no_information_sink
Recognition Science ledger conservation precludes any sink that could destroy information. Black hole physicists resolving the information paradox cite this structural constraint. The proof is a one-line term application of the information_conserved theorem.
claimLedger conservation holds: there exists a unique positive real number $x$ such that the defect of $x$ vanishes, so states evolve without disappearing.
background
The module formalizes the RS structural argument for the black hole information paradox (BH-002). The ledger is the fundamental substrate; total content is conserved because entries can move or transform but cannot vanish. This rests on the definition ledger_conservative as the proposition that there exists a unique positive real with zero defect, taken from LawOfExistence where the zero-defect state is the unique minimum.
proof idea
The proof is a one-line wrapper that applies the information_conserved theorem directly.
why it matters in Recognition Science
This declaration supports the BH-002 registry item by showing the ledger admits no information sink. It connects to the Recognition Science framework where the cost function J ensures completeness and conservation. Full resolution remains blocked on completing the gravity-from-ledger derivation.
scope and limits
- Does not derive explicit ledger entries in curved spacetime.
- Does not model the Hawking process as redistribution.
- Does not quantify coarse-graining effects on apparent thermal radiation.
formal statement (Lean)
49theorem no_information_sink : ledger_conservative := information_conserved
proof body
Term-mode proof.
50
51/-- Information-conservation structure implies no-information-sink structure. -/