RH-W-16: Three-Parameter Near-Zero Spectral Tube

Incorporating the kernel scale h itself into the parameter domain, establishing the first 3D rational box |h−1797/10000|≤10⁻⁸, |d−893/5000|≤10⁻⁷, |σ|≤10⁻⁷ — the eight corner points each assemble a complete true Weil interval matrix, with trilinear convex interpolation plus second-order Taylor remainder, providing an exact proof that 10⁻⁸<λ_min<5×10⁻⁸ is strictly satisfied throughout the entire non-degenerate 3D volume.

RH_CLAIM = False — The claim status output by the verifier within the package itself, reproduced as is. 3D finite parameter tube ⇏ RH; no true Weil negative witness was found.

Connections

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

Belongs toResearch Starting Point v1.9 · Three-Parameter Near-Zero Spectral Tube

Previous PackageRH-W-15: Interval–Taylor Parameter Tube Expansion

Next PackageRH-W-17: Chamber-Aware Slicing and Event Thin Layer

Batch 0116 / 20

"This round established the first 3D continuous near-zero positive spectral parameter box... It proves that the near-zero positive spectral structure exists not only at a single point or a fixed-scale plane, but extends to at least a non-degenerate 3D volume. However, it remains merely a finite-dimensional result on a fixed 10-dimensional dictionary: a 3D finite parameter tube ⇏ RH." — Excerpt from Section 10 of Document 01 in this package.

GAP Ledger

From RH-W-16_subgaps_v0.1.csv in the package; the status and evidence are recorded by the package itself, not my retrospective judgment.

Octagonal Non-Rigorous Spectral Observation

From corner_spectrum_observation.csv in the package — Midpoint generalized eigenvalues of the eight corner points, for exploratory observation only, not participating in the certificate.

Reproduce

Purely rational exact verifier (does not regenerate transcendental matrices, only uses stored intervals):

python verify_three_parameter_tube.py

Complete reconstruction of the eight-corner matrix (slower, requires regenerating eight sets of jump-resolved Archimedean matrices):

python build_three_parameter_tube.py

01 · Three-Parameter Near-Zero Spectral Tube

Main document — why h is a genuinely new direction (simultaneously changing support width/sampling position/Gram/endpoints/prime-power/Archimedean tail), the trilinear corner architecture, the second derivative in the scale direction, and the exact upper and lower bound certificate.

02 · Scale Curvature Certificate and Computational Architecture

The added computational burden in this round (the octagon requires eight sets of Archimedean data), reusable data layers, separation of certificates and exploration, and the next engineering problem (chamber-aware subdivision).

03 · GAP Updates and Batch 01 Progress

Closed/kept open sub-nodes, Batch 01 progress 16/20, remaining nodes (W-17 Chamber-Aware Slicing, W-18 Certificate Backend Unification, W-19 Adversarial Reproducibility Audit, W-20 Batch 01 Integration).

Verification Output

From ALL_VERIFY.txt in the package, reproduced line by line.

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Files

The octagonal complete interval certificate (three_parameter_tube_certificate.json) is relatively large and is not listed individually; it is in the full zip file.

Download Complete Package (299.6 KB)

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