commit
plain-language theorem explainer
The commit operation selects a guaranteed existing outcome index from an uncommitted ledger of branches and returns a committed ledger carrying that outcome together with a unit-norm amplitude. Quantum theorists deriving the measurement postulate inside Recognition Science cite this definition to replace the ad-hoc collapse axiom with ledger commitment. The body locates the matching branch via find? and normalizes its amplitude when nonzero, defaulting to the constant 1 otherwise.
Claim. Let $L$ be an uncommitted ledger over $n$ outcomes whose branches sum to unit weight, and let $i$ be an index that appears in at least one branch. The commitment map produces a committed ledger whose outcome field is $i$ and whose amplitude field is the original branch amplitude divided by its norm (or the constant 1 when the amplitude vanishes).
background
The module QF-001 treats the measurement problem as the transition from superposition to definite outcome inside a ledger. An UncommittedLedger is a list of LedgerBranch records together with the normalization condition that the sum of their weights equals 1; each branch carries an outcome index and a complex amplitude. A CommittedLedger is the post-commitment structure consisting of a single Fin n outcome, an Amplitude value, and the explicit proof that its norm is 1. Upstream results supply the amplitude definition used in DoubleSlit and SMatrixUnitarity, while the eight-tick ledger axioms from the imported EightTick module guarantee that commitment preserves the overall recognition balance.
proof idea
The definition is a direct pattern match on the result of branches.find? for the predicate outcome = i. When a branch is returned and its amplitude is nonzero, norm_div_norm_eq_one is applied to obtain the unit vector; the zero-amplitude and none cases are handled by the constant 1 with a simp-generated proof of unit norm.
why it matters
This definition supplies the concrete map required by the downstream theorem measurement_postulate_derived, which states that the quantum measurement postulate follows from the uncommitted-to-committed transition together with recognition weights. It thereby closes the ledger-actualization step used in zeno_from_ledger_actualization and zenoAntiZenoCrossover. Within the Recognition Science chain the construction realizes the core insight that measurement is forced ledger balance, yielding the Born rule as a consequence of J-cost ordering rather than an added postulate.
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