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LESR · Root 6217 local analysis (Paper 09C–09U) LESR 09M · B04 split closure Neo.K / Aletheia

B04 Split Closure and Removal of the First High-Order Frontier: From Remainder Over-Enclosure to Full-Parent Research Closure — Root-Neighbourhood Sharpening and a Chartwise Radial Interval Lift

The B04 'frontier' is interval over-enclosure, not geometry: shrinking the root neighbourhoods on the (−,+,+) chart from ±0.02 to ±0.003 drops its fourth-derivative bound to 16,865.6, and a chartwise interval radial-derivative compiler closes the radial freedom; B04 is 'research-closed' (worst lower bound 0.100642).

B04's obstacle came from interval over-enclosure, not geometry; after sharpening the root neighbourhoods B04 closes under research arithmetic. The margin over 0.1 is only 6.4e-4; the same research-closure qualifiers apply.

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PreviousLESR 09K · Research closure of B01 · Uniform Cubic Bound and Research Closure of B01: Eight Cubic Charts, a Fourth-Order Interval Taylor Remainder, and the Research Closure of the First Full Bridge Parent

NextLESR 09O · The explicit quartic–quintic repair and B06 research closure · Explicit Quartic–Quintic Repair and Research Closure of B06: From the Positive-ρ Re-Centering Idea to Explicit Higher-Order Coefficients — Ψ₄, Ψ₅ and a Sixth-Order Interval Remainder

This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.

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