Q.C. Zhang From Relation to Reality

Complement-Twisted Positive Duality: From One-Time Signature to Singlet Completion and Exchange Dynamics

Connects the one-time carrier to singlet completion and exchange dynamics through a complement-twisted positive duality — without assuming probability, maximally entangled tensors, or the physical composite.

Published
DOI 10.5281/zenodo.22072861
Key relation
positive duality h + canonical complement ⟹ singlet completion

Abstract

A supplied rank-two Complementarity-First carrier has a positive duality h and a canonical complement #. The companion time paper used the local twist h(x,y^#) to obtain an index-one form. Here the same complement acts on one leg of the identity-pairing tensor, Γ_# = e ⊗ e - Σ_{i=1}^m e_i ⊗ e_i, with ω_# = (1/4)Γ_#. Relative to the supplied duality this construction is basis independent, product-positive, and normalized by the rank-two deterministic effect. It gives P(a,b | n,m) = (1/4)(1 - ab n·m). The m = 1 branch is separable; for m ≥ 2, physical admission with the sharp product interface gives CHSH magnitude 2√2. On the selected complex-qubit carrier, ω_# is the Bell singlet projector. The structural complement is positive but not completely positive. For a separately supplied exchange generator we derive G(X) = 2i[ω_#,X]. A partial-swap witness rejects one specific statically self-dual partial-transpose-image cone under the frozen process representation; the stronger carrier-relative PSD closure remains an inherited result. Entangled extensions of Euclidean-ball systems and canonical maximally entangled cone tensors are established prior art. The contribution claimed here is the typed local/tensor/process synthesis, not priority for singlet correlations, maximally entangled tensors, probability, or the physical composite.

Where it sits in the release

CFT-P2 is the structural bridge of the time arc, carrying the one-time signature into singlet completion and exchange dynamics. It is careful about what it does not assume: no probability, no maximally entangled tensors, and no physical composite.

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