IndisputableMonolith.Gravity.CosmicCensorshipFromJCost
Module packaging a J-cost certificate for cosmic censorship: a nonnegative domain cost and a positive canonical threshold that together certify no naked singularities form under the Recognition cost. Gravity workers cite the certificate bundle when linking RS cost positivity to horizon protection. The argument is definitional plus elementary positivity lemmas, not a full GR existence proof.
claimDefine a domain cost $C$ built from the Recognition $J$-cost, prove $C \ge 0$ and $C$ agrees with $J$ on the equality locus, fix a positive canonical threshold $\theta > 0$, and package these into an inhabited cosmic-censorship certificate asserting that cost barriers prevent naked singularities.
background
Recognition Science measures mismatch by the unique cost $J(x) = (x + x^{-1})/2 - 1$ forced by the Recognition Composition Law (forcing chain T5). In the gravity sector this cost is lifted from ratios to spacetime domains: a domain cost that vanishes only when the configuration is on-shell with respect to the $\phi$-ladder and the eight-tick ledger.
The module sits in the Gravity domain and imports only Constants (RS time quantum $\tau_0$) and Cost (the $J$ apparatus). Cosmic censorship is treated operationally: a positive cost threshold separates admissible exterior geometries from configurations that would expose a singularity. No full Cauchy-problem machinery is assumed; the certificate is a pure cost-positivity witness.
proof idea
Definition module with short positivity lemmas. domainCost is introduced as the domain-level lift of $J$; domainCost_at_eq records agreement on the equality locus; domainCost_nonneg is the nonnegativity claim inherited from $J \ge 0$. canonicalThreshold and canonicalThreshold_pos fix a strictly positive barrier. CosmicCensorshipCert bundles these facts; cert and cert_inhabited supply a concrete inhabited instance. No deep analytic estimates appear.
why it matters in Recognition Science
Gives the Gravity layer a named, inhabitable certificate that cosmic censorship is the geometric reading of $J$-cost positivity, tying horizon protection to the same T5 uniqueness that forces $J$. Downstream consumers (none yet wired in the graph) can assume the certificate rather than re-prove cost nonnegativity. Aligns with the RS program of deriving classical GR constraints from the cost functional rather than imposing them axiomatically. Does not close the full Penrose conjecture; it only supplies the RS-native cost certificate.
scope and limits
- Does not prove the classical Penrose cosmic censorship conjecture in GR.
- Does not construct dynamical spacetimes or solve Einstein equations.
- Does not bound curvature invariants or trapped surfaces analytically.
- Does not claim the threshold value is observationally fixed.
- Does not address quantum or evaporating horizons.