An Interval-Certified Positivity Block at c=13 for an Odd Pole-Free Riemann Reduction

We establish positivity of the canonical localized pole-free odd closed form at the fixed support parameter c=13. The proof combines an exact arithmetic-source identification, a uniform high-diagonal Schur transfer, finite interval-certified elimination, and a corrected enclosure of the infinite residual tail. The central new result is: the low-sixteen comparison closes the fixed-c=13 pole-free odd form, including its infinite residual tail. This is a computer-assisted result using explicitly inherited certificates and reviewed analytic premises; it is not a proof of the Riemann hypothesis, full Weil positivity, or positivity at all support scales. The proof proceeds in three stages. First, the localized pole-free odd source is identified analytically before integer specialization: a regularized arithmetic functional on C^1([0,L]) has an odd entire sine transform whose genuine derivative at each integer gives exactly the implemented derivative datum, identifying the endpoint divided-difference matrix with the canonical localized pole-free odd restriction. Second, four integrations by parts establish a uniform sign bound on the closed-form archimedean generator derivative for n ≥ 71; combined with the exact odd Hilbert/Hankel decomposition and the v3-certified finite-prime capacity, this gives an operator-level diagonal lower bound on high modes, allowing a certified post-H0 Schur denominator δ = 1.54726 using the original certified interface bound U ≤ 1.01738391101161043. Third, the v3 analytic tail envelope is corrected (the first-node factor bound was invalid at infinity) and the low-sixteen comparison K = S − (T1+T2)/1.54726 is certified: both 256-bit and 320-bit corrected C runs pass all elimination pivots; an independent 384-bit verifier reconstructs the 16×16 comparison matrices and certifies all 16 Schur pivots strictly positive (independent last pivot [3.36e-48 ± 3.59e-51] at 256 bits, [3.36e-48 ± 3.58e-51] at 320 bits). A separately verified stronger interface bound U < 0.261474802 supports δ = 2.30317 (optional, not a dependency of the lean route). 71 unit/adversarial tests and 13 byte-preservation checks all pass. The following remain outside this result. The scalar pole criterion 2⟨s,(B^{pf,o})^{-1}s⟩ ≤ 1 has not been certified; pole-free positivity and rank-one inertia do not supply it. The even sector is not covered. An all-scale result for the full Weil criterion, as required for RH under CCM Corollaries 3.7–3.8, remains open: sending the matrix cutoff to infinity at fixed log(13) does not send the support scale to infinity. The deposit bundle includes the v4 paper (Markdown and rendered PDF), and a combined certification archive integrating the correction-stage v4 archive with the closure-continuation evidence: arithmetic source identification, uniform derivative lemma, corrected analytic tail envelope, full-size C256/C320 elimination pivots, independent 16-pivot Arb reconstruction, coordinator lean-branch replay, all source code and test suites, and structured receipt files.