IndisputableMonolith.Physics.QuantumEntanglementEntropyAreaLaw
This module introduces definitions for entanglement regimes and area-law certificates in Recognition Science. Quantum information theorists or holography researchers would reference it when connecting RS constants to entropy scaling. The module is a pure definition block that imports the RS time quantum and declares sibling objects without theorems.
claimEntanglementRegime and EntanglementAreaLawCert formalize the regime where entanglement entropy obeys an area law $S_A \propto \text{Area}(\partial A)$ in RS-native units with $\tau_0 = 1$ tick.
background
The module imports IndisputableMonolith.Constants, whose sole documented object is the fundamental RS time quantum $\tau_0 = 1$ tick. It sits inside the Physics domain and declares four sibling objects: EntanglementRegime, entanglementRegime_count, EntanglementAreaLawCert, and entanglementAreaLawCert. No module-level doc-comment is supplied; the setting is therefore the standard RS-native units where $c=1$, $\hbar=\phi^{-5}$, and the forcing chain T0-T8 supplies the underlying J-cost and phi-ladder structure.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the entanglement-area-law objects that later physics derivations would cite when extending the Recognition Composition Law or the eight-tick octave to quantum information. With zero downstream uses recorded, it currently functions as a leaf definition block whose parent theorems remain in sibling or importing modules.
scope and limits
- Does not prove the area law from the J-functional equation.
- Does not compute explicit entropy values for any state.
- Does not link the certificate to the phi-ladder mass formula.
- Does not address time evolution or Berry creation thresholds.