addEntry
The definition constructs an updated black hole ledger by prepending a falling entry to the list of entries and adding its information count to the running total. Researchers modeling unitary evolution during black hole evaporation in Recognition Science would cite this construction to track preserved information. It proceeds by explicit structure construction followed by list simplification and ring normalization to reestablish the sum invariant.
claimLet $L$ be a black hole ledger consisting of a list $E$ of falling entries, a total information count $I$, and the invariant that $I$ equals the sum of information contents over $E$. For a falling entry $e$ carrying information $i$, the updated ledger is the structure with list $e :: E$, total $I + i$, and the same invariant reestablished by the list-sum property.
background
The module QG-003 resolves the black hole information paradox by treating information as ledger entries that remain preserved under compression at the horizon and decompression via Hawking radiation. A black hole ledger is the structure whose fields are a list of falling entries, a natural-number total information count, and the consistency condition that the total equals the sum of the individual information values. A falling entry is the structure carrying a natural-number information content in bits, a real infall time, and the marker that the entry is preserved rather than destroyed.
proof idea
The definition is a direct structure constructor that builds the new ledger from the cons of the entry onto the existing list and the arithmetic sum of the totals. Consistency is discharged by a one-line tactic block that applies simp to the map-cons and sum-cons lemmas, rewrites the original ledger's consistency hypothesis, and closes with ring.
why it matters in Recognition Science
This definition supplies the update operation required by the downstream theorem information_preserved_on_infall, which states that the total information after infall equals the prior total plus the new entry's information. It realizes the ledger-compression step in the module's resolution of the black hole information paradox, ensuring the total count is maintained so that unitarity is never violated. Within Recognition Science the construction aligns with the fundamental ledger that records all events and supports the holographic bound and eight-tick octave structure.
scope and limits
- Does not model the dynamical process of Hawking radiation emission.
- Does not incorporate quantum-field-theoretic details at the horizon.
- Does not address the firewall paradox or related extensions.
- Does not prove global unitarity of the full spacetime evolution.
formal statement (Lean)
124def addEntry (ledger : BlackHoleLedger) (entry : FallingEntry) : BlackHoleLedger :=
proof body
Definition body.
125 ⟨entry :: ledger.entries,
126 ledger.totalInfo + entry.information,
127 by simp only [List.map_cons, List.sum_cons]; rw [ledger.consistent]; ring⟩
128
129/-- **THEOREM**: Information is preserved when falling into a black hole. -/