IndisputableMonolith.Quantum.EntanglementOntologyStructure
Module that treats entanglement as structural content carried by interference cross terms on the recognition ledger. It sits downstream of the Born-rule derivation from J-cost and packages the ontology that links ledger correlations to measurable interference. Physicists citing RS quantum structure use it to fix what "entangled" means without extra Hilbert-space postulates. The content is definitional and structural rather than a deep existence proof.
claimEntanglement ontology is the structural content of a bipartite (or multipartite) ledger state carried by interference cross terms: non-factorizing amplitudes whose Born weights $P=|\psi|^2$ produce correlations that cannot be written as a product of local sector measures. The module records that this structure implies observable interference and is induced from the ledger.
background
Recognition Science derives quantum probabilities from the J-cost on the eight-tick (DFT-8) sector forcing chain. The upstream Born-rule module states that $P=|\psi|^2$ is the unique normalised, phase-invariant, additive measure on 8-mode sectors consistent with the two-branch $\exp(-C)$ rule.
In that setting, a pure product assignment on disjoint mode sets has vanishing cross terms. Nonzero cross terms are the ledger's way of encoding non-separable correlations. This module names that structural content "entanglement ontology": entanglement is not an extra postulate but the presence of those interference contributions in the recognition amplitudes.
Sibling names in the module point to three pieces: induction of the ontology from the ledger, the structure object itself, and the implication from entanglement to interference.
proof idea
Definition and structure module rather than a single deep theorem. It introduces the entanglement-ontology object as the cross-term content of ledger amplitudes, records the map from ledger data into that structure, and states that the presence of the ontology forces interference signatures in the Born weights. Arguments lean on the unique Born measure from the imported Born-rule development; no independent probability calculus is rebuilt here.
why it matters in Recognition Science
Gives RS a precise place to hang entanglement without importing textbook Hilbert-space axioms as primitives. By tying entanglement to interference cross terms already controlled by J-cost and the eight-tick sector picture, it keeps the quantum layer inside the same forcing chain that yields the Born rule. Downstream use is not yet wired in the graph (no used_by edges), so the module is presently a structural hub for quantum ontology rather than a leaf lemma under a named parent theorem. It supports any later claim that ledger non-factorization is exactly what experiments call entanglement.
scope and limits
- Does not derive the Born rule; that is imported from the BornRule module.
- Does not prove experimental Bell inequalities or CHSH bounds.
- Does not construct multipartite entanglement monotones or entropy measures.
- Does not address mixed-state or decoherence dynamics beyond structural cross terms.
- Does not claim a unique tensor-product Hilbert space realization.