RH-W-01-D/E/F/G: Double Vanishing Moments, Correlation Closure, and Mellin–Fourier Interface

Constructed a non-empty, parameterizable, and computable GBUMP test function family that precisely satisfies two Mellin vanishing moments and whose multiplicative correlation function is closed in C_c^∞; closed six sub-GAPs (A/B/C/D/E/G) for this specific subfamily.

PARTIALLY_CLOSED_BY_GBUMP_FAMILY — Self-stated nature from the files in the package: "Test function generator and scope proof; not a proof of RH, does not establish new positivity results for the Weil quadratic form", reproduced here as-is.

Connections

Regarding its relationship with other packages, I try to use the words from its own documents, not my interpretation.

Belongs toResearch Starting Point v0.3 · First GAP Closure

Previous Package · v0.1RH-W-01: Weil Route Test Function Space Fixed

Next PackageRH-W-02: Weil Test Function Core, Range, and Topology

"This round is therefore closed for this specific subfamily: A (all terms of the explicit formula are valid), B (zero sum and absolute convergence), C (surface singularity at x=1 is removable), D (multiplicative correlation function closure), E (exact construction of two vanishing moments), G (explicit conversion between multiplicative Mellin and additive Fourier representations). F has established a dual-implementation consistency test; H has established candidate metadata and verifiers, but has not yet been formalized in Lean/Isabelle." — Excerpt from Section 0 "Deliverables of this Round" in Document 02 of this package.

Sub-GAP Ledger (v0.2) · Sub-GAP Ledger

From RH-W-01_subgaps_v0.2.csv within the package — the status here only holds for the specific GBUMP subfamily, not claiming that the entire v0.1 function class is closed.

Reproduce

Numerical regression and metadata verification (only detects implementation errors; mathematical validity is provided by the analytic derivations in the main document):

python validate_w01_v02.py

01 · B0 Baseline Specification (following v0.1)

The main specification document from the previous round, included exactly as is in this package, for direct citation in this round's derivations.

02 · GBUMP Generating Family and Closure Theorem

Main document of this round — Euler operator D(D+1), Mellin zero-cancellation theorem, explicit parameterized generator, multiplicative correlation closure theorem, additive Fourier representation, and GAP status update table.

Verification Output

From VALIDATION.txt within the package, the raw output of the numerical regression, reproduced line by line.

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Files

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