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PreprintCC BYZenodo (CERN European Organization for Nuclear Research)

FDCL Part II: Spectral Reduction and Renormalization on FDCL Graphs

  • Bin Seol1
  1. 1Independent Researcher
Open at sourceDOICite

Abstract

Harmonic elimination preserves boundary energy but changes the mass and introduces a spectral-parameter remainder. This preprint compares its killed-Green coefficient with averages of a global hitting potential on finite connected weighted graphs with positive diagonal masses. An interpolation bridge, harmonic-space distance and variance estimates give conditional same-index eigenvalue enclosures. Classical inverse updates and target-selection principles yield computable score intervals and stopping rules. For connected finite-range periodic graphs, the low-band discrepancy coefficient is related to the mass-weighted mean hitting time. A quadratic correction gives an eighth-order fibre eigenvalue approximation, with complex-contour and Taylor-model remainder certificates. Fixed-motif, fixed-correction, fixed-radius interval partitions enclose the least fourth- and eighth-order constants for 48 specified motifs. Fourteen one-dimensional eighth-order constants are exact rational numbers; two further maxima occur at proved endpoints. The paper also retains FDCL discrete and metric spectra, sharp pinning, harmonic-mass bounds and counterexamples to specified frozen refinement recursions. The self-similar voxel mean converges at order 3^(-n), with its limit enclosed in [1.504212027913, 1.508358735603]. Version 2.0 substantially expands the earlier Part II preprint, Spectral Reduction and Renormalization on FDCL Graphs, version 1.0, https://doi.org/10.5281/zenodo.23227296. The manuscript is dated 20 October 2026. Release contents are the 105-page English manuscript, a seven-page scientific figure guide, editable LaTeX source, verification code and supporting data. Written theorems, exact witnesses, validated interval certificates and floating observations have separately stated scopes. Finite computations do not replace general proofs or establish every all-level limiting identification. AI assistance and author responsibility: OpenAI ChatGPT and Codex and Anthropic Claude assisted substantively with mathematical arguments, proof and audit-method development, verification code, computation, data analysis, literature comparison, drafting and revision. Bin Seol directed the research, experiments and cross-domain stress tests, managed the data and evolving definitions, and selected, reviewed and revised the final claims. He is the sole human author and takes responsibility for accuracy, integrity, source attribution and originality. Related counting-mass preprint: Cell averages of hitting times in harmonic graph condensation, https://doi.org/10.5281/zenodo.23345161. Proof-methodology reference: FDCL Part IX, version 1.2, https://doi.org/10.5281/zenodo.23384719. This is a preprint. The author-created manuscript, code, data and figures are released under CC BY 4.0; cited works and external software retain their own rights.

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Cite

BibTeXRIS
BibTeX
@misc{seol2026fdcl,
  title = {{FDCL Part II: Spectral Reduction and Renormalization on FDCL Graphs}},
  author = {Bin Seol},
  howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23227295},
  url = {https://doi.org/10.5281/zenodo.23227295},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - FDCL Part II: Spectral Reduction and Renormalization on FDCL Graphs
AU  - Bin Seol
PY  - 2026
DA  - 2026/10/08
PB  - Zenodo (CERN European Organization for Nuclear Research)
DO  - 10.5281/zenodo.23227295
UR  - https://doi.org/10.5281/zenodo.23227295
AB  - Harmonic elimination preserves boundary energy but changes the mass and introduces a spectral-parameter remainder. This preprint compares its killed-Green coefficient with averages of a global hitting potential on finite connected weighted graphs with positive diagonal masses. An interpolation bridge, harmonic-space distance and variance estimates give conditional same-index eigenvalue enclosures. Classical inverse updates and target-selection principles yield computable score intervals and stopping rules. For connected finite-range periodic graphs, the low-band discrepancy coefficient is related to the mass-weighted mean hitting time. A quadratic correction gives an eighth-order fibre eigenvalue approximation, with complex-contour and Taylor-model remainder certificates. Fixed-motif, fixed-correction, fixed-radius interval partitions enclose the least fourth- and eighth-order constants for 48 specified motifs. Fourteen one-dimensional eighth-order constants are exact rational numbers; two further maxima occur at proved endpoints. The paper also retains FDCL discrete and metric spectra, sharp pinning, harmonic-mass bounds and counterexamples to specified frozen refinement recursions. The self-similar voxel mean converges at order 3^(-n), with its limit enclosed in [1.504212027913, 1.508358735603]. Version 2.0 substantially expands the earlier Part II preprint, Spectral Reduction and Renormalization on FDCL Graphs, version 1.0, https://doi.org/10.5281/zenodo.23227296. The manuscript is dated 20 October 2026. Release contents are the 105-page English manuscript, a seven-page scientific figure guide, editable LaTeX source, verification code and supporting data. Written theorems, exact witnesses, validated interval certificates and floating observations have separately stated scopes. Finite computations do not replace general proofs or establish every all-level limiting identification. AI assistance and author responsibility: OpenAI ChatGPT and Codex and Anthropic Claude assisted substantively with mathematical arguments, proof and audit-method development, verification code, computation, data analysis, literature comparison, drafting and revision. Bin Seol directed the research, experiments and cross-domain stress tests, managed the data and evolving definitions, and selected, reviewed and revised the final claims. He is the sole human author and takes responsibility for accuracy, integrity, source attribution and originality. Related counting-mass preprint: Cell averages of hitting times in harmonic graph condensation, https://doi.org/10.5281/zenodo.23345161. Proof-methodology reference: FDCL Part IX, version 1.2, https://doi.org/10.5281/zenodo.23384719. This is a preprint. The author-created manuscript, code, data and figures are released under CC BY 4.0; cited works and external software retain their own rights.
ER  -