A Minimal-Surface Counterexample to a Seshadri Lower Bound

For every integer d at least 7, a classical integral plane pencil followed by a double base change gives a smooth minimal complex projective surface S with ample canonical bundle, K_S^2=6(d-1)(d-3), and an ample integral line bundle L with L^2=6 and epsilon(S,L;x) at most 1/(d-1). This strictly contradicts the proposed bound 1/(2+|K_S^2|^(1/4)) in Szemberg's 2007/2008 question, repeated as OWR21/2009 Conjecture2 and Primer-v2 Question6.1.6. The d=7 witness has K_S^2=144, polarization degree1 on the exhibited curve, and point multiplicity6. The proof supplies finite-degree pencil existence, all-curve ampleness, smoothness, connectedness, minimality and the degree-one lifted singular fibre. The additive2 is outside the fourth root, correcting a catalogue transcription. Miranda's pencil and polarization are credited through Ein-Lazarsfeld1993, Bauer1999 and Bauer-Szemberg2010 Proposition2.1; the cover and positivity ingredients are classical. Two independent primary-source priority audits found no explicit earlier exact resolution in inspected text, but priority cannot be fully cleared. The full Bansal-Majumder2025 survey, Roy2019 thesis and other thesis bodies were not inspected; longer sources and citation bodies were selectively read and final journal versions were not globally compared. No firstness, new-method or verified continued-open-status claim is made. Only an upper Seshadri bound at a special point on varying surfaces is asserted, not an exact value, fixed-surface vanishing, rank-one or very-general-point violation. The authored-only package preserves18 original inputs, independent derivations and source receipts, four review families, pinned inventories, exact symbolic controls and a nine-job offline replay driver. SymPy1.14.0 and mpmath1.3.0 must be preinstalled. Raw third-party documents and account data are excluded. Finite controls supplement the geometric proof; integrity is not authenticity or priority. AI tools were used extensively in solving, research, writing, source comparison, reproduction and adversarial verification. This is an unrefereed preprint with internal AI adversarial reviews; it has not received human peer review or proof-assistant certification.