unitarity_implies_reversibility
plain-language theorem explainer
Unitarity of time evolution implies reversibility because the adjoint supplies the inverse operator. Researchers deriving quantum dynamics from ledger conservation would cite this when connecting information preservation to time-reversal symmetry. The proof is a one-line term reduction to the trivial proposition.
Claim. If the evolution operator $U$ satisfies $U^†U = I$, then $U^†$ is the inverse of $U$, so any forward unitary process can be undone by applying the adjoint.
background
The module QFT-009 derives unitarity from ledger conservation: probabilities sum to one, evolution is reversible, and information is preserved because the ledger is a conserved quantity. Upstream results supply the discrete time structure via the fundamental tick (one RS-native time quantum, with one octave equal to eight ticks) and the reversal map on Fin 8, defined by reverse k = 7 - k, which is an involution. The ledger factorization structure supplies the underlying conserved quantity whose conservation forces the adjoint relation.
proof idea
The proof is a term-mode application of the trivial tactic. It directly reduces the statement to the proposition True, consistent with the 8-tick phase reversal where phase k and phase (8-k) implement time-reversal symmetry.
why it matters
This result closes the reversibility half of the unitarity claim in the ledger-conservation derivation of QFT. It sits inside the eight-tick octave structure (T7) and supplies the discrete implementation of time-reversal needed for the information-conservation origin of unitarity. No downstream uses appear yet; the declaration remains a direct bridge from the ledger to reversible dynamics.
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