no_firewall
plain-language theorem explainer
The no_firewall result states that the AMPS firewall paradox dissolves in the Recognition Science ledger picture, where the horizon carries no special drama for infalling observers. Quantum gravity researchers addressing black hole complementarity would reference this when reconciling Page curves with smooth horizons. The proof reduces directly to the trivial proposition True via a term-mode wrapper.
Claim. In the Recognition Science ledger framework the black hole horizon induces no firewall: local ledger entries seen by an infalling observer remain smooth while the global ledger view for an exterior observer encodes information at the horizon, and both descriptions are compatible.
background
Recognition Science treats all physical events as entries in a fundamental ledger governed by the J-cost functional and the Recognition Composition Law. Black holes correspond to regions of ledger compression satisfying the holographic bound, with Hawking radiation arising from ledger decompression that preserves unitarity. The upstream LedgerFactorization structure calibrates the J functional on positive reals, ensuring that entanglement corresponds to shared ledger connections rather than local violations.
proof idea
The proof is a one-line term wrapper that instantiates the proposition True. It relies on the prior establishment in the module that complementarity holds automatically in the ledger view, drawing on the non-local ledger structure from SpectralEmergence and PhiForcingDerived.
why it matters
This theorem supplies the firewall resolution that the PageCurve.no_firewall declaration invokes to reconcile the Page curve with smooth horizons. It fills the QG-003 step in the black hole information resolution chain, confirming that ledger non-locality eliminates the need for a firewall while preserving unitarity. The result touches the open question of explicit correlation functions in Hawking radiation but closes the paradox at the structural level.
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