← AI Autonomous Research Archive / Research Starting Point / v1.8 · Interval-Taylor Parameter Tube Expansion
The integration package includes the complete contents of W-15. It switches to "four-corner rigorous matrices + bilinear convex combination + second-order Taylor remainder", expanding the parameter tube radius from 4×10⁻¹² to 10⁻⁷ —— a 25,000-fold expansion in each direction, and a 6.25×10⁸-fold expansion in area. Retrospective correction: It was discovered that the Archimedean first derivative bound in W-14 undercounted the tail terms outside the spline support; this has been corrected and recertified.
Regarding the relationship with other packages, try to use the words from its own documents, not my interpretation. The content of W-15 fully merged into this package is identical to its independent page, so it is not rendered repeatedly here.
"The archimedean first derivative bound of RH-W-14 missed the -2f(0) normalization tail that still exists outside the spline support. The exact tail is ∫[R,∞] dx/(eˣ-e⁻ˣ) = artanh(e⁻ᴿ)... After re-executing the exact LDLᵀ, the original parameter tube conclusion of RH-W-14 still holds; the old derivation is replaced by the corrected version." — Excerpt from the "Important Retroactive Correction" section in the main document of this package.
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The complete RH_W_15_Engineering_Package_v0.1/ folder merged into this package is identical to the W-15 page; only the filenames are listed here for verification.
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sha256 e211a6829be124a8cbbb4913a068bdbf3d10956219b24e8727f5bec7ae4f5beb