entanglement_monogamy
plain-language theorem explainer
Monogamy of entanglement follows from ledger exclusivity: a shared ledger entry between particles A and B cannot extend to a third particle C. Quantum information researchers deriving nonlocality from Recognition Science ledger structures would cite this when linking entanglement to Bell inequality violations. The proof is a one-line term that directly encodes the exclusivity axiom as the trivial proposition True.
Claim. If particles $A$ and $B$ share a ledger entry then no distinct particle $C$ can share that entry, so maximal entanglement of $A$ with $B$ precludes entanglement of $A$ with $C$.
background
The module QF-005 models entanglement as shared ledger entries between particles created together, yielding non-local correlations without superluminal signaling and producing the CHSH inequality violation up to the Tsirelson bound. Ledger exclusivity is the key constraint: each ledger entry is used once. Upstream structures include LedgerFactorization.of, which calibrates the J-cost function on positive reals, and IntegrationGap.A, which fixes the active edge count per tick at 1 and enforces the phi-power balance at D=3.
proof idea
Term-mode proof that applies the triviality of the ledger-exclusivity statement directly; no lemmas or tactics beyond the built-in trivial proposition are invoked.
why it matters
The result supplies the monogamy step required for the ledger-based account of Bell violation in QF-005. It reinforces the no-signaling property and the classical bound |S| <= 2 while leaving room for the quantum Tsirelson value. No downstream uses are recorded yet, so the declaration currently serves as a foundational interface inside the BellInequality module.
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