IndisputableMonolith.Gravity.BlackHoleEntropyFromLedger
The module establishes the leading-order Recognition Science black-hole entropy as S_lead(A) = A/4. Quantum gravity researchers cite it to connect the discrete ledger to semiclassical thermodynamics. It imports the constants and cost modules to introduce S_lead together with positivity and equality statements.
claimThe leading-order black-hole entropy in Recognition Science is given by $S_ {rm lead}(A) = A/4$, where $A$ denotes the horizon area in RS-native units.
background
This module sits in the Gravity domain and imports Constants, which fixes the fundamental RS time quantum as τ₀ = 1 tick, and Cost, which supplies the J-cost functional. It introduces S_lead as the leading entropy term extracted from the discrete ledger. The setting draws on the Recognition Composition Law and the phi-ladder for horizon-state counting.
proof idea
This is a definition module, no proofs. It declares S_lead along with auxiliary results such as S_lead_pos, S_lead_eq_BH, and black_hole_entropy_one_statement by direct reference to the imported constants and cost functions.
why it matters in Recognition Science
This module supplies the base entropy formula S_lead = A/4 that BlackHoleHorizonStates and BlackHoleInformationPreservation both import. BlackHoleHorizonStates deepens the result by deriving the same formula combinatorially from admissible Q₃-orbit states on the horizon. It fills the leading term in the RS black-hole thermodynamics treatment inside the T0-T8 forcing chain.
scope and limits
- Does not derive subleading logarithmic corrections.
- Does not resolve the black-hole information paradox.
- Does not perform explicit state counting beyond leading order.
- Does not equate the formula to loop-quantum-gravity or string-theory expressions.