decoherence_gives_classicality
plain-language theorem explainer
When one branch in an uncommitted ledger dominates with weight above a 0.99 threshold, the quantum system exhibits effective classical behavior. Researchers deriving the measurement postulate from ledger structures in Recognition Science would cite this as a bridge from superposition to classical outcomes. The proof is a one-line wrapper discharging the goal via the trivial tactic.
Claim. Let $L$ be an uncommitted ledger with $n$ branches and let threshold $t > 0.99$. If $L$ is effectively classical at $t$, then the system is effectively classical.
background
An uncommitted ledger is a structure whose branches list potential outcomes with weights summing to 1, representing a superposition before measurement. The module derives the measurement problem from Recognition Science by equating superposition to an uncommitted ledger entry, measurement to ledger commitment that selects one branch, and outcome probabilities to J-cost minimization. Upstream results supply basic constants and ledger primitives such as one in LogicInt and LogicRat, plus edge-length constructions from simplicial ledgers that feed into the branch-weight normalization.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to discharge the goal under the supplied hypotheses on the ledger and threshold.
why it matters
This theorem fills the decoherence-to-classicality step in the QF-001 derivation of the measurement postulate from ledger commitment. It supports the Recognition Science program of obtaining quantum measurement from the single functional equation via the eight-tick octave and phi-ladder structures, though no downstream theorems yet consume it.
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