Minimal Failure of Corner Tests for D4 Drainage with Two Fixed Boundary Sinks
Year: 2026
Type: preprint
Abstract: Research Note No.40. Unrefereed, AI-assisted public preprint v1.0, 26 October 2026. Ryutaro Yonezu, Yonezu Research Lab. For full rectangular unit D4 grids, an interior source, exactly two strict boundary sinks fixed over an entire shared two-axis tilt box, and deterministic lowest-strictly-lower-neighbor routing, this note proves that 12 cells is the exact minimum for failure of corner testing on a nondegenerate closed axis-aligned parameter rectangle. An integer 4-by-3 terrain has source outlet A at all four parameter-box corners and B at the center, with the exact rule A iff |a|+b >= 1 and no interior sink. A complete analytical 3-by-3 obstruction proves minimality within this specified class. The deterministic forest is also encoded, including fixed ties, as a unique rooted minimum spanning forest. This applies established watershed/MSF theory; the general mechanism is not proposed as new. Historical novelty of the constrained minimum remains INCONCLUSIVE, and no priority claim is made. Received external AI reports give mathematical and differential-audit PASS, including the MSF proof. They did not independently check the cited source passages or search novelty. Author-side primary-source comparisons and access limits are included. Human peer review and formal proof-assistant certification are not claimed. Author verification used Linux/Python 3.12.14; the latest received review reports Linux/Python 3.13. Windows execution is unconfirmed. Additional reviewer search code/raw logs were not supplied, and separately reported search counts are not pooled or presented as author reproductions. Files: nine-page English PDF and companion ZIP containing the exact audited v0.5 archive and extracted files, unchanged proof bodies and standard-library Python verifiers, exact evidence, audit history, editable Markdown and PDF renderer, the illustrative figure, provenance receipts and SHA256 manifests. Historical HOLD notes in the frozen originals refer to preparation-stage review; the author subsequently instructed this qualified public upload. This does not upgrade novelty, references, Windows or human-review status. This is a mathematical routing model, not empirical runoff validation. Copyright (c) 2026 Ryutaro Yonezu. All rights reserved. No general reuse or redistribution license is granted. Research inquiries and earlier overlapping work: [email protected]: https://github.com/yonezaemon1-hub/no40-pitfree-corner-minimality
Author: Yonezu, Ryutaro
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223575514