A Passive, Defect-Tolerant 494.95-MHz Topolectrical Filter: Gaussian Chord Apodization, Three T³ Holonomies, Solid-Torus Routing, and a Möbius Differential Twist

Han Jae Jun

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Passive Defect-Tolerant 494.95-MHz Topolectrical Filter

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Source title: A Passive, Defect-Tolerant 494.95-MHz Topolectrical Filter: Gaussian Chord Apodization, Three T³ Holonomies, Solid-Torus Routing, and a Möbius Differential Twist

Printed author: Mr.K · Archive author: Han Jae Jun

Year: 2026 · Working manuscript, not a verified journal publication.

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This cumulative R01–R03 work constructs a passive, reciprocal 494.948-MHz lumped RF filter from a Gaussian envelope on three chord couplers, three T 3 graph-loop holonomies, annular solid-torus routing, and a crossed-rail Möbius differential twist. The underlying 7 + 6 bipartite graph, realified to 26 differential modes, possesses two exact index modes. R03 restores the full 52-physical-conductor description and adds a precisely specified quasi-static grounded image-charge geometry model of 52 pad centers. We derive the exact differential/common-mode Schur complement and prove a quadratic common-mode conversion bound. The 52-conductor model shifts the two unloaded nominal midgap frequencies by approximately −3.929 and −3.612 MHz; A-node self-capacitance trimming alone leaves a 0.162-MHz splitting. Seven additional balanced signed A–A corrections reduce the maximum shift to 3.738 Hz, and a full set of 91 correction coordinates restores two 494.948-MHz resonances to numerical precision. A Banach contraction theorem, backed by an independently executable conservative interval/residual matrix certificate (Lipschitz constant less than 0.000472), proves exact existence and uniqueness of all 91 passive signed corrections for the specified electrostatic surrogate; the shunt elements are rigorously positive. A new generalized eigenvalue theorem proves immunity of these two modes to arbitrary B-sublattice inductance and capacitance defects when A-sublattice inductors remain equal. A finite-frequency 52-rail reciprocal two-port calculation with parameterized conductor/dielectric loss gives a peak S21 of −3.525 dB near 493.375 MHz for Qcoil(f0) = 80. No measured component values, commercial pad tolerances, 3-D full-wave extraction, or physical fabrication are claimed. R04 proves a … [excerpt; full original in PDF]

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@unpublished{Han2026toporfr20posterreference150cumulative20261013,
  author = {Han Jae Jun},
  title = {Passive Defect-Tolerant 494.95-MHz Topolectrical Filter},
  year = {2026},
  note = {Research source ZIP: TOPO_RF_R20_POSTER_REFERENCE150_CUMULATIVE_20261013.zip; independent theorem proof audit not certified},
  url = {https://han-jae-jun-research.vercel.app/research/topo-rf-r20-poster-reference150-cumulative-20261013.html}
}

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