IndisputableMonolith.Relativity.Compact
The Compact module aggregates results on static spherical metrics and black hole entropy within Recognition Science relativity. It imports StaticSpherical and BlackHoleEntropy to establish that the Bekenstein-Hawking entropy follows from the ledger capacity limit under maximum recognition flux. The module itself contains no proofs and serves as a container for these specialized derivations.
claimThe primary object is the entropy formula $S_{BH} = A / 4 ell_p^2$ arising from maximum recognition flux on the ledger capacity limit.
background
Recognition Science derives relativity results from the unified forcing chain (T0-T8) and the Recognition Composition Law. The Compact module operates in the relativity domain by collecting compact-object solutions. Its BlackHoleEntropy import derives the Bekenstein-Hawking entropy from the ledger capacity limit with the explicit objective to prove that $S_{BH} = A / 4 ell_p^2$ arises from maximum recognition flux. The StaticSpherical import supplies the supporting metric constructions.
proof idea
This is an aggregating module with no proofs of its own. It consists solely of imports from StaticSpherical and BlackHoleEntropy, exposing their results without additional structure or tactics.
why it matters in Recognition Science
The module supplies the black-hole entropy derivation that feeds parent relativity constructions in the Recognition framework. It closes the compact-objects portion of the relativity development by linking ledger capacity directly to the standard entropy formula, consistent with the T8 spatial-dimension step.
scope and limits
- Does not derive dynamic or time-dependent metrics.
- Does not address rotating or Kerr geometries.
- Does not compute numerical values for ell_p from the phi-ladder.
- Does not connect entropy results to the alpha band or mass formula.