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LESR · Root 6217 local analysis (Paper 09C–09U) LESR 09T · The last cell and finite-chart migration Neo.K / Aletheia

B11 Final Bridge Closure and the Local Positive-Rotation Bridge Seal: the Last Cell, Finite-Chart Migration, a 64-QP Atlas-Agnostic Boundary Certificate, and Research Closure of [10⁻⁴, 0.003]

B11 is 'research-closed', hence all 11 bridge parents (ρ ∈ [1e-4, 0.003]) are closed. The paper discovers that a first-order sign identity is not a finite-chart identity (a '−−−' representative migrates to '+−−') and repairs this with 64 atlas-agnostic quadratic programs (8 sign regions × 8 finite charts; universal lower bound 0.16529554824965303 at ρ = 0.003); radial cover 73,728 cells.

All 11 bridge parents close under research arithmetic; along the way a finite-chart migration problem is repaired with 64 atlas-agnostic QPs. The boxed m_6217(ρ) ≥ m_6217(0) + 0.1ρ² carries the qualifier 'under the accumulated declared research-certificate stack'. The 64-QP repair pairs the universal first-order term with any finite chart's higher-order data and is the logical hinge for 09U; this site has not refereed it, and layer two should test it first. '5000/5000 random states lie in the known atlas' is called a structural diagnostic, not an exhaustive-atlas theorem.

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PreviousLESR 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
NextLESR 09U · Monotone inheritance of the micro gate and the local seal · Micro-Gate Monotone Inheritance and the Local Positive-Rotation Seal: Dominating [0, 10⁻⁴] from the Atlas-Agnostic Lower Bound at ρ = 0.003, and Completing Research Closure of [0, 0.003]

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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