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Complementarity-First Unified Dynamics

Authors: Zhang, Qingchun;

Complementarity-First Unified Dynamics

Abstract

A complementarity-first program begins with typed relational opposition rather than with a preselected spacetime, Hilbert space, probability law, or action. That starting point is generative but underdetermined: a carrier, rank law, real form, orientation, transport, composition, variation space, probability semantics, scale, and history rule must still be supplied or derived. This paper assembles the finite/local Unified Dynamics program from a source-controlled finite corpus. A real doubled carrier W= E⊕E∗ with cross-pairing, grading, positive exchange, and paired transport gives distinct positive and symplectic descendants. Its broad GL(E) form fails to produce a gravitational incidence/coframe entrance, motivating a parent-neutral rank-two Jordan/spin-factor enrichment. On the selected J3 = R ⊕R3 carrier, one conditional reduction yields Lorentzian null incidence, affine coframes, independent Lorentz transport, curvature and torsion, simple bivectors, and a compatible spatial-parity representation, while complement-operation coherence O31 remains open; composition with the companion gravity theorem chain reaches an exact flat Palatini–Regge response and a two-polarization lattice endpoint. A second conditional reduction yields the local qubit spin factor, compact reversible transport, nonlocally silent global directions, and a trace-evaluation coordinate. The trace rule is not forced by kinematics alone: an explicit non-Born family survives until mixture affinity or independent-product factorization with continuity is added. The finite sources establish specific non-implications among causal orientation, relational ordering, thermodynamic monotonicity, and record formation; they do not establish unrestricted pairwise independence. Calibrated persistent records can reconstruct finite Lorentz geometry without exhausting spinorial structure. A common BF-type pairing–curvature kernel supports both gravity and compact relational sectors, but the required variation spaces differ; this is the controlling obstruction to completed dynamical unification. The Quantum-Bridge program closes several minimal/encoded-carrier quantum gaps, while preserving hidden-carrier and elementary-type residuals. On the gravity side, a failed broad transfer is retained, then refined into source-local H2/H2R and symmetry-protected zero-germ branches with distinct mechanisms and evidence tiers. Finally, theorem C210A-GT1 proves a conditional triangulation-general local curved-Regge identity for every closed occurrence satisfying H1–H6, with 1,818 authenticated historical admissions on three fixtures. The strongest result is a finite/local dual-reduction architecture with exact bridges, negative results, and explicit selectors. It is not a completed, continuum, arbitrary-mesh, predictive, or scale-fixing unification.

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