# Verification and scope report

A Closed Curve with Finite Critical Menger Curvature and No Tangent at One Point

The six-page English manuscript contains the complete written counterexample to source subquestion (2), including the endpoint kernel, near/far scale estimates, simple closed gluing, remote triples and arclength normalization. The original three-question bundle remains PARTIALLY_SOLVED. No full-record closure is counted.

Originating-researcher detailed self-audit: passed. Independent review: not performed. Proof-assistant verification: not performed. The 500 rational triangle cases give 1500 exact identity/inequality checks; 200 finite-series checks verify the kernel coefficient and one rational bound checks the closing height. Eight floating quadrature cases illustrate the average estimates. These are diagnostics, not a formal proof. Normal and optimized runs agree.

All six rendered pages were directly inspected: formulas, author footnote, page endings and references are legible, with no clipping or missing glyphs. Desktop compilation and portable-source compilation pass; final LaTeX log has no box or reference warnings.

Known Mobius-energy counterexamples and Sobolev methods are credited. Bounded primary-source review does not certify novelty or priority, especially for consequences of older results. Dohmen-Scholtes's separate circle-minimum theorem is credited. AI tools assisted retrieval, derivation, diagnostics and exposition. License: CC BY 4.0.