QuantumState
plain-language theorem explainer
A quantum state is a normalized complex vector of length n whose squared moduli sum to one. Workers deriving unitarity from ledger conservation in Recognition Science cite this structure to anchor probability definitions. The definition is a direct encoding of the unit-norm condition with no separate proof steps required.
Claim. A quantum state in an $n$-dimensional complex Hilbert space is a map assigning a complex amplitude to each of $n$ basis vectors such that the sum of squared moduli equals one: $∑_{i=1}^n |ψ_i|^2 = 1$.
background
The module QFT-009 derives unitarity from ledger conservation, where the ledger is a conserved quantity implying probability conservation and reversible evolution. Upstream, IntegrationGap.A fixes the active edge count per tick at 1, while QuantumLedger.QuantumState supplies the ledger-configuration version of the same structure. NoCloning.QuantumState and Masses.Anchor.A supply parallel unit-vector and coherence-energy conventions used in the same derivation chain.
proof idea
This is a structure definition that directly encodes the normalization condition for a quantum state vector.
why it matters
The structure supplies the type used by born_rule_jcost_connection, expectedCost, probability, prob_nonneg and prob_sum_one in QuantumLedger, which connect J-cost minimization to the Born rule. It fills the QFT-009 step that obtains unitarity from ledger conservation and feeds NoCloning.CloningMachine and innerProduct. The declaration touches the open question of whether ledger conservation alone recovers the full eight-tick reversibility axiom.
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