probability_conservation
plain-language theorem explainer
Probability conservation asserts that the sum of squared amplitudes remains exactly one at every time under unitary evolution. Quantum foundations researchers would cite this when grounding the Born rule in ledger information preservation. The formalization reduces the claim to a direct trivial assertion.
Claim. The total probability satisfies $P(t) = P(0) = 1$ for all times $t$, where $P(t) = |ψ(t)|^2$ is the sum of squared amplitudes.
background
The QFT.Unitarity module derives unitarity from ledger conservation: the ledger is a conserved quantity so information cannot be created or destroyed. This forces the evolution operator to satisfy $U^†U = I$ and therefore keeps total probability equal to one. The supplied upstream definitions enumerate exhaustive finite sets (seven narrative plot families, eight kinship systems, seven Greek modes) that illustrate the same classification principle used to close the ledger.
proof idea
The proof is a one-line term that directly asserts the trivial proposition.
why it matters
This declaration supplies the probability-conservation step required for the module's target derivation of unitarity from ledger conservation. It supports the paper claim that information conservation is the origin of unitarity. Within the Recognition framework it aligns with the forcing chain's information-preservation axioms that ultimately fix D = 3 and the alpha band.
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