Explain the Lean inductive `AccretionRegime` in module `IndisputableMonolith.Astrophysics.AccretionDiskFromJCost`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

The inductive AccretionRegime appears in module IndisputableMonolith.Astrophysics.AccretionDiskFromJCost.

(1) In plain English it enumerates five accretion regimes for disks around compact objects: sub-Eddington thin, thick, slim, photon-trapped, and super-critical.

(2) In Recognition Science it encodes the claim that accretion disks transition through exactly five regimes (configDim D = 5) with the slim-to-photon-trapping change occurring when the mass-accretion-rate ratio crosses J(φ) ∈ (0.11, 0.13).

(3) The formal statement is inductive AccretionRegime where | subEddingtonThin | thick | slim | photonTrapped | superCritical deriving DecidableEq, Repr, BEq, Fintype. The five constructors define the inhabitants; the deriving clauses supply decidable equality, string representation, boolean equality, and finiteness.

(4) Visible dependencies: accretionRegimeCount proves Fintype.card AccretionRegime = 5 by decide; AccretionDiskCert packages the count together with a transition_threshold : CanonicalCert; accretionDiskCert builds the certificate from the count and the imported cert.

(5) The declaration does not prove the numerical value of the J(φ) threshold, the physical mapping of each regime to observables, or any derivation of the transition itself.