recentBreakthroughs
plain-language theorem explainer
Recent breakthroughs deriving the black hole Page curve are listed as quantum extremal surfaces, the island formula, replica wormholes, and holographic entanglement entropy. A physicist addressing the information paradox would cite this enumeration to frame Recognition Science's ledger-based account. The definition is a direct list assignment with no lemmas or computation.
Claim. The list of post-2019 results on the Page curve consists of quantum extremal surfaces, the island formula for radiation plus island entropy, replica wormholes in the Euclidean path integral, and holographic entanglement entropy.
background
The Quantum.PageCurve module derives the Page curve for black hole evaporation from Recognition Science principles. The curve tracks radiation entanglement entropy: it rises early as entangled pairs are emitted, peaks at the Page time when half the black hole has evaporated, and falls later as late radiation entangles with early radiation. Recognition Science treats entanglement as shared ledger entries whose conservation prevents information loss and redistributes it instead.
proof idea
This definition is a direct list assignment. No lemmas are applied; the four strings are enumerated verbatim from the supplied breakthroughs.
why it matters
The definition supplies context for the module's RS predictions section, which asserts an exact Page curve, scrambling on discrete time steps, phi-ladder energies in the Hawking spectrum, and ledger islands matching the island formula. It precedes sibling declarations such as page_curve_from_ledger and information_preserved_by_page_curve. It cites the Nature paper proposition on Page Curve from Ledger Dynamics and aligns with the eight-tick octave for discrete scrambling steps.
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