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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"q-alg/9709031","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-09-20T05:22:34Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a8aaf102802808d9d8ec83cdee748887c4aed7998e3a82e756c14cfdfa376f1c","abstract_canon_sha256":"4cc2c1d4792dc37220ccb9a5a29e0bcfdbfe1abd20177b07badd280d505d6ad4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:09:11.921556Z","signature_b64":"DrHw0cEZ++QiiOpqjwow/HuzmtXgHtJrFbop/ELyOV1NlKV3vH4/ge1yq5eQRskwGVIT90R+1BYrzvVn1DOMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70cf46f96104f024315669dc90f33a9410f3f2f90dba11e1e9a5c350d7a91064","last_reissued_at":"2026-07-04T15:09:11.921174Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:09:11.921174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $r^4=r^3+1$. 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