HorizonLedger
plain-language theorem explainer
HorizonLedger defines a four-field structure holding lists of real numbers for ledger entries outside and inside a black hole horizon, shared entries spanning the horizon, and a real entanglement measure. Quantum gravity researchers studying the firewall paradox would cite it to encode non-local information flow in Recognition Science. The declaration is a bare structure definition with no associated proof or computation.
Claim. A structure consisting of lists $outside_entries, inside_entries, shared_entries : List(ℝ)$ and a real number $entanglement$ that records non-local ledger connections across the event horizon.
background
Recognition Science tracks physical quantities via a ledger of J-costs and defects, where the J-function obeys the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). The Quantum.Firewall module targets the AMPS firewall paradox by treating the ledger as fundamentally non-local, so that shared entries connect exterior Hawking radiation to interior partner particles without drama. Upstream results include LedgerFactorization.of, the structure of (ℝ₊, ×) with J-calibration, and SpectralEmergence.of, the structure forcing SU(3)×SU(2)×U(1) gauge content and three generations from simplicial data.
proof idea
This is a direct structure definition introducing the HorizonLedger type with four named fields; no lemmas or tactics are invoked.
why it matters
The structure supplies the concrete data model for the ER=EPR identification in which shared ledger entries realize the wormhole. It underpins the module's claim that non-local ledger connections resolve the firewall trilemma while preserving unitarity and horizon smoothness, as outlined in the module documentation targeting a Nature paper on the firewall paradox. It prepares the ground for sibling declarations such as er_equals_epr_from_ledger and information_preserved.
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