IndisputableMonolith.Astrophysics.Solar_Radius_RS
Module packaging a Recognition Science certificate for the solar radius via a domain cost and a canonical positive threshold. Astrophysicists citing RS mass/length ladders would use the inhabited SolarRadiusCert record. The argument is definitional: nonnegativity of the cost, positivity of the threshold, and a bundled certificate, not a deep derivation from first principles.
claimThe module defines a domain cost $C$ on the relevant RS scale, proves $C \ge 0$ and an evaluation identity, introduces a canonical threshold $\theta > 0$, and packages an inhabited certificate $\mathrm{SolarRadiusCert}$ asserting that the solar radius sits at the certified RS scale relative to $\theta$ and $C$.
background
Recognition Science works in native units with $c = 1$ and length/time tied to the tick $\tau_0$ and the golden ratio $\phi$ forced at T6. The Cost import supplies the J-cost family (unique under the Recognition Composition Law, T5), which measures dimensionless mismatch from equilibrium; nonnegativity of costs is the usual starting point for certificates.
Astrophysical radii enter RS through the $\phi$-ladder and yardstick scalings rather than through GR stellar-structure ODEs. This module sits in that layer: it does not re-derive hydrostatic equilibrium. It only records a domain cost, a canonical threshold, and a certificate object that downstream astrophysics can inhabit when checking the solar radius against the RS scale.
Constants supplies the RS time quantum $\tau_0 = 1$ tick and related unit anchors used when converting ladder rungs into physical lengths.
proof idea
Definition-and-certificate module, not a long forcing proof. It introduces domainCost with an evaluation identity and a nonnegativity lemma, defines canonicalThreshold with a positivity proof, then bundles SolarRadiusCert and shows the certificate type is inhabited. Upstream Cost/Constants are used only as the ambient cost and unit language; no deep tactic scripts beyond those local lemmas.
why it matters in Recognition Science
Gives the astrophysics layer a named, inhabitable solar-radius certificate so RS length claims can be cited without ad-hoc numerics. Sibling objects (domain cost, canonical threshold, cert) are the local API. No downstream used_by edges are recorded yet; the module is a leaf packaging step toward stellar-scale checks on the $\phi$-ladder, parallel to mass-yardstick certificates elsewhere in the monolith. It does not close T0–T8; those already force $J$, $\phi$, the eight-tick octave, and $D = 3$.
scope and limits
- Does not derive the solar radius from hydrostatic equilibrium or opacity tables.
- Does not prove uniqueness of the Sun among stars; only packages a radius certificate.
- Does not re-prove J-uniqueness, phi-forcing, or D = 3.
- Does not supply observational error bars or SI unit conversions beyond RS anchors.
- Does not claim a downstream theorem edge; used_by is currently empty.