IndisputableMonolith.Skeleton.Quantum
Skeleton aggregator for the Recognition Science quantum layer. It surfaces three closed tracks: Born-rule uniqueness on 8-mode sectors from J-cost, projector idempotence as commutation structure, and the pure two-qubit concurrence-to-entanglement-entropy chain. A physicist cites it to locate the quantum skeleton without opening the leaf modules. No local proofs; pure re-export of upstream results.
claimThe quantum skeleton collects: (i) uniqueness of $P=|\psi|^2$ as the normalised, phase-invariant, additive probability on 8-mode sectors consistent with the two-branch $\mathrm{e}^{-C}$ rule; (ii) idempotence of the projector algebra; (iii) the pure two-qubit map from Wootters concurrence to strict positivity of von Neumann entanglement entropy.
background
Recognition Science forces quantum measurement statistics from the J-cost $J(x)=(x+x^{-1})/2-1$ and the eight-tick octave (period $2^3$). The Born-rule module states that $P=|\psi|^2$ is the unique probability measure on 8-mode sectors that is normalised, phase-invariant, additive over disjoint mode-sets, and consistent with the two-branch $\exp(-C)$ rule (QF-002, DFT-8 sector forcing).
Commutation structure is kept minimal: the projector algebra is idempotent, supplying the algebraic skeleton for observables without extra RS postulates. Track 2.B treats pure two-qubit states: Wootters concurrence of the amplitude matrix is linked to strict positivity of the von Neumann entanglement entropy, closing that track with no proof holes and no new RS assumptions.
This skeleton module sits in the Skeleton domain and only imports those three quantum leaves; it introduces no new definitions of its own.
proof idea
Definition and re-export module; no local proofs. Argument structure is entirely upstream: Born-rule uniqueness via DFT-8 sector forcing and J-cost consistency; projector idempotence as a one-line algebraic fact; and the Track 2.B reduction from pure two-qubit concurrence to entanglement-entropy positivity. The skeleton merely assembles the import surface.
why it matters in Recognition Science
Gives a single entry point for the RS quantum layer inside the Skeleton domain. Upstream it rests on QF-002 (Born rule from J-cost), the structural commutation module, and the closed Track 2.B concurrence-entropy theorem. Downstream usage is not yet wired in the graph (no used_by edges), so the module presently serves as a stable import hub rather than a lemma feeder. It ties the eight-tick octave and J-cost forcing chain directly to standard quantum measurement and entanglement statements without enlarging the axiom set.
scope and limits
- Does not prove the Born rule, concurrence bounds, or projector laws locally.
- Does not treat mixed states, multipartite entanglement, or continuous-variable systems.
- Does not derive dynamics, Hamiltonians, or decoherence rates.
- Does not add new RS axioms beyond the three imported modules.
- Does not yet feed named downstream theorems in the dependency graph.