isSuperposition
plain-language theorem explainer
The definition marks a quantum state as a superposition exactly when its amplitude map is nonzero on at least two distinct basis indices. Workers formalizing the measurement postulate via ledger commitment in Recognition Science reference it to separate uncommitted multi-branch states from definite outcomes. It is introduced as a direct existential predicate on the amplitude component of the QuantumState structure.
Claim. A quantum state $ψ$ in dimension $n$ is a superposition when there exist distinct indices $i,j$ such that the amplitude of $ψ$ at $i$ and at $j$ are both nonzero.
background
Within the module a QuantumState n is a structure carrying an amplitude map from Fin n to Amplitude together with the normalization condition that the sum of squared moduli over all basis states equals one. The surrounding development treats superposition as an uncommitted ledger entry in which multiple branches coexist before measurement forces commitment to a single recorded value. Upstream structures in QuantumLedger and Information.NoCloning supply analogous amplitude-plus-normalization representations of finite-dimensional states.
proof idea
The definition is supplied directly by the existential quantifier over a pair of distinct Fin n indices whose amplitudes under the state's map are both nonzero.
why it matters
This definition supplies the basic predicate needed to distinguish uncommitted ledger states from definite ones inside the Recognition Science account of wavefunction collapse. It directly supports the module's core claim that measurement corresponds to ledger commitment and thereby prepares the ground for extracting the Born rule from relative J-costs. No downstream theorems are recorded among the used-by edges.
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