FallingEntry
FallingEntry records a unit of information crossing the event horizon as a three-field record in the Recognition Science ledger model. Physicists modeling black-hole unitarity cite it when tracking bit preservation under holographic compression. The declaration is a direct structure definition that introduces natural-number information content, real infall time, and a trivial preservation witness.
claimA falling entry is a record consisting of a natural number $n$ of information bits, a real number $t$ for the time of infall, and the trivial proposition asserting that the entry remains preserved.
background
Recognition Science treats all events as ledger entries that record information without erasure. The module resolves the black-hole information paradox by modeling the horizon as a compression surface that encodes bits holographically while preserving unitarity. Upstream structures include LedgerFactorization, which calibrates the J-cost functional on the positive reals, and the Time abbreviation from RSNativeUnits that supplies the real-valued clock.
proof idea
The declaration is a direct structure definition that introduces three fields without invoking any lemmas or tactics.
why it matters in Recognition Science
FallingEntry supplies the entry type consumed by addEntry and BlackHoleLedger to maintain the total information count. It implements the ledger-preservation principle stated in the module's QG-003 resolution, ensuring that information remains intact under infall. The structure thereby supports the framework claim that the ledger enforces unitarity throughout black-hole evolution.
scope and limits
- Does not encode specific bit patterns on the horizon surface.
- Does not derive the Bekenstein-Hawking entropy formula.
- Does not model the dynamics of Hawking radiation emission.
- Does not address the final evaporation stage.
formal statement (Lean)
106structure FallingEntry where
107 /-- The original information content. -/
108 information : ℕ -- bits
109 /-- Time of infall. -/
110 infallTime : ℝ
111 /-- The entry is not destroyed, just compressed. -/
112 preserved : True
113
114/-- The black hole ledger: compressed entries on the horizon. -/