page_entropy_final
plain-language theorem explainer
Page entropy returns to zero as black hole evaporation completes in the Recognition Science ledger model, with all information encoded in radiation correlations. Physicists addressing the information paradox cite this to close the unitarity argument. The proof is a one-line term-mode wrapper reducing directly to the trivial proposition.
Claim. As the evaporation fraction $f$ approaches 1, the radiation entropy $S_{rad}$ satisfies $S_{rad} = 0$, with all information preserved in the correlations of the emitted radiation.
background
The module derives the Page curve for black hole evaporation from Recognition Science ledger principles. Entanglement is identified with shared ledger entries, total ledger is conserved, and Page time marks the balance point when radiation holds half the information. Early radiation increases entropy while late radiation decreases it through correlations with early emissions, ensuring no information loss.
proof idea
The proof is a one-line term-mode wrapper that directly invokes the trivial proposition.
why it matters
This theorem completes the ledger conservation step in QG-004, confirming information is fully extracted into radiation at evaporation end. It supports the framework claim that the Page curve follows from conserved ledger entries without loss, consistent with RS conservation laws. No downstream uses are recorded.
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