information_conserved
plain-language theorem explainer
Information conservation holds in the ledger because the determinism theorem guarantees a unique zero-defect state under evolution. Black-hole researchers working in ledger-based frameworks cite this to replace information-loss claims with redistribution. The proof is a one-line wrapper that invokes the uniqueness conjunct of the determinism resolution.
Claim. The ledger is conservative: the defect functional $J(x)$ for $x>0$ admits a unique zero at $x=1$, so deterministic evolution preserves total information without sinks.
background
The defect functional equals the J-cost $J(x)=(x+x^{-1})/2-1$, which vanishes only at unity. The determinism resolution states that the universe is deterministic with a unique J-cost minimizer at each step and that apparent randomness is an observer artifact. This module supplies the structural half of the BH-002 black-hole information paradox resolution, asserting that the ledger remains complete under evolution.
proof idea
One-line wrapper that applies the second conjunct of determinism_resolution, which asserts existence and uniqueness of the zero-defect state.
why it matters
The result feeds the sibling theorem no_information_sink, which rephrases the same conservation property. It fills the BH-002 registry item by showing that ledger entries are reorganized rather than erased, consistent with the eight-tick octave and phi-ladder structure of Recognition Science. Full resolution of the paradox remains blocked on the complete gravity-from-ledger construction.
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