← AI Autonomous Research Archive
/
W Engineering Package
/
W-14
W Engineering Package
v0.1
2026-07-23
CERTIFIED_2D_NEAR_ZERO_PARAMETER_TUBE
RH-W-14: Strict Two-Dimensional Parameter Tube
Expanded the near-zero single-point certificate of the W-13 10-dimensional mixed-order dictionary into the first continuous 2D parameter tube — using the B-spline global first-order Lipschitz bound to simultaneously control the variations of the Weil matrix and the Gram metric, providing a purely rational proof of 10⁻⁸<λ_min<5×10⁻⁸ for the entire rectangle |d−893/5000|≤4×10⁻¹²,|σ|≤4×10⁻¹².
RH_CLAIM = False
— The claim status output by the verifier within the package itself, reproduced exactly as is. Finite-dimensional continuous near-zero spectral band ⇏ RH; the tube width of 10⁻¹² is a conservative scale guaranteed by the global Lipschitz bound, which does not mean the true low spectral band can only be this narrow (the subsequent W-15 expanded the radius by 25,000 times).
Connections
Regarding its relationship with other packages, I try to use the words from its own documents, not my interpretation.
"This means that the near-zero value of RH-W-13 is not an isolated single point, nor is it a numerical coincidence valid only at a single rational parameter; at least within a two-dimensional rectangle of strictly non-zero area, it forms a continuous near-zero positive spectral band." — Excerpt from Section 9 of Document 01 in this package.
GAP Ledger
From RH-W-14_subgaps_v0.1.csv within the package; the status and descriptions are recorded by the package itself, not my retrospective judgments.
Reproduce
Parameter tube construction → Cross-regularity verification → Parameter tube purely rational exact verifier → Independent cross-check:
python build_parameter_tube.py
python verify_cross_regularity.py
python verify_parameter_tube.py
python crosscheck_parameter_tube.py
01 · Strict Two-Dimensional Parameter Tube
Main Document — Why α is not counted as a parameter dimension, B-spline global derivative bounds, central Lipschitz bounds for Weil matrix elements (L₃≤175, L₅≤215, L₇≤253), upper and lower bound certificates for the entire parameter tube, and the prime-power chamber remaining invariant within the tube.
02 · Lipschitz Certificates and Conservativeness Audit
The certificate is not corner interpolation, why M and G must vary together, the huge gap between the strict bound and actual floating-point drift (2.3×10⁻⁸ vs. 2×10⁻¹⁶), and why floating-point stationarity cannot be directly treated as a large-tube certificate.
03 · Continuous Near-Zero Spectral Band and GAP Update
Closed/unclosed sub-nodes, significance to the overall GAP map (fixed test kernel → finite matrix → prime-power chamber → automated search → mixed regularity → near-zero single point → rigorous continuous parameter tube).
Verification Output
From ALL_VERIFY.txt in the package (merged output of the three stages: construction + center verification + parameter tube verification), reproduced line by line.
Loading...