IndisputableMonolith.Astrophysics.RS_AST_Structural_010
Astrophysics module packaging structural certificate 010: a nonnegative domain cost built from the RS J-cost, a positive canonical threshold, and an inhabited certificate record tying them together. Observers of RS structural claims in astrophysics cite it as a self-contained cert bundle. The module is mostly definitions plus elementary positivity and evaluation lemmas.
claimThe module introduces a domain cost $C$ (nonnegative, evaluated at equality points), a canonical threshold $\theta>0$, and a certificate record $\mathsf{RSASTStructural010Cert}$ inhabited by a concrete witness assembling $C$ and $\theta$ for RS astrophysics structural claim 010.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS-native tick $\tau_0=1$.
In the astrophysics layer, structural claims are packaged as small certificate records rather than free-floating inequalities. This module defines a domain-level cost (a pull of J-cost onto the relevant domain), proves it is nonnegative, records its value under equality of arguments, and fixes a positive canonical threshold against which the cost is compared.
The local setting is certificate infrastructure for RS_AST structural item 010: definitions plus the elementary analytic facts needed so downstream astrophysics theorems can assume an inhabited cert rather than re-prove cost positivity.
proof idea
Definition-heavy module. domainCost is introduced as a Cost-derived functional on the domain; domainCost_nonneg and domainCost_at_eq are short algebraic or Cost-library appeals. canonicalThreshold is a positive constant (canonicalThreshold_pos). RSASTStructural010Cert is a structure bundling these; cert and cert_inhabited supply a concrete inhabitant. No deep tactic proof; the argument is assembly of Cost nonnegativity and a fixed positive threshold into an inhabited certificate.
why it matters in Recognition Science
Gives the astrophysics side a named, inhabited structural certificate (010) so later RS astrophysics results can depend on a single cert object rather than ad-hoc cost inequalities. Imports only Constants and Cost, so it sits early in the astrophysics stack: domain cost and threshold are the primitive analytic content; the cert record is the export surface.
No downstream used_by edges are recorded yet; the module is a leaf packaging unit. In the broader RS forcing picture it does not touch T5–T8 directly, but it reuses the J-cost uniqueness lineage via Cost whenever domain mismatch is scored. It closes a small scaffolding gap: structural claim 010 becomes a typed, inhabited certificate instead of an informal inequality.
scope and limits
- Does not derive domainCost from first principles beyond the Cost import.
- Does not prove any astrophysical observation or mass/ladder formula.
- Does not connect certificate 010 to T5–T8 or the eight-tick octave.
- Does not assert uniqueness of the canonical threshold choice.
- Does not discharge broader RS_AST claims beyond inhabiting this cert record.