verification certificate asserts that every fermion has positive mass, that the predicted mass in any sector scales exactly by the golden ratio φ when the rung index increases by one, and that the model defines exactly nine fermions.
background
The module states the Standard Model mass verification under the Recognition Science mass law, where particle mass equals the sector yardstick times φ raised to (rung minus 8 plus gap from charge Z), with all quantities derived from cube geometry and charge structure. The referenced structure collects three assertions: positivity of fermion masses, the φ-scaling relation for predicted masses, and the count of nine fermions. It draws on the upstream theorem that the mass law exhibits φ-scaling by increasing rung by 1 scales mass by φ, the theorem proving all fermion masses positive, and the cardinality theorem fixing nine fermions.
proof idea
The definition constructs the verification certificate record by assigning the positivity field directly from the theorem proving all fermion masses positive, the scaling field from the mass rung scaling theorem, and the cardinality field from the finite type cardinality theorem.
why it matters in Recognition Science
This definition certifies the proved positivity and φ-scaling properties of the mass law for the nine Standard Model fermions, matching the module documentation that these aspects are established. It packages results from the phi-ladder mass formula in the Recognition Science framework, where φ arises as the self-similar fixed point and scaling follows from the forcing chain. No downstream uses appear yet, leaving open the step to full numerical PDG comparisons via interval arithmetic.
scope and limits
- Does not supply numerical PDG comparisons or experimental bounds.
- Does not derive sector yardsticks or gap corrections from geometry.
- Does not extend to bosons or particles beyond the nine fermions.
- Does not perform interval arithmetic on the φ-power predictions.
formal statement (Lean)
168def sm_verification_cert : SMVerificationCert where
169 all_positive := all_fermion_masses_pos
proof body
Definition body.
170 phi_scaling := mass_rung_scaling
171 nine_fermions := fermion_count
172
173end
174
175end SMVerification
176end Masses
177end IndisputableMonolith