The (72,108) Candidate for the Planar Jacobian Conjecture: A Containment Note

We record what this audit establishes about GGHV's (8,28) case — the unique uneliminated existence candidate below degree 125 for the planar Jacobian Conjecture, with (deg P, deg Q) = (72,108) — after a source-level audit against arXiv:2204.14178 withdrew the Newton-polygon data, infinity-branch census, corner sieve, branchwise valuations and Bézout pincer of the previous editions. Those editions made three errors: (i) they used a φ-hybrid Newton polygon (GGHV's pre-φ polygon with one vertex transported by the final map and four left in the earlier coordinates); (ii) they transposed every branchwise valuation vector; (iii) they treated one of the two surviving sub-cases of GGHV's Proposition 4.3 as the whole case. All three are documented in the ledger of Appendix A, with the gates that would have caught them. What survives, for both sub-cases: (i) a degree floor deg(Q²−P³) ≥ 38, Davenport's 1965 bound plus one from the Keller bracket; (ii) an unconditional ceiling deg(Q²−P³) ≤ 215, refined to 179 under the unproved premise that the C-adic coefficient q₂ is constant; (iii) generic-fibre genus bounds g ≤ 35 in sub-case (1) and g ≤ 7 in sub-case (2), via Baker's theorem and birationality; (iv) refutations of four elimination shortcuts proposed and tested within this project. The decision problem is GGHV's own unsolved polynomial system for the (8,28) case, which must dispose of both normal forms. Conclusion. The (8,28) case is underdetermined. Both verification pipelines behind this note are AI systems (independence level I1); the gates of Appendix A must be run by a human before deposit.