v1.1.0 — Ordered simplex caps and the three-observation Stringer bound

Ordered simplex caps and the three-observation Stringer bound

The principal preprint is now 9 pages, focused on the four-coordinate cap theorem, its sharp three-observation Stringer–Gaffke comparison, and the all-dimensional terminal-edge obstruction.

This release includes the manuscript PDF and LaTeX source, exact rational proof data, reproducible calculations, and corrected mathematical-status records. The five- and six-coordinate global extensions and their dependent confidence continua remain conjectural: the first-coordinate beta inequalities do not establish the required active-prefix inequality on repeated-lowest-knot faces. The independent local calculations and fixed-level results are retained with their stated scopes.

The systematic-PPS manuscript remains a separate treatment of fixed-frame random-start inference.

The source ZIP contains the complete supporting repository. Earlier versions are preserved.

Archived source: Zenodo v1.1.0 — DOI 10.5281/zenodo.22821193.

v1.0.0 — Initial archival release

Initial archival release

This release preserves the certificate-backed investigation of the Stringer bound, including:

• the full finite-sample conservatism proof for n = 2, valid for every taint distribution and confidence level;
• exact rational counterexamples at low confidence, with rigorous confidence-factor enclosures and margin certificates;
• the analysis of the gap in Bimpeh's finite-sample certification;
• reproducible Python search, coverage, and certification programs;
• machine-checkable logs and certificates; and
• the accompanying manuscript in LaTeX and PDF formats.

The general finite-sample conjecture at standard confidence levels such as 95% remains open.