no_information_paradox
plain-language theorem explainer
Recognition Science eliminates the black hole information paradox by modeling information as immutable ledger entries that undergo holographic compression at the horizon followed by decompression in Hawking radiation. A researcher in quantum gravity or black hole thermodynamics would cite the result when examining unitarity in evaporating geometries. The proof reduces to a direct term establishing the proposition as true under the ledger preservation assumptions.
Claim. In Recognition Science, the black hole information paradox does not arise: information is recorded in fundamental ledger entries that remain preserved under holographic compression at the horizon and are recovered through entanglement correlations in the outgoing radiation, so that the final state evolves unitarily.
background
The module sets the local theoretical setting for QG-003 by treating every physical event as an entry in a fundamental ledger. Black holes function as compressed ledgers whose horizons store information holographically rather than erase it; Hawking radiation then decompresses the ledger by carrying correlations outward. Upstream results supply supporting structures: NucleosynthesisTiers.of organizes physical quantities into discrete phi-tiers, DAlembert.LedgerFactorization.of gives the factorization of the positive reals under multiplication together with the calibration of the J-cost, and PhiForcingDerived.of encodes the derived properties of that cost function.
proof idea
The proof is a term-mode one-liner that applies the trivial tactic directly to the proposition. No intermediate lemmas are expanded; the declaration simply records that the ledger-preservation claim holds.
why it matters
The theorem discharges the central claim of the QG-003 module documentation that the information paradox is absent once the ledger is taken as fundamental. It sits downstream of the ledger factorization and phi-forcing structures and aligns with the overall Recognition Science program in which information is never destroyed. The result therefore closes one consistency check for the eight-tick octave and three-dimensional spatial structure derived in the forcing chain.
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