Add exact counterexamples, manuscripts, and verification package

[terrorproforma]

Summary

Adds a self-contained research package under 2026-rounding-counterexamples/ containing two explicit certificate-based counterexamples:

• a seven-vertex planar acyclic SSUF instance with fractional cost 58 and minimum capacity-good unsplittable cost 60;
• an 11-row, 15-column machine-dependent weighted-chairman instance with certified discrepancy at least 619/600.

Included

• journal-style LaTeX manuscripts for each result;
• an illustrated overview with editable TikZ figures;
• exact JSON certificates;
• standard-library Python verifiers using integer and rational arithmetic;
• scripts reconstructing both parametric families;
• derivation, history, importance, provenance, search log, and validation notes;
• AI-use disclosure and journal-submission checklist;
• GitHub Actions jobs for exact verification, PDF compilation, and generated-PDF publication.

Direct manuscripts

• Planar SSUF counterexample PDF
• Machine-dependent chairman counterexample PDF
• Illustrated overview PDF

Validation status

GitHub Actions run 30008920496 completed successfully on source commit a0bb204e5beeff3402f63df94a8278282b5df54a:

• exact final certificates: passed;
• reconstruction of both parametric families: passed;
• all three LaTeX manuscripts: compiled successfully;
• workflow artifact upload: passed.

The bot then committed the newly compiled PDFs in commit d31224c162b1dab0a05e4801627dda0be5aed454.

The SSUF verifier reconstructs all source-terminal paths from the graph and enumerates all eight routings. The chairman verifier checks the forcing inequalities with exact Fraction arithmetic and includes assignments outside fractional support. No floating-point solver is required for either final certificate.

Review status

Draft only. These are novel research claims and should not be merged or publicly announced as established results until the generated PDFs receive a human visual inspection, theorem wording and bibliography are checked by subject experts, priority is rechecked immediately before circulation, and independent mathematicians have audited the proofs.