One Reciprocal in One Coefficient: Anatomy of a Failed Interface-Tail Certificate at c=13

Version 4 of this record certified an interval-arithmetic bound on the interface between modes 17{:}5000 and modes 5001{:} infty of the localized pole-free odd form at c=13, and used that bound to close a 16 times16 Schur comparison and conclude coercivity of the form. The interface bound does not follow from the released code. The released certification/tail_bound.py computes the infinite-mode interface contribution with the prefactor 9/64 at the point where the derivation requires (8/3)^2=64/9. The two numbers are reciprocals. Correcting the coefficient multiplies the released tail by 4096/81=50.5679012345679 ldots, the corrected tail is bounded above by 1.641829102700734064 rather than 0.03246781184540026, and both closure routes in v4 lose their positive global gate. Seven v4 statements are withdrawn as certificates: the interface tail U_ infty le0.03246781184540026; the total interface bound U_{ mathrm{final}} le1.01738391101161043; the optional complete interface bound U<0.261474802; the post-H_0 operator denominators 1.54726 and 2.30317; the inference from positive 16 times16 comparison pivots to coercivity of the full form; the conclusion that fixed-c=13 pole-free odd coercivity is established; and the Schur separation delta_{ mathrm{Schur}} approx0.1611237793846104656, which v4 defines as lambda_H-U_{ mathrm{final}} and which therefore inherits the defect. Ten v4 results are not downstream of the defective coefficient and are retained: the algebraic identities; the finite contribution U_0 le0.98491609916621017; the arithmetic-source identification; the derivative lemma alpha'_{ mathrm{cf}}(n)>0 for n ge71; the pre-interface growing-diagonal estimate; the independent high-block certificate D^{pf}_{H,H} succeq1.17850769039622089 ,I; the fresh finite-interface bound 0.22900698926272015 for modes 5001{:}10000; the finite elimination pivots and positivity of S; the corrected residual-tail T_2 envelope for modes 40001{:} infty; and the interval LDL computations on the emitted low-sixteen matrices, the last retained only as a conditional finite-matrix computation that certifies no operator lower bound. The defect is a failure of the released sufficient proof. It is not a proof that the true interface norm exceeds the required threshold, not a counterexample to the localized operator inequality, and not evidence for or against the Riemann hypothesis. Fixed-c=13 pole-free odd coercivity is not established by v4. This paper withdraws the defective certificate and then records the repair carried out after the withdrawal. The correction applies to the deposited argument regardless of that repair. Version 5 corrects version 4 (DOI 10.5281/zenodo.22330843). It withdraws the defective interface-tail certificate and the conclusions that depend on it, states exactly which v4 results survive, sets the replacement gate, and then reports the repair carried out at cutoff 40000: a new interval-certified finite block on rows 10001:40000, the corrected analytic tail above 40000, a composed interface bound below 0.454943, a reopened global gate at mode 5001, and a supported comparison denominator of 2.10 at which both archived low-sixteen datasets pass. The repaired comparison holds with explicitly inherited premises and does not retroactively validate v4. The replay bundle is deposited with the record. Concept DOI 10.5281/zenodo.22293309.

Authors

Institutions

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-09
DOI
https://doi.org/10.5281/zenodo.22672234
Primary Topic
Electromagnetic Scattering and Analysis
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

One Reciprocal in One Coefficient: Anatomy of a Failed Interface-Tail Certificate at c=13

Honeycutt, Edwin Marshall, III
Zenodo (CERN European Organization for Nuclear Research)
Electromagnetic Scattering and Analysis
preprint

One Reciprocal in One Coefficient: Anatomy of a Failed Interface-Tail Certificate at c=13

Honeycutt, Edwin Marshall, III
preprint en

Abstract

Version 4 of this record certified an interval-arithmetic bound on the interface between modes 17{:}5000 and modes 5001{:} infty of the localized pole-free odd form at c=13, and used that bound to close a 16 times16 Schur comparison and conclude coercivity of the form. The interface bound does not follow from the released code. The released certification/tail_bound.py computes the infinite-mode interface contribution with the prefactor 9/64 at the point where the derivation requires (8/3)^2=64/9. The two numbers are reciprocals. Correcting the coefficient multiplies the released tail by 4096/81=50.5679012345679 ldots, the corrected tail is bounded above by 1.641829102700734064 rather than 0.03246781184540026, and both closure routes in v4 lose their positive global gate. Seven v4 statements are withdrawn as certificates: the interface tail U_ infty le0.03246781184540026; the total interface bound U_{ mathrm{final}} le1.01738391101161043; the optional complete interface bound U<0.261474802; the post-H_0 operator denominators 1.54726 and 2.30317; the inference from positive 16 times16 comparison pivots to coercivity of the full form; the conclusion that fixed-c=13 pole-free odd coercivity is established; and the Schur separation delta_{ mathrm{Schur}} approx0.1611237793846104656, which v4 defines as lambda_H-U_{ mathrm{final}} and which therefore inherits the defect. Ten v4 results are not downstream of the defective coefficient and are retained: the algebraic identities; the finite contribution U_0 le0.98491609916621017; the arithmetic-source identification; the derivative lemma alpha'_{ mathrm{cf}}(n)>0 for n ge71; the pre-interface growing-diagonal estimate; the independent high-block certificate D^{pf}_{H,H} succeq1.17850769039622089 ,I; the fresh finite-interface bound 0.22900698926272015 for modes 5001{:}10000; the finite elimination pivots and positivity of S; the corrected residual-tail T_2 envelope for modes 40001{:} infty; and the interval LDL computations on the emitted low-sixteen matrices, the last retained only as a conditional finite-matrix computation that certifies no operator lower bound. The defect is a failure of the released sufficient proof. It is not a proof that the true interface norm exceeds the required threshold, not a counterexample to the localized operator inequality, and not evidence for or against the Riemann hypothesis. Fixed-c=13 pole-free odd coercivity is not established by v4. This paper withdraws the defective certificate and then records the repair carried out after the withdrawal. The correction applies to the deposited argument regardless of that repair. Version 5 corrects version 4 (DOI 10.5281/zenodo.22330843). It withdraws the defective interface-tail certificate and the conclusions that depend on it, states exactly which v4 results survive, sets the replacement gate, and then reports the repair carried out at cutoff 40000: a new interval-certified finite block on rows 10001:40000, the corrected analytic tail above 40000, a composed interface bound below 0.454943, a reopened global gate at mode 5001, and a supported comparison denominator of 2.10 at which both archived low-sixteen datasets pass. The repaired comparison holds with explicitly inherited premises and does not retroactively validate v4. The replay bundle is deposited with the record. Concept DOI 10.5281/zenodo.22293309.

Zenodo (CERN European Organization for Nuclear Research)
Honeywell (United States) (US)
Electromagnetic Scattering and Analysis
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.