IndisputableMonolith.StandardModel.RS_STD_Structural_007
Structural certificate module for RS Standard Model item 007. It defines a non-negative domain cost equal to a fixed value at a reference point, a strictly positive canonical threshold, and an inhabited certificate packaging those facts. Model auditors cite it as the cost/threshold interface for this structural slot. Content is definitional plus elementary non-negativity and positivity lemmas.
claimThe module supplies a domain cost $C$ with $C \ge 0$ and $C$ matching a prescribed value at a reference argument, a canonical threshold $\theta > 0$, and an inhabited certificate asserting these structural properties for RS Standard Model item 007.
background
Recognition Science measures mismatch with a non-negative cost functional (the $J$-cost lineage from the Cost import). In RS-native units the fundamental tick is $\tau_0 = 1$ (Constants). Standard Model structural certificates package elementary positivity and normalization facts so later mass, charge, or generation arguments can assume a clean cost/threshold interface without re-proving it.
This module sits in the StandardModel domain. Sibling declarations introduce domainCost (a real-valued cost on the relevant domain), prove it is non-negative and hits a fixed value at a reference point, define canonicalThreshold with a positivity lemma, and wrap the package as RSSTDStructural007Cert with an inhabited instance cert.
proof idea
Definition module with short supporting lemmas, not a deep derivation. Domain cost is introduced by definition; non-negativity and the reference-point equality are discharged by direct unfolding and elementary real arithmetic. The canonical threshold is a positive constant (or constant expression) with a one-line positivity proof. The certificate structure bundles those facts; inhabitance is by constructing the record from the lemmas already proved.
why it matters in Recognition Science
Gives the Standard Model stack a named, machine-checked structural slot (007) for cost non-negativity and a positive threshold. Downstream SM arguments that need a cost yardstick or a separation threshold can import the inhabited certificate rather than re-open Cost. No downstream edges are recorded yet in the graph, so this module is presently a leaf interface: it closes a local scaffolding obligation and stands ready for generation, coupling, or mass-ladder certificates that cite RS-STD structural facts. It does not itself force $\phi$, the eight-tick octave, or $D=3$; those live in the T0--T8 forcing chain.
scope and limits
- Does not derive particle masses, charges, or mixing angles.
- Does not prove uniqueness of the domain cost among all RS costs.
- Does not force phi, the eight-tick period, or D = 3.
- Does not connect the threshold to experimental SM bounds.
- Does not discharge any sorry outside this structural package.