summary
plain-language theorem explainer
Recognition Science derives quantum unitarity from ledger conservation by encoding states in a conserved ledger that forces norm preservation and thus U†U = I. Researchers in quantum foundations would cite this summary when tracing reversibility to the Recognition Composition Law. The definition constructs a fixed list of six steps without computation or lemmas.
Claim. The unitarity summary is the list of statements: ledger conservation is fundamental; quantum states are encoded in the ledger; conservation implies norm preservation; norm preservation requires the evolution operator to satisfy $U^†U = I$; unitarity implies reversibility; and measurement collapse is effective rather than fundamental.
background
The module QFT.Unitarity derives unitarity from ledger conservation in Recognition Science. The ledger is treated as a conserved quantity that encodes quantum states |ψ⟩, with the Recognition Composition Law ensuring information cannot be created or destroyed. This forces probability conservation and therefore the evolution operator condition $U^†U = I$ with reversibility. Upstream results include the collision-free property from OptionAEmpiricalProgram.is and the algebraic tautology in SimplicialLedger.EdgeLengthFromPsi.is, which together establish the ledger structure supporting state encoding.
proof idea
The definition is a direct list construction that enumerates the six logical steps listed in the doc-comment. No lemmas are applied and no tactics are used; it is a one-line wrapper around the string list.
why it matters
This definition supports the QFT-009 target of deriving unitarity from ledger conservation, as stated in the module doc-comment. It connects to the Recognition Science framework where information conservation forces reversibility via the eight-tick octave. No downstream theorems reference it yet, but it outlines the path to the paper proposition on information conservation as the origin of unitarity.
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