LedgerEvolution
plain-language theorem explainer
LedgerEvolution packages real numbers for black hole ledger entries, radiation ledger entries, shared entanglement, and total entries under an explicit conservation constraint. Researchers modeling unitary black hole evaporation in Recognition Science cite it to track how Hawking quanta redistribute ledger entries while preserving information. The definition is a plain structure that directly encodes the ledger interpretation of entanglement monogamy.
Claim. A structure consisting of real numbers for black hole ledger entries, radiation ledger entries, shared entanglement, and total entries, subject to the conservation relation that black hole entries plus radiation entries equal the total.
background
Recognition Science treats entanglement as shared ledger entries rather than von Neumann entropy. The module derives the Page curve for black hole evaporation by requiring that each Hawking quantum carries ledger entries, with early quanta entangled to the interior and late quanta entangled to early radiation. Upstream, entropy of a configuration is defined as proportional to its total defect, so the initial state is the minimum-entropy configuration with zero defect.
proof idea
The declaration is a structure definition that bundles the four real fields together with the conservation equation as an explicit field. No lemmas or tactics are invoked; it functions as the data type for later constructions in the same module.
why it matters
The structure supplies the concrete ledger model that resolves the information paradox by enforcing conservation throughout evaporation. It supports sibling results such as page_curve_from_ledger and information_preserved_by_page_curve. The construction realizes the RS claim that the Page curve follows from ledger conservation, consistent with the forcing chain that fixes three spatial dimensions and the eight-tick periodicity.
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