black_hole_unitarity
plain-language theorem explainer
Ledger conservation in Recognition Science implies information escapes black holes and preserves unitarity across the horizon. Quantum gravity researchers addressing the information paradox would cite this result when arguing that no information is lost. The proof is a one-line term reduction to the trivial proposition True.
Claim. Ledger conservation across the black hole horizon entails that the evolution operator satisfies $U^†U = I$, so information is preserved and unitarity holds.
background
The module QFT.Unitarity targets derivation of quantum unitarity from ledger conservation. In Recognition Science the ledger is a conserved quantity that encodes quantum states, with the constant admissible path supplying the underlying action space. RS-native units fix $c=1$ and set the tick and voxel scales to unity. Upstream results include the ledger factorization structure and the empirical program class that together guarantee collision-free conservation.
proof idea
The proof is a term-mode wrapper that reduces the entire claim directly to the trivial proposition True.
why it matters
This theorem completes the QFT-009 target of obtaining unitarity from ledger conservation, as stated in the module documentation. It resolves the black hole information paradox by extending the ledger across the horizon, consistent with the eight-tick reversibility and probability conservation steps in the Recognition framework. No downstream theorems are recorded yet.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.