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Exchange Realization of Relational Coherence: Exact Synthesis and Resource Bounds

Qingchun Zhang

Published Sep 10, 2026• 0 citations

Abstract

This preprint studies a cycle-reflection operation on a supplied six-qubit realization of paired trigram configurations. A four-matched-pulse identity and a minimum within its stated serial grammar are separated from an ordinary-exchange endpoint construction. The raw full-source reflection and its full domain-safe alternative are different tasks: the latter is excluded by a collective-symmetry obstruction in the admitted source-only exchange model. Strict preservation of the addressable sector throughout the path is also excluded for the full task, while finite-action lower bounds quantify peak no-address population and time-integrated exposure. The paper presents an explicit low-excursion balanced word and a conditional joint clock–amplitude error certificate. Root settings and trajectory inputs remain tied to their supplied computer-assisted certificates. The second internal review reproduced all ten advertised numerical routes and twenty-four outputs using the original programs; this is same-program reproducibility, not independent implementation or external peer review. A separate Lean supplement covers the finite raw/safe operator algebra and the obstruction for arbitrary finite words of the declared algebraic factors. It does not formalize the numerical roots, matrix exponentials, continuous-time dynamics or resource theorems. No global pulse optimum, measured hardware feasibility, general noise tolerance, or automatic connection to the companion recovery code is claimed.

DOI: 10.5281/zenodo.22696553

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Motivated by Complementarity-First's distinction between a relational operation and its physical implementation, we study one-use source refresh in a supplied autonomous classical Hamiltonian model. A moving courier must reach a stationary source, exchange arbitrary internal contents with it, and expose the fresh input and retained old output at one fixed readout time. A positive completed-square kinetic coupling makes the completed exchange depend on spatial area rather than entering speed. A separate position-dependent recovery interaction transfers energy from a main mechanical carrier to a courier that may be nearly stopped. For four real four-coordinate internal registers and two mechanical pairs, the combined construction admits the fixed product domain ||(x,y,b,c)|| ≤ 1, 18.6193 ≤ α ≤ 18.6248, with mechanical preparation independent of the unknown internal data. Exact-rational certificates for a reduced three-coordinate release law, together with recovery estimates, give source completion before time 47 and an interaction-free readout at 33π/2. Certification here concerns reduced-system arithmetic, not a formal-kernel proof or validated integration of all twenty coordinates. Fresh loading is exact; the source/old-output pair has error at most ε_pre ||(x,y,b)||, with ε_pre < 0.007338, against its declared ideal comparison. This is not a whole-processor accuracy bound. The full endpoint retains two additional main-port passages, the remaining internal registers, and both mechanical records. Its mechanical energy allocation excludes immediate reapplication of the same ready-state contract, while a source-only witness excludes an exact payload-only linear reduction. The result supplies a bounded one-use implementation conditional on the stated architecture. Physical rearming, all-input/all-word linear control, and primitive selection of the carrier and interactions remain outside the theorem.