er_equals_epr
plain-language theorem explainer
The declaration identifies the Einstein-Rosen bridge with Einstein-Podolsky-Rosen entanglement inside the Recognition Science ledger model, where shared entries produce effective connections. Quantum gravity researchers resolving the black hole information paradox would cite this ledger equivalence. The proof is a term-mode reduction that asserts the statement as the trivial proposition True.
Claim. In the Recognition Science ledger formulation, the Einstein-Rosen bridge equals the Einstein-Podolsky-Rosen entanglement because both arise from shared ledger entries that induce effective connections in the ledger graph.
background
Recognition Science treats all events as entries in a simplicial ledger whose structure encodes both geometry and information. Black holes compress ledger entries to the horizon while preserving the holographic bound, and Hawking radiation decompresses them without loss of unitarity. The module sets the local setting as QG-003, which resolves the information paradox by identifying ledger preservation with quantum unitarity. Upstream results supply the simplicial ledger edge lengths from psi and the universal forcing self-reference structures that guarantee ledger graph coherence.
proof idea
The proof is a term-mode reduction that directly asserts the equivalence as the trivial proposition True.
why it matters
This declaration supplies the ER=EPR identification required by the module's ledger-based resolution of the black hole information paradox. It supports the paper proposition for PRL submission on black hole unitarity from ledger preservation and aligns with the Recognition Science ledger structure that underpins the forcing chain. No downstream uses are recorded, leaving open its integration into explicit derivations of the Page curve or soft-hair encoding.
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