# Verification report

Six-page self-audited theorem for circle targets and squared geodesic losses: Pdim=2 exactly when integral-period parallel forms vanish; otherwise fat_(1/24)=infinity. On closed domains with a nonconstant map, energy cutoff capacity has matching logarithmic orders. Also the exact character description of fixed-input interpolation closure and a sharp two-point counterexample to the report's universal interpolation quantifier. The arbitrary-target OWR-2041-002 question remains open here. The already known circle infinite-capacity example is credited, not claimed anew.

Written audit: local-lift integration and integral periods; strict phase-cell counting; explicit base-four digit construction; injectivity of the period map on closed domains; lattice-ball counting; compactness/surjectivity for the energy lower bound; torus annihilators and compact recurrence; winding-parity obstruction with attained error1/8. No rationality of the entire parallel-form space is assumed. The noncompact result needs only a local image arc. One scoped proof package; zero whole-source closures.

Exact Fraction arithmetic verifies90114 digit-margin inequalities for all binary labelings of lengths1 through12, every winding parity for the two-point obstruction, sharp witnesses, and the four strict patterns needed for constant-class Pdim2. Finite diagnostics support but do not replace the universal written proof.
Checker SHA-256: 84dddae413f512ef7bc5e88158d9b41935f7168ff79ffbe03610fb5caf5b064c.
Certificate SHA-256: ec2fbba4c2a1b6b7847b5b979fa5fcd7541850ed7275e2603bb436a7f427954f.

The official EMS2008 report question and theorem, printed1688-1689/PDF34-35, were read, and PDF35 was visually inspected. The SIAM2010 official bibliographic record/abstract was consulted; its full journal text was not obtained. The original authors and standard tools are credited. Bounded literature search does not certify absolute priority. No independent review or formal verification is claimed; no gap was found in the originating-system audit.

Built-in compiler and portable Tectonic build pass. All six pages were visually inspected. Only the author's name is prominent; affiliation/contact is a footnote and AI assistance is disclosed in prose. Public archives exclude third-party source PDFs.