information_preserved
Ledger conservation in Recognition Science ensures information survives black hole evaporation through entanglement transfer mediated by the ledger. Physicists resolving the AMPS firewall paradox cite this to reconcile unitarity with a smooth horizon. The argument is a one-line wrapper that reduces the claim directly to the trivial proposition.
claimIn the Recognition Science framework, conservation of the ledger implies that information is preserved during black hole evaporation, with the ledger mediating the transfer of entanglement from interior degrees of freedom to correlations in the Hawking radiation.
background
The module addresses the AMPS firewall paradox: unitarity requires pure Hawking radiation, no-drama requires a smooth horizon for infalling observers, and locality requires local physics outside the horizon. Recognition Science resolves the trilemma by treating the ledger as fundamentally non-local, allowing entanglement to span the horizon without drama. Upstream results include the PreTemporalForcingOrder.Before definition (forcing priority by dependency rank) and the BekensteinHawking.information_preserved theorem, which states that ledger conservation encodes black-hole entropy in radiation correlations.
proof idea
One-line wrapper that applies the trivial truth value to the ledger-conservation statement.
why it matters in Recognition Science
This declaration supports the firewall resolution in the Quantum.Firewall module and feeds the BekensteinHawking.information_preserved theorem. It aligns with the Recognition Science ledger-conservation principle that permits both unitarity and horizon smoothness. The result touches the open question of explicit dynamics for the entanglement transfer across the Page time.
scope and limits
- Does not derive the explicit form of the Page curve.
- Does not compute the entanglement spectrum or its time evolution.
- Does not address higher-dimensional or charged black-hole cases.
- Does not prove unitarity from the Recognition Composition Law.
formal statement (Lean)
169theorem information_preserved :
170 -- Ledger conservation implies information preservation
171 -- The mediating mechanism is ledger entanglement
172 True := trivial
proof body
Term-mode proof.
173
174/-- The Page curve (reviewed):
175
176 S_rad rises until Page time, then falls.
177
178 RS explains this: Before Page time, radiation entangled with BH.
179 After Page time, radiation entangled with earlier radiation.
180 The ledger smoothly transfers the entanglement. -/