All-load stability of a deterministic-first-chunk file-sharing chain

We prove positive recurrence for every fixed positive real arrival rate in the four-population deterministic-first-chunk continuous-time Markov chain with a permanent seed, invisible empty waiting rooms, and immediate departure of completed peers. The exact six-rate model is the subject of the 2010 Oberwolfach stability conjecture and the checked January 5, 2011 author proof of Norros, Reittu and Eirola. A single coercive Foster function combines remaining workload, rounded cohort imbalance, and bounded finite birth-death Poisson correctors with monotone ratio cutoffs. The contribution is the all-load extension; the elementary workload argument already covers arrival rates below one half. The deposit contains the six-page paper and a source and verification ZIP with complete proofs, frozen original work, fresh independent exact rational and negative controls, reading and access ledgers, and reproduction instructions. No stationary moment, performance bound, uniformity in the arrival rate, or conclusion for another chunk-selection protocol is asserted. The priority review is bounded: the final 2011 publisher body, final 2015 journal extension of the Allerton work and some later bodies were not inspected. No worldwide-firstness or continuing-openness certification is asserted. AI tools were extensively involved in mathematical research, proof development, computational verification, manuscript preparation and adversarial auditing. This is an unrefereed preprint and has not undergone formal independent human peer review. Internal AI reviews do not constitute human peer review.