Certified source elimination for localized odd Weil forms
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Abstract
We give a quantitative local correction and a form-domain continuation method for the complete odd Weil form. On the support |u|<(1/2)log 8 we verify a positive scalar floor together with a 3×10^(-11) directional floor along the normalized first-collar polar profile. The sharp coefficient of that profile lies between 3×10^(-11)+10^(-40) and 5.641396988×10^(-11). The lower certificate compresses to every intermediate support between (1/2)log 7 and (1/2)log 8. For a compact physical source with a certified gap, we construct an explicit logarithmic Fourier reference and a finite inverse upper using form-core trials and exterior and constraint annihilators. The resulting certificates are complete at every strict finite cap. A rational example exhibits a strict cap certified by the completed receiver although every fixed-extension primal trial fails. Directional inverse metrics, exact polar elimination and portable interval and rational verification provide the local application and its continuation inputs.
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- Certified-source-elimination.pdf147.4 KiB · pdf
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ae8ccfd7033e27e6520835f8b58ff29bb6ad774c9238175da550d3dbc6cb9ef5 - Certified-source-elimination-publication.zip208.0 KiB · package
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Research details
- Subjects
- Mathematics · Number Theory · Functional Analysis · Numerical Analysis
- Keywords
- Weil forms, Schur complements, coercivity, inverse bounds, form domains, interval arithmetic
- Manuscript date
- 2026-10-26
- Reader reuse
- No additional permission granted
Scope
On odd physical support |u|<(log 8)/2, a complete localized Weil certificate gives scalar floor 10^(-40) and first-collar directional floor 3×10^(-11), with the stated sharp-coefficient bracket and intermediate support compressions. Compact gapped sources admit the specified annihilator-completed inverse continuation certificates.
Disclosures
AI assistance was used in research, computation, verification and manuscript preparation.
Reproduction
The 16-page manuscript and editable sources are supplied in this 28-member package. README.md and local-certificate/README.md give build and Python 3.12/NumPy 2.3.5/python-flint 0.9.0 reproduction commands. The full localized runner regenerates interval Grams, finite/infinite tail bounds, scalar/directional certificates and polynomial upper trials at 2048-bit matrix precision, then runs exact-rational final checks. code/verify_annihilator_receiver.py supplies separate rational controls and code/verify_first_step.py the separate 192-bit quantitative comparison. Generated outputs use a reader-selected empty directory.