Odd Weil-form bounds by positive exterior elimination
Loading original first page…
Abstract
We give a complete lower certificate for the odd part of the original minimal theta-weighted Weil form. A positive infinite-rank exterior is absorbed through its directional covariance with the signed low-frequency features. An endpoint chord for the receiving resolvent reduces the required information to two finite matrices, without assuming a positive lower bound for the true feature Gram. At arithmetic cutoff eight this yields q_H[h] ≥ −1.88 × 10⁻⁹ ‖h‖₂² for every odd h in the original form domain V. The proof retains the original polar constraint, four odd exact derivative-null rows, the complete arithmetic remainder and all low/exterior mixed terms. Directed ball arithmetic verifies the resulting matrix of order 4085. The method also has a concrete boundary: at arithmetic cutoff eleven, with the same frequency band and multiplication parameter, the actual positive exterior has odd ambient norm greater than 1.7. We prove the first-moment receiver’s optimality in its finite information class and a convergent higher-moment refinement.
Read the full paper in the original PDF.
Edition files
- main.pdf154.7 KiB · pdf
SHA-256
465c300bbc47c5238bbadca5a16e76a76a8bf5d8d80c98a094fe036a0f578490 - Odd-Weil-form-bounds-publication-package.zip110923.3 KiB · package
SHA-256
35aad2b6895a97fda5020e73f3aa882e25d868a3e5945d1811a9c6d69bc400e6
Available editions
Research details
- Subjects
- Mathematics · Number Theory and Special Functions · Analysis and Spectral Theory
- Keywords
- Weil form, theta function, operator lower bounds, Schur complement, directed ball arithmetic, spectral certificates
- Manuscript date
- 2026-10-26
- Reader reuse
- No additional permission granted
Scope
Complete original odd-domain weighted Weil-form lower bound with allowance 1.88e-9; positive-exterior directional moment elimination and a method boundary at arithmetic cutoff eleven.
Disclosures
AI assistance was used in mathematical development, literature comparison, manuscript preparation and computational verification.
Reproduction
The supplementary ZIP contains the editable manuscript, deterministic build helper, directed-arithmetic certificate generator, saved dyadic data, separate finite-target reconstruction, scalar analytic verifiers and a complete SHA-256 member manifest. Its README distinguishes full regeneration from saved-data reconstruction.