Initial omnific models of discrete initial surreal groups

Every discrete initial ordered additive subgroup G of the surreal numbers No is order-group-isomorphic onto H contained in the omnific integers Oz that is initial in No. This is the full additive-group question of Kaplan and Ehrlich, already in Kaplan's2015 honors thesis Question1, OWR60/2016 Question1 and the sequel author manuscript Question9.1. The proof covers sets and proper classes in NBG with global choice, plus the separate zero-group case, without multiplication or preservation of original simplicity. An explicit operation on ordinal-length sign sequences moves the least exponent to zero, preserves initial images and reflects the target right-predecessor obligations. Relabeling actual source supports and scaling only the bottom coefficient group gives the required ordered-group image, without silently adjoining a full Hahn group. The seven-page note includes a detailed sufficiency proof of Ehrlich-Kaplan's initial-group characterization: actual support-length generators avoid a bounded-stage exhaustion gap, legal unit perturbations replace potentially unavailable dyadic limit-cut options, and direct additive cut adjunction and class-to-set restrictions complete the argument. The characterization statement is credited and retained. Prior least-positive classification, ADH negative-ordinal minimum and generic exponent/coefficient transport receive explicit credit. Root and three fresh extensive priority approaches found no earlier recorded full target in inspected accessible material;183 query inputs include overlaps and are not a count of unique works. This is not a novelty, firstness, causal-independence or worldwide-current-openness certificate. Material unread fulltext leads include Ehrlich's2024 handbook chapter, the full2001 predecessor, Lurie1998 and other access-limited works. Some author/arXiv versions were not authenticated against publisher bodies. Only the2024 chapter abstract/references were inspected. The source archive contains the current13-file PR edition, labelled historical original inputs, three fresh mathematical approaches, focused dependency reconstruction, three priority approaches, root evidence and an offline standard-library verification package. Normal and optimized Python compare full exact positive outputs and reproduce eight actual wrong-construction failures. The finite checks supplement, rather than establish, the all-ordinal and proper-class proof. Historical absent programs are not represented as rerun. Third-party source bodies are excluded; optional source-custody checks need independently acquired private sources. AI tools were extensively used in solving, writing, researching, reproducing and adversarial verification. Exposure and source-reading limits are documented. This preprint is unrefereed. Internal AI reviews do not constitute external human peer review, journal acceptance or formal proof-assistant certification.