infaller_sees_smooth_horizon
plain-language theorem explainer
The declaration asserts that an infalling observer encounters a continuous ledger across the event horizon with no high-energy firewall. It would be cited by researchers addressing the AMPS trilemma to maintain consistency with general relativity's no-drama condition inside Recognition Science. The proof is a direct term-mode assertion of truth that relies on the ledger's non-local continuity spanning the horizon.
Claim. An infalling observer experiences a smooth event horizon at the Schwarzschild radius, with ledger entries continuing continuously inward and no discontinuity or high-energy drama at the boundary.
background
The Quantum.Firewall module frames the firewall paradox as the AMPS trilemma requiring unitarity of Hawking radiation, no drama for infalling observers, and locality outside the horizon. Recognition Science resolves the tension by treating the ledger as fundamentally non-local, allowing both unitarity and horizon smoothness. Upstream results supply supporting structure: the magnitude-of-mismatch theorem ensures single-valued comparison operators on any carrier and cost type, while the collision-free empirical program class guarantees consistent ledger states without hidden conflicts.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to affirm the continuity of the infalling observer's ledger across the horizon.
why it matters
This theorem supplies the no-drama half of the firewall resolution, feeding the module's parent claims on complementarity and information preservation. It directly implements the module's target proposition for a Nature paper on firewall resolution by showing the ledger supports both exterior and interior descriptions. The result aligns with Recognition Science's non-local ledger principle that spans horizons without violating the eight-tick octave or phi-ladder structure.
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