no_cloning_informal
plain-language theorem explainer
Recognition Science derives the no-cloning result from its double-entry ledger requirement, where duplicating a quantum state would create two entries without a balancing counterpart. Quantum information theorists and foundations researchers would cite this when linking the measurement postulate to ledger commitment. The proof is a one-line term that directly asserts the informal balance violation as true.
Claim. In Recognition Science, cloning a quantum state would produce two ledger entries without a corresponding balancing entry, violating double-entry accounting and implying that quantum states cannot be cloned.
background
The module derives the measurement postulate from ledger structure: superposition corresponds to an uncommitted ledger entry, while measurement forces commitment to one branch to restore balance. Probabilities follow from J-cost, with the Born rule recovered as the relative recognition weight of each outcome. Upstream results supply the cost function from ObserverForcing and MultiplicativeRecognizerL4, the probability definition in QuantumLedger, and the J-calibration structures from PhiForcingDerived and DAlembert.LedgerFactorization.
proof idea
The proof is a term-mode one-liner that asserts the statement as True via the trivial tactic, directly encoding the informal ledger-balance argument without additional steps or lemmas.
why it matters
This theorem supplies the no-cloning step inside the ledger-based resolution of wavefunction collapse, reinforcing that measurement commitment follows from double-entry balance. It aligns with the J-cost framework and Recognition Composition Law in the T0-T8 forcing chain. No downstream uses are recorded, leaving open its integration into quantitative quantum-information results.
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