IndisputableMonolith.Astrophysics.PlanetaryMigrationFromJCost
Module packaging a J-cost model of planetary orbital migration: a domain cost on radial scale factors, a positive canonical threshold, and an inhabited certificate that migration is forced when the cost exceeds that threshold. Astrophysicists working in Recognition Science cite it for the discrete-cost side of migration rather than continuum torque balance. The content is mostly nonnegativity and positivity lemmas plus a certificate structure, not a long derivation.
claimDefine a domain cost $C$ on radial scale factors via the RS $J$-cost, prove $C\ge 0$ and a matching identity at equality cases, fix a canonical positive threshold $\theta>0$, and package an inhabited certificate asserting planetary migration whenever the domain cost meets or exceeds $\theta$.
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced at T5 of the unified forcing chain. The Cost import supplies that $J$ and its elementary inequalities; Constants supplies the RS tick $\tau_0$ used to anchor discrete time.
In this astrophysics layer the same $J$ is lifted to a domain cost on orbital or radial scale factors: how expensive it is, in recognition units, for a planet to sit off a preferred rung of the $\phi$-ladder. Nonnegativity of that cost and a positive canonical threshold turn the continuous migration problem into a certificate: when cost clears the threshold, migration is the forced relaxation.
The module sits beside other RS astrophysics certificates; it does not re-derive $J$ or $\phi$, only applies them to planetary radial adjustment.
proof idea
Definition-and-certificate module, not a single deep proof. domainCost is introduced from $J$; domainCost_nonneg and domainCost_at_eq discharge the basic analytic facts (nonnegativity, equality cases) by reduction to Cost lemmas. canonicalThreshold and canonicalThreshold_pos fix a strictly positive cutoff. PlanetMigrateCert, cert, and cert_inhabited assemble those pieces into an inhabited Prop certificate that migration holds once cost meets the threshold. No multi-step tactic script beyond the standard nonnegativity and positivity arguments.
why it matters in Recognition Science
Gives the RS-native, $J$-cost account of planetary migration as a thresholded domain-cost certificate rather than as Type-I/II disk torques. Downstream consumers (none linked yet in the graph) would import the inhabited cert when closing larger solar-system or exoplanet forcing statements. It ties migration to the same T5 $J$-uniqueness and $\phi$-ladder language used for masses and coupling constants, keeping astrophysics inside the single-functional-equation framework. Open graph edge: no used_by parents yet, so the certificate is available but not yet wired into a global planetary theorem.
scope and limits
- Does not derive disk torques, viscosity, or Type-I/II migration rates from hydrodynamics.
- Does not fix numerical AU scales or match a specific exoplanet catalog.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not treat multi-planet resonances or stochastic migration.
- Does not re-prove J-uniqueness or the forcing chain T5–T8.