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| < (log 8)/2 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 (log 7)/2 and (log 8)/2. 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.pdf146.9 KiB · pdf
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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
The complete localized odd physical Weil form, its first-collar directional coefficient and continuum compression, and finite inverse certificates for compact physical sources with a certified gap. The strict-cap completeness theorem uses form-dense primal trials and dual-dense source-complement and exact-constraint annihilators.
Disclosures
AI assistance was used in research, computation, verification and manuscript preparation.
Reproduction
The source package includes the complete analytic local certificate and portable regeneration programs. Run local-certificate/Reproduce corrected first step.py with an empty output directory to regenerate the full interval Gram, finite and infinite-tail covariances, lower certificates and native polynomial upper. Python 3.12, NumPy 2.3.5 and python-flint 0.9.0 are specified. Separate standard-library rational checks and a clean LaTeX reader build are included.