PageCurveFalsifier
plain-language theorem explainer
The structure encodes falsification criteria for the black hole Page curve derivation from ledger conservation in Recognition Science. A researcher investigating the information paradox would cite these conditions to delineate testable predictions of entanglement as shared ledger entries. It assembles three propositions with a negation of their disjunction to enforce consistency under the Recognition Composition Law.
Claim. A structure with propositions $P$ (observed page curve deviates from the predicted form), $I$ (information is lost during evaporation), $L$ (ledger conservation is violated), and the assertion $(P ∨ I) → ⊥$.
background
The module derives the Page curve for black hole evaporation from RS principles, where entanglement equals shared ledger entries and the curve follows from ledger conservation. Early times show rising radiation entropy from entangled pairs, the Page time occurs when half the black hole has evaporated, and late times show decreasing entropy as late radiation entangles with early radiation. This restores information without loss, consistent with the eight-tick octave and phi-ladder mass scaling.
proof idea
This is a structure definition with no proof body, directly encoding the three propositions and the implication that the first two cannot hold simultaneously.
why it matters
It supplies the falsification interface for the QG-004 derivation of the Page curve, feeding downstream results on information preservation by the page curve and absence of firewalls. The structure closes the loop on ledger conservation as the mechanism resolving the information paradox, aligning with T5 J-uniqueness and the Recognition Composition Law. It leaves open the experimental accessibility of direct Page curve observation.
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