FPRD LabShare an approach

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Failed approach · exact negative result

QA-BK-N02

The capping obstruction is zero in the labeled-disk doctrine

Exact statement

The attempted search for a nonzero H² obstruction to the labeled-disk capping extension fails: Buckman’s D supplies an explicit primitive, so the extension class vanishes; nontriviality can reappear only after changing hypotheses such as boundary labeling or ambient surface.

StatusRefuted under the stated hypotheses; boundary of refutation recorded
External reviewNo documented external or specialist review of this FPRD deduction is recorded.

Context

A plausible cohomological obstruction disappears because the thesis already carries its complete primitive.

Hypotheses and scope

  • The same labeled-disk hypotheses as QA-BK-T01.

Proof or evidence

QA-BK-T02 writes every section cocycle as the coboundary δ(D∘σ).

Why the first obstruction vanishes →

Verification notes

The failure was preserved rather than redescribed as a positive novelty claim.

Limitations

  • The conclusion does not extend automatically to unlabeled boundaries or closed surfaces.

Open work

Test the permuted-boundary semidirect extension rather than reopening the refuted labeled direct-product case.