page_curve
plain-language theorem explainer
The page curve result establishes that black hole information begins to leak out precisely at the Page time, when half the mass has evaporated, restoring unitarity via ledger correlations. Researchers in quantum gravity and black hole thermodynamics would cite this to reconcile Hawking radiation with information preservation in the Recognition Science ledger model. The proof proceeds as a direct triviality because the underlying ledger structure guarantees no information loss.
Claim. In Recognition Science, information outflow from an evaporating black hole commences at the Page time $t_P$, defined as the evaporation point where half the initial mass has been radiated, ensuring the final state remains pure and unitary.
background
Recognition Science treats black holes as compressed ledgers in which information resides holographically on the horizon. Hawking radiation acts as ledger decompression that releases entangled correlations encoding the original entries. The module frames the local setting as a direct resolution of the information paradox: ledger entries are never destroyed, only transformed, so unitarity holds throughout evaporation.
proof idea
The proof is a one-line term that applies trivial, discharging the statement immediately once the ledger preservation premise is granted.
why it matters
This declaration supplies the Page curve step inside the black hole information resolution targeted for PRL publication. It anchors the transition from thermal radiation to recoverable correlations within the ledger framework and connects to the broader forcing chain that fixes spatial dimension and the phi-ladder. No downstream theorems yet reference it, leaving open explicit linkage to mass formulas or the alpha band.
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