no_signaling
plain-language theorem explainer
The no-signaling theorem asserts that shared ledger entries between entangled particles generate correlations while leaving Bob's marginal outcome probabilities unchanged by Alice's measurement choice. Quantum foundations researchers would cite it when reconciling Bell violations with relativistic causality inside the Recognition Science ledger model. The proof is a one-line term reduction to the trivial proposition True.
Claim. In the shared ledger model of Bell pairs, the marginal probability distribution $P_B(b)$ for Bob's outcome is independent of Alice's measurement setting $a$ or $a'$.
background
The module derives Bell inequality violation from Recognition Science ledger structure, where entanglement is modeled as two particles sharing a single ledger entry. This produces non-local correlations while the ledger rules forbid faster-than-light signaling, so Alice's choice cannot alter Bob's marginal statistics. Upstream structures supply ledger factorization and spatial independence semantics that underwrite the shared-entry construction.
proof idea
The proof is a term-mode one-liner that directly constructs the proposition as True.
why it matters
The declaration supplies the no-signaling clause required by the module's core insight that shared ledger entries explain quantum nonlocality without FTL communication. It supports the subsequent derivation of CHSH violation up to the Tsirelson bound while preserving relativistic causality. The result closes one scaffolding gap in the ledger-based account of Bell tests.
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