IndisputableMonolith.StandardModel.RS_STD_Structural_005
Structural certificate module for Standard Model item 005 in the Recognition Science stack. It packages a nonnegative domain cost, a positive canonical threshold, and an inhabited certificate record tying those quantities together. Cite it when auditing SM structural claims that need a cost-threshold witness rather than a dynamical derivation. The module is mostly definitions plus elementary positivity and evaluation lemmas.
claimDefine a domain cost $C$ (nonnegative), a canonical threshold $\theta>0$, and a certificate record asserting the structural 005 relation between $C$ and $\theta$ in RS-native units. The certificate type is inhabited.
background
Recognition Science treats Standard Model structure as forced data on the phi-ladder and the J-cost, not as free Lagrangian parameters. This module sits in the StandardModel domain and imports only Constants (RS time quantum $\tau_0=1$ tick) and Cost (the J-cost infrastructure).
Sibling objects introduce a domain-level cost functional, its pointwise evaluation identity, nonnegativity, a canonical positive threshold, and a bundled certificate RSSTDStructural005Cert with an inhabitation witness. The local goal is bookkeeping: fix the cost-threshold pair that later SM structural claims can quote without re-deriving positivity or units.
No forcing-chain step (T5--T8) is proved here; the module assumes the ambient RS cost and constant conventions and exposes a narrow structural interface labeled 005.
proof idea
Definition-heavy module. Cost and threshold are introduced as defs; nonnegativity and positivity are short lemmas; evaluation at a point is an equality lemma. The certificate is a structure (or Prop bundle) assembled from those pieces, closed by an inhabitation proof that supplies concrete witnesses. No deep tactic script or upstream theorem chain beyond the Cost/Constants imports.
why it matters in Recognition Science
Gives a named, auditable hook for Standard Model structural claim 005 so downstream SM developments can depend on a single certificate rather than ad hoc inequalities. Used_by is currently empty in the mirror graph, so this is a leaf interface: it stabilizes notation and sign constraints for later particle-content or coupling-structure arguments in the RS Standard Model layer.
It does not itself force gauge groups, generations, or couplings from T5--T8; it only certifies the local cost-threshold packaging those arguments may need. Landmarks such as $J$-uniqueness, $\phi$, the eight-tick octave, and $D=3$ remain upstream context, not theorems of this file.
scope and limits
- Does not derive Standard Model gauge groups, representations, or generation count.
- Does not prove J-uniqueness, phi-forcing, eight-tick structure, or D=3.
- Does not compute masses, alpha, or rung placements on the phi-ladder.
- Does not supply dynamical evolution; only static cost, threshold, and certificate data.
- Does not claim downstream consumers yet; used_by is empty in the graph.