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Phase-Controlled Exciton Transport, Gaussian Noise and Projector-Loop Holonomy

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Printed title: Phase-Controlled Exciton Transport, Gaussian Noise and Projector-Loop Holonomy

Original byline: Mr.K · Archive author: Han Jae Jun

Manuscript year: 2026. Not a claim of peer-reviewed publication.

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We investigate phase-frustrated ciliary arrays and synthetic excitonic networks using four distinct structures: Gaussian regularization and correlated noise; a three-torus T 3 of phase controls; a solid-torus homotopy collar; and an anti-periodic, Möbius-type frame lift. For a three-site exciton ring we derive the exact hopping-flux spectrum, disorder-splitting bounds, Lindblad trapping formulas, noise-assisted and noise-suppressed transport regimes, and explicit observability obstructions. We obtain coherent and population-based loop-phase diagnostics, Gaussian-bath identifiability and falsification conditions, and finite-time estimation certificates. A hierarchy of rank-one spectral-projector, Riesz-resolvent, residual, finite-mesh, and Schur- complement bounds yields nonvanishing loop traces and integer-winding stability under specified operator-error envelopes. The strongly coupled synthetic four-state family admits a 1/125 block-error ball, an infinite-dimensional positive complementary sector, and arbitrary continuous changes of spectator strength. A shared unitary conjugation and independent scalar energy shifts leave the cyclic projector trace exactly unchanged; a Gaussian residual- covariance bound can reduce the dimensional dependence of conditional confidence certificates. We also construct a counterexample showing that independent, nonshared conjugations can change winding. These results are mathematical statements about precisely specified effective models and certified surrogate data. Chemical aromaticity, physical nonorientability, and excitonic hopping holonomy are not interchangeable. Existing structural and photophysical evidence for candidate macrocycles does not establish a molecular excitonic Hamiltonian with the requisite basis, spectral gaps, and … [source excerpt; see full PDF]

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Original ZIPGTSM_BIOPHYSICS_INTEGRATED_V31_20261014.zip
Main PDFpdf/main/gtsm-biophysics-integrated-v31-20261014.pdf
PDF pages133
PDF SHA-256069af14fee2032658a4881780563ab238e645d69ab06328cab0916255f07a5f8
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@unpublished{Han2026gtsmbiophysicsintegratedv3120261014,
  author = {Han Jae Jun},
  title = {Phase-Controlled Exciton Transport, Gaussian Noise and Projector-Loop Holonomy},
  year = {2026},
  note = {Research source ZIP: GTSM_BIOPHYSICS_INTEGRATED_V31_20261014.zip; independent theorem proof audit not certified},
  url = {https://han-jae-jun-research.vercel.app/research/gtsm-biophysics-integrated-v31-20261014.html}
}

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Original source version: GTSM_BIOPHYSICS_INTEGRATED_V31_20261014.zip

Main PDF SHA-256: 069af14fee2032658a4881780563ab238e645d69ab06328cab0916255f07a5f8

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