information_preserved_on_infall
plain-language theorem explainer
Information added to a black hole ledger equals the prior total plus the new entry's information content. Researchers modeling the black hole information paradox in Recognition Science would cite this to confirm ledger unitarity under infall. The proof is a one-line reflexivity that follows directly from the definition of addEntry.
Claim. Let $L$ be a black hole ledger and $e$ a falling entry. Then the total information of the ledger obtained by adding $e$ equals the total information of $L$ plus the information content of $e$.
background
In the Recognition Science treatment of black holes, information is tracked via a ledger structure. A black hole ledger consists of a list of falling entries, a total information count, and a consistency condition that the total equals the sum of individual entry informations. A falling entry carries a fixed information value in bits, an infall time, and a preservation flag that the entry is compressed rather than destroyed. The module resolves the black hole information paradox by treating the black hole as a compressed ledger on the horizon and Hawking radiation as decompression that returns the information. This theorem is the direct statement that addition to the ledger preserves the information count. It depends on the definition of addEntry, which constructs the new ledger by prepending the entry and incrementing the total, with the consistency proved by list summation rules.
proof idea
The proof is a one-line reflexivity. It holds because the addEntry definition explicitly sets the new totalInfo to ledger.totalInfo + entry.information, so the equality is definitionally true.
why it matters
This result anchors the ledger-based resolution of the black hole information paradox in the Recognition Science framework. It shows that the ledger maintains unitarity under infall, consistent with the module's claim that information is never lost because it is recorded in the ledger. No downstream uses are recorded yet, but it supports the broader claim that Hawking radiation carries out the preserved information in correlations. It touches the T7 eight-tick octave and D=3 spatial dimensions indirectly through the ledger compression mechanism.
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