IndisputableMonolith.Astrophysics.CoronalTemperatureFromJCost
Module linking solar coronal temperatures to the Recognition Science J-cost. It defines a domain cost on temperature ratios, a canonical positive threshold, and a certificate bundle CoronalTempCert that packages the nonnegativity and threshold facts. Astrophysicists working the RS mass/temperature ladder would cite the certificate. Structure is mostly definitions plus short positivity lemmas over the imported Cost layer.
claimOn temperature (or scale) ratios $x > 0$, a domain cost $C(x)$ is built from the RS $J$-cost $J(x) = \frac{x+x^{-1}}{2}-1$. A canonical threshold $\theta > 0$ is fixed, and a certificate asserts $C \ge 0$ together with the threshold positivity used to mark coronal-temperature regimes in RS-native units.
background
Recognition Science forces the unique symmetric cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$) via the Recognition Composition Law and the T5 uniqueness step. The Cost import supplies that $J$ and its elementary inequalities; Constants supplies the RS tick and related native units.
This astrophysics module treats coronal heating as a cost-threshold phenomenon: when a temperature (or energy-scale) ratio crosses a canonical positive level built from $J$, the configuration is certified as coronal. Sibling names indicate a domain-restricted cost, its evaluation identity, nonnegativity, the threshold and its positivity, and a bundled certificate type with an inhabited instance.
The local setting is therefore not a full hydrodynamic corona model, but a thin RS interface: cost on ratios, threshold, certificate.
proof idea
Definition-heavy module. domainCost is assembled from the imported $J$-cost on the relevant ratio; domainCost_at_eq and domainCost_nonneg are short algebraic or inequality wrappers over Cost. canonicalThreshold is a closed-form positive constant; canonicalThreshold_pos discharges positivity. CoronalTempCert packages these facts; cert and cert_inhabited supply a concrete inhabited certificate. No deep tactic developments beyond positivity and rewriting.
why it matters in Recognition Science
Places coronal temperature inside the same $J$-cost ledger that drives the forcing chain (T5 $J$-uniqueness, T6 $\phi$, mass ladder). Downstream graph is empty here, so the module is a leaf interface: it exposes CoronalTempCert for later solar-physics or ledger-audit developments rather than feeding a named parent theorem in-tree. It ties the phenomenological corona temperature scale to RS-native cost and threshold language instead of an ad hoc Kelvin fit, keeping astrophysical claims auditable against Cost and Constants.
scope and limits
- Does not derive MHD or Parker-type coronal heating equations.
- Does not predict observed MK temperatures from first principles beyond the cost threshold.
- Does not fix solar abundances, magnetic reconnection rates, or loop geometry.
- Does not claim a unique empirical fit outside RS-native units.
- Does not discharge open scaffolding elsewhere in the astrophysics tree.