Partial representation results and open problems for convex normal sequential effect algebras

Abstract The unrestricted question whether every convex normal sequential effect algebra is order-isomorphic to the unit interval of a real unital JB-algebra remains unresolved here. We prove representation in finite dimension without assuming norm continuity of the sequential product in its first variable, using the characteristic function of the homogeneous cone. For arbitrary dimension and sharp capacity, we reformulate reciprocal antitonicity as a bounded native-filter Schwarz test and isolate its exact state-variance obstruction. In sharp capacity two, selected square-contact conditions admit a one-sided rational contrast formulation; positive unital maps satisfy a native square inequality, but the remaining signed defect comparison is open. We also describe boundary-filter limits, projective state-face actions, native transition intervals, a normal-state-free commutative example, and an infinite-dimensional rational-context construction whose totality and directed-completeness failures are explicit. Every conditional reconstruction and failed inference is separated from the general order-representation problem. The unresolved mathematical obligations are retained as numbered open problems. AI assistance disclosure The manuscript was prepared with assistance from OpenAI Codex, including drafting, internal adversarial mathematical review, and exact arithmetic diagnostics. Internal AI review is not independent external peer review. Verification scope and unresolved parts The written manuscript proofs passed INTERNAL_ADVERSARIAL_REVIEW_V1 at their explicitly stated scopes. Thirty-four claim groups were reviewed, and four clarifications were repaired and read back. Named exact computations certify their specified instances only. Six primary-reference DOI records were verified; bibliographic identity is not proof validation. The unrestricted assertion that every convex normal sequential effect algebra has an arbitrary order-isomorphic real unital JB interval representation, and its negation, remain OPEN. Fourteen numbered OPEN PROBLEM statements are retained. No Lean, proof assistant, or independent external mathematical review was performed. The frozen campaign prohibited formal proof assistants. The cumulative supplementary archive retains inherited scoped results and was not freshly revalidated in its entirety. Novelty is not certified.