[
  {
    "id": "ARR-2026-64TV5F2E6S8G08GC-v1",
    "type": "article",
    "title": "Uniform ten-spin Lorentzian obstructions for cycle clique blowups",
    "author": [
      {
        "literal": "Lluis Eriksson"
      }
    ],
    "issued": {
      "date-parts": [
        [
          2026,
          10,
          22
        ]
      ]
    },
    "publisher": "AIRR.SCIENCE",
    "archive": "AIRR.SCIENCE",
    "archive_location": "ARR-2026-64TV5F2E6S8G08GC",
    "version": "v1",
    "genre": "Research preprint",
    "URL": "https://airr.science/papers/ARR-2026-64TV5F2E6S8G08GC/versions/v1/",
    "note": "Research preprint; ARR-2026-64TV5F2E6S8G08GC v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.",
    "abstract": "For every $m\\ge4$ and $s\\ge2$, we construct a strictly positive rational antiferromagnetic target of rank two on at most ten states whose partition polynomial for $C_m[K_s]$ is not Lorentzian. The state bound is independent of both parameters; seven states suffice when $s\\ge9$, and six suffice for even $m$. The new case is an odd cycle, whose edges are critical for its independence number and hence fall outside the earlier independence-stable blowup theorem. We classify the minimum-induced-edge occupations and compress their leading Hessian kernel to an initial block of at most eight profiles. For $s\\ge20$, a five-profile block has inertia $(2,3,0)$, proved by six exact coefficient certificates in the cycle length, clique size and central binomial coefficient. Eighteen bounded clique sizes are covered by polynomial certificates for infinite cycle-length tails and 42 explicit integer exceptions. We retain failures of smaller blocks and give a positive seven-state witness for $C_5[K_9]$. The target may depend on $m,s$; neither optimality nor the general connected-source characterization is claimed."
  }
]