IndisputableMonolith.ConeExport.Theorem
The ConeExport.Theorem module acts as a placeholder container for holographic entropy bounds in the Recognition Science framework. It imports causality reachability, light cone structures, and RS constants to organize future theorems on entropy within causal cones. Researchers deriving information limits from the phi-ladder and J-uniqueness would cite it once populated. The module structure groups sibling facts and bounds for modular export.
claimHolographic entropy bounds in causal cones: $S(C) $ with exports ConeEntropyFacts, cone_entropy_bound, cone_bound_export.
background
The module imports IndisputableMonolith.Causality.Reach for reachability, IndisputableMonolith.Constants defining the RS time quantum τ₀ = 1 tick, and IndisputableMonolith.LightCone as a shim exposing the light cone namespace. These supply the causal and temporal primitives needed for entropy calculations in cones.
proof idea
This is a definition module, no proofs. It organizes imports and sibling declarations (ConeEntropyFacts, cone_bound_export, cone_entropy_bound) as a placeholder structure.
why it matters in Recognition Science
The module feeds the Recognition Science framework by preparing holographic entropy bounds that connect causal cones to the J-cost and phi-ladder. It supports downstream development toward links with the unified forcing chain (T5 J-uniqueness, T7 eight-tick octave) and Recognition Composition Law, though currently empty.
scope and limits
- Does not contain explicit entropy bound theorems.
- Does not derive numerical values in RS units.
- Does not apply mass formula or alpha band results.
- Does not close any scaffolding with concrete proofs.