QuantumState
plain-language theorem explainer
QuantumState defines a normalized map from n basis indices to complex amplitudes. Researchers formalizing wavefunction collapse via ledger commitment cite this structure when connecting amplitudes to Born-rule probabilities. The declaration is a direct structure definition that embeds the unit-norm condition as a field.
Claim. A quantum state on $n$ basis vectors is a function $a : [n] → ℂ$ equipped with the condition $∑_{i=0}^{n-1} |a(i)|^2 = 1$.
background
The module derives the measurement postulate from Recognition Science ledger structure: superposition corresponds to uncommitted entries, measurement to commitment, and outcome probabilities to J-cost. QuantumState supplies the basic object for this derivation. Upstream, CostAxioms.Normalization states that the cost functional vanishes at unity (F 1 = 0). IntegrationGap.A fixes the active-edge count per tick at 1. Parallel structures appear in QuantumLedger and NoCloning, each carrying the same unit-norm field.
proof idea
This is the structure definition itself. It introduces the type with two fields (amplitudes map and normalized sum-of-squares condition) and requires no lemmas or tactics.
why it matters
The structure is referenced by born_rule_jcost_connection, expectedCost, probability, and prob_sum_one in QuantumLedger. Those results interpret |ψ|² as recognition weight and link it to J-cost minimization, fulfilling the module target QF-001. The construction sits inside the eight-tick octave and phi-ladder framework; it supplies the finite-dimensional carrier needed before the variational principle selects committed branches.
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