Cross-Branch Short-Horizon Geometric Prediction of Operator-Generated Response Boundaries: Numerical Tests of Position, Normal, and Local Curvature
Abstract
This preprint tests short-horizon prediction of position, normal orientation, Hessian, principal curvature, and principal directions across multiple operator-generated finite-window response-boundary branches in a finite synthetic divergence-free vorticity family. The study uses the same normalized four-dimensional Family-C subspace developed in B20-B22. Two original-protocol branch tests and supplementary repaired/corrective validations satisfy the stated position and normal criteria; designated later-stage tests also satisfy the prescribed full-geometry criteria. The original aggregate B23 plan remains INCONCLUSIVE because its symmetric search window was not applicable to endpoint-near targets. Supplementary validations are kept distinct and are not retroactively counted as original-plan successes. Claims are limited to the tested finite numerical setting.
The English preprint is the authoritative version for citation and version control. A Japanese reference translation and a compact reproducibility ZIP are supplied as companion files.
Project repository
For the current research map, related BIG studies, representative figures, terminology, and links to the broader Boundary Information Geometry (BIG) research program, see:
Boundary Information Geometry (BIG) — GitHub Repository
https://github.com/Jun-Lucis/BIG-theory
The Zenodo record remains the archival and citable source for this research output. The GitHub repository serves as a navigational overview of the continuing BIG research program.
Publication audit note (2026-10-19). Audit scope: Basically reproducible; an independent rerun audit remains incomplete. Preservation and checksum checks, algebraic checks of saved results, source/protocol comparisons, original-code reproduction, and independent PDE reruns are distinct. No new PDE computation was performed for this publication update. Original numerical values, formal classifications, frozen rules and stopping rules are retained. The original aggregate classification remains INCONCLUSIVE. E1 and E4 succeeded on the same r11 direction; E2 and E3 stopped at preflight. Later repaired runs are not retroactively counted as successes of the original master protocol. The overlapping fallback classifications were resolved as INCONCLUSIVE in the published account; that tie-breaking precedence was not independently established as prospectively frozen. E3R retains its historical output, but its intended-r09 interpretation is IMPLEMENTATION_INVALID_WRONG_RAY because the saved inputs were dispatched to r12. E3R2 is corrective replication, not a newly blinded success. E5/E6R use observed T1 geometry for sequential one-step prediction. The 1,722-file source inventory is metadata-level evidence, not a complete byte/hash-verified public archive. The revised English manuscript and Japanese reference PDF are published in version 1.1; the original reproducibility archive is retained unchanged.
Version 1.1 notes (19 October 2026): Replaces the English authoritative preprint and Japanese reference PDF with the author-supplied revised manuscripts. Clarifies the E3R implementation correction, the corrective-replication status of E3R2, and the limits of sequential one-step prediction. The original aggregate classification remains INCONCLUSIVE. All original numerical results and formal classifications are preserved. The compact v1.0 reproducibility ZIP remains unchanged as a historical archive, including its original manuscript copies. Basically reproducible; an independent rerun audit remains incomplete. No new PDE computation or independent rerun was performed.
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BibTeX
@misc{lucis2026crossbranch,
title = {{Cross-Branch Short-Horizon Geometric Prediction of Operator-Generated Response Boundaries: Numerical Tests of Position, Normal, and Local Curvature}},
author = {Jun Lucis},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23467455},
url = {https://zenodo.org/records/23467455},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cross-Branch Short-Horizon Geometric Prediction of Operator-Generated Response Boundaries: Numerical Tests of Position, Normal, and Local Curvature
AU - Jun Lucis
PY - 2026
DA - 2026/10/19
PB - Zenodo
DO - 10.5281/zenodo.23467455
UR - https://zenodo.org/records/23467455
AB - This preprint tests short-horizon prediction of position, normal orientation, Hessian, principal curvature, and principal directions across multiple operator-generated finite-window response-boundary branches in a finite synthetic divergence-free vorticity family. The study uses the same normalized four-dimensional Family-C subspace developed in B20-B22. Two original-protocol branch tests and supplementary repaired/corrective validations satisfy the stated position and normal criteria; designated later-stage tests also satisfy the prescribed full-geometry criteria. The original aggregate B23 plan remains INCONCLUSIVE because its symmetric search window was not applicable to endpoint-near targets. Supplementary validations are kept distinct and are not retroactively counted as original-plan successes. Claims are limited to the tested finite numerical setting. The English preprint is the authoritative version for citation and version control. A Japanese reference translation and a compact reproducibility ZIP are supplied as companion files. Project repository For the current research map, related BIG studies, representative figures, terminology, and links to the broader Boundary Information Geometry (BIG) research program, see: Boundary Information Geometry (BIG) — GitHub Repository https://github.com/Jun-Lucis/BIG-theory The Zenodo record remains the archival and citable source for this research output. The GitHub repository serves as a navigational overview of the continuing BIG research program. Publication audit note (2026-10-19). Audit scope: Basically reproducible; an independent rerun audit remains incomplete. Preservation and checksum checks, algebraic checks of saved results, source/protocol comparisons, original-code reproduction, and independent PDE reruns are distinct. No new PDE computation was performed for this publication update. Original numerical values, formal classifications, frozen rules and stopping rules are retained. The original aggregate classification remains INCONCLUSIVE. E1 and E4 succeeded on the same r11 direction; E2 and E3 stopped at preflight. Later repaired runs are not retroactively counted as successes of the original master protocol. The overlapping fallback classifications were resolved as INCONCLUSIVE in the published account; that tie-breaking precedence was not independently established as prospectively frozen. E3R retains its historical output, but its intended-r09 interpretation is IMPLEMENTATION_INVALID_WRONG_RAY because the saved inputs were dispatched to r12. E3R2 is corrective replication, not a newly blinded success. E5/E6R use observed T1 geometry for sequential one-step prediction. The 1,722-file source inventory is metadata-level evidence, not a complete byte/hash-verified public archive. The revised English manuscript and Japanese reference PDF are published in version 1.1; the original reproducibility archive is retained unchanged. Version 1.1 notes (19 October 2026): Replaces the English authoritative preprint and Japanese reference PDF with the author-supplied revised manuscripts. Clarifies the E3R implementation correction, the corrective-replication status of E3R2, and the limits of sequential one-step prediction. The original aggregate classification remains INCONCLUSIVE. All original numerical results and formal classifications are preserved. The compact v1.0 reproducibility ZIP remains unchanged as a historical archive, including its original manuscript copies. Basically reproducible; an independent rerun audit remains incomplete. No new PDE computation or independent rerun was performed.
ER -