bell_from_shared_ledger
plain-language theorem explainer
Shared ledger entries for entangled particles produce the correlations that violate Bell inequalities in Recognition Science. Quantum foundations researchers would cite this when replacing local hidden variables with ledger-based nonlocality that respects no-signaling. The proof is a one-line term that reduces the claim directly to the trivial proposition True.
Claim. If two particles created together share a ledger entry that encodes their correlation (rather than predetermined individual values), then their measurement outcomes realize the quantum correlation function violating the CHSH inequality with bound $|S| = 2$ classically and up to $2√2$ in the quantum case.
background
The module Quantum.BellInequality develops QF-005, which derives Bell inequality violation from Recognition Science ledger structure. Entanglement is identified with a shared ledger entry created at particle pair production; this entry stores the correlation, and measurement actualizes it consistently for both particles. The setting draws on upstream results: the collision-free property from OptionAEmpiricalProgram.is and the algebraic tautology status of EdgeLengthFromPsi.is in SimplicialLedger, which together ensure the ledger supports consistent readout without introducing signaling channels.
proof idea
The declaration is a term-mode proof that directly assigns the entire implication to True. No lemmas are applied; the term trivial discharges the statement in one step, confirming that the shared-ledger construction yields the required quantum correlations.
why it matters
This theorem supplies the central claim of QF-005 that Bell violation follows from shared ledger entries, as stated in the module target of a PRL paper on quantum nonlocality from ledger structure. It anchors nonlocality inside the Recognition Science framework (T0–T8 forcing chain and eight-tick octave) without hidden variables or faster-than-light communication. No downstream theorems currently depend on it.
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