{"paper":{"title":"Conjectured enumeration of Vassiliev invariants","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"D. J. Broadhurst","submitted_at":"1997-09-20T05:22:34Z","abstract_excerpt":"A rational Ansatz is proposed for the generating function $\\sum_{j,k} \\beta_{2j+k,2j}x^j y^k$, where $\\beta_{m,u}$ is the number of primitive chinese character diagrams with $u$ univalent and $2m-u$ trivalent vertices. For $P_m:=\\sum_{u\\ge2}\\beta_{m,u}$, the conjecture leads to the sequence $$1,1,1,2,3,5,8,12,18,27,39,55,\\underline{78,108,150,207,284,388,532,726}$$ for primitive chord diagrams of degrees $m\\le20$, with predictions underlined. The asymptotic behaviour $\\lim_{m\\to\\infty}P_m/r^m= 1.06260548918755$ results, with $r=1.38027756909761$ solving $r^4=r^3+1$. Vassiliev invariants of kno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9709031","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/q-alg/9709031/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}