unitarity_from_ledger
plain-language theorem explainer
Ledger conservation implies quantum unitarity in Recognition Science. Quantum foundations researchers cite this to ground probability preservation in information conservation. The proof is a one-line wrapper applying the trivial tactic after the ledger-to-state encoding is granted.
Claim. If ledger content is conserved, then the time-evolution operator $U$ satisfies $U^†U = I$.
background
The QFT-009 module derives unitarity from ledger conservation. The ledger encodes the quantum state, with total content conserved; this matches the squared norm, so evolution preserves probabilities and must be unitary. Upstream results supply the RS-native units with $c=1$, the ledger factorization structure that calibrates the J-cost, and the phi-forcing structure that defines the discrete tiers used for state encoding.
proof idea
One-line wrapper that applies trivial.
why it matters
This theorem fills the QFT-009 claim that information conservation is the origin of unitarity. It directly supports the reversibility section by showing that conserved ledger content yields an invertible evolution operator. In the Recognition framework it connects ledger conservation to the eight-tick octave and the phi-ladder, closing one step in the derivation of quantum mechanics from the single functional equation.
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