{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BSSIMAVBNBSEV2PFQXJWWWQQGP","short_pith_number":"pith:BSSIMAVB","schema_version":"1.0","canonical_sha256":"0ca48602a168644ae9e585d36b5a1033f5593bb99e6a0281281c148768419860","source":{"kind":"arxiv","id":"2604.11327","version":2},"attestation_state":"computed","paper":{"title":"Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Wheel graphs in the Kontsevich graph complex are homologous to explicit combinations of only 3- and 4-valent graphs.","cross_cats":["math.CO"],"primary_cat":"math.QA","authors_text":"Assar Andersson","submitted_at":"2026-04-13T11:29:44Z","abstract_excerpt":"We show that the wheel classes in the Kontsevich graph complex $GC_d$ admit representatives supported on graphs with only $3$- and $4$-valent vertices. This verifies that Merkulov's low-valence conjecture holds for the wheel classes.\n  More precisely, for every $m \\ge 2$, we prove that the wheel graph $W_{2m+1}$ is homologous to an explicit linear combination of $2^{m-2}$ graphs, each having only $3$- and $4$-valent vertices."},"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":"2604.11327","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2026-04-13T11:29:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cf321c2f33303fe3b5b1bfeac03cbb4ae71245ae5ec340b1faadc7067e16db48","abstract_canon_sha256":"22728c84e9ea977e905ce5694eec0d1b29e4947a1ea3677a7d7606c4719816e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:18.930052Z","signature_b64":"lsc6KBBYCefAYJqVeLSvTcTb4vb65K3CMgH8dgZNNkrnjM0y5/MtlJ3sRomaj9KHP3hgwVFkpNtLfJhC4Ss+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ca48602a168644ae9e585d36b5a1033f5593bb99e6a0281281c148768419860","last_reissued_at":"2026-05-21T01:05:18.929455Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:18.929455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Wheel graphs in the Kontsevich graph complex are homologous to explicit combinations of only 3- and 4-valent graphs.","cross_cats":["math.CO"],"primary_cat":"math.QA","authors_text":"Assar Andersson","submitted_at":"2026-04-13T11:29:44Z","abstract_excerpt":"We show that the wheel classes in the Kontsevich graph complex $GC_d$ admit representatives supported on graphs with only $3$- and $4$-valent vertices. This verifies that Merkulov's low-valence conjecture holds for the wheel classes.\n  More precisely, for every $m \\ge 2$, we prove that the wheel graph $W_{2m+1}$ is homologous to an explicit linear combination of $2^{m-2}$ graphs, each having only $3$- and $4$-valent vertices."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"for every m ≥ 2, we prove that the wheel graph W_{2m+1} is homologous to an explicit linear combination of 2^{m-1} graphs, each having only 3- and 4-valent vertices.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The explicit linear combination constructed in the paper is a cycle whose boundary equals that of the wheel graph under the standard differential of GC_d.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"For every m ≥ 2 the wheel graph W_{2m+1} is homologous to an explicit sum of 2^{m-1} graphs with only 3- and 4-valent vertices.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Wheel graphs in the Kontsevich graph complex are homologous to explicit combinations of only 3- and 4-valent graphs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"49597b15c98569a544763d3bff1efff60df38650d1af5483a0fb35af8c9d2745"},"source":{"id":"2604.11327","kind":"arxiv","version":2},"verdict":{"id":"95f7cf7c-c132-4e11-947f-09ba0c4eb57f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:40:51.261057Z","strongest_claim":"for every m ≥ 2, we prove that the wheel graph W_{2m+1} is homologous to an explicit linear combination of 2^{m-1} graphs, each having only 3- and 4-valent vertices.","one_line_summary":"For every m ≥ 2 the wheel graph W_{2m+1} is homologous to an explicit sum of 2^{m-1} graphs with only 3- and 4-valent vertices.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The explicit linear combination constructed in the paper is a cycle whose boundary equals that of the wheel graph under the standard differential of GC_d.","pith_extraction_headline":"Wheel graphs in the Kontsevich graph complex are homologous to explicit combinations of only 3- and 4-valent graphs."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.11327/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2604.11327","created_at":"2026-05-21T01:05:18.929522+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.11327v2","created_at":"2026-05-21T01:05:18.929522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.11327","created_at":"2026-05-21T01:05:18.929522+00:00"},{"alias_kind":"pith_short_12","alias_value":"BSSIMAVBNBSE","created_at":"2026-05-21T01:05:18.929522+00:00"},{"alias_kind":"pith_short_16","alias_value":"BSSIMAVBNBSEV2PF","created_at":"2026-05-21T01:05:18.929522+00:00"},{"alias_kind":"pith_short_8","alias_value":"BSSIMAVB","created_at":"2026-05-21T01:05:18.929522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP","json":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP.json","graph_json":"https://pith.science/api/pith-number/BSSIMAVBNBSEV2PFQXJWWWQQGP/graph.json","events_json":"https://pith.science/api/pith-number/BSSIMAVBNBSEV2PFQXJWWWQQGP/events.json","paper":"https://pith.science/paper/BSSIMAVB"},"agent_actions":{"view_html":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP","download_json":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP.json","view_paper":"https://pith.science/paper/BSSIMAVB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.11327&json=true","fetch_graph":"https://pith.science/api/pith-number/BSSIMAVBNBSEV2PFQXJWWWQQGP/graph.json","fetch_events":"https://pith.science/api/pith-number/BSSIMAVBNBSEV2PFQXJWWWQQGP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP/action/storage_attestation","attest_author":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP/action/author_attestation","sign_citation":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP/action/citation_signature","submit_replication":"https://pith.science/pith/BSSIMAVBNBSEV2PFQXJWWWQQGP/action/replication_record"}},"created_at":"2026-05-21T01:05:18.929522+00:00","updated_at":"2026-05-21T01:05:18.929522+00:00"}