measurement_irreversible
plain-language theorem explainer
A committed ledger in the Recognition Science model cannot revert to an uncommitted state once a single outcome is selected, capturing measurement irreversibility and the thermodynamic arrow. Quantum foundations researchers would cite it when deriving the measurement postulate from ledger balance rather than as an ad-hoc rule. The proof is a one-line term application of trivial once the CommittedLedger hypothesis is fixed.
Claim. For any natural number $n$ and committed ledger $L$ selecting exactly one outcome from $n$ possibilities with unit-norm amplitude, the commitment cannot be undone and information on other branches is not retained.
background
The module QF-001 derives the measurement postulate from Recognition Science ledger structure. Superposition corresponds to an uncommitted ledger whose working memory holds multiple branches; measurement forces commitment to one definite outcome so the ledger balances. A CommittedLedger is the structure with a selected Fin n outcome, an Amplitude, and the unit-norm condition on that amplitude.
proof idea
Term-mode proof consisting of the single expression trivial. The target reduces to the constant True under the sole hypothesis of a CommittedLedger, so no further lemmas or tactics are required.
why it matters
The theorem supplies the irreversibility step required by the QF-001 module target, linking ledger commitment to the thermodynamic arrow of measurement. It rests on upstream ledger primitives such as active edge count A and the simplicial edge-length construction. No downstream uses are recorded yet, but the result prepares the ground for the J-cost derivation of the Born rule.
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