{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:AZPVABVJEBPAS6E6TDJWOLFCGS","short_pith_number":"pith:AZPVABVJ","schema_version":"1.0","canonical_sha256":"065f5006a9205e09789e98d3672ca2349bf0b7b60ad7d1e69b850ce7e76c5ad0","source":{"kind":"arxiv","id":"2311.01922","version":2},"attestation_state":"computed","paper":{"title":"Welded graphs, Wirtinger groups and knotted punctured spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Benjamin Audoux, Jean-Baptiste Meilhan","submitted_at":"2023-11-03T14:01:00Z","abstract_excerpt":"We develop a general diagrammatic theory of welded graphs, and provide an extension of Satoh's Tube map from welded graphs to ribbon surface-links. As a topological application, we obtain a complete link-homotopy classification of so-called knotted punctured spheres in $4$-space, by means of the $4$-dimensional Milnor invariants introduced previously by the authors. On the algebraic side, we show that the theory of welded graphs can be reinterpreted as a theory of Wirtinger group presentations, up to a natural set of transformations; these groups arise as the fundamental group of the exterior "},"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":"2311.01922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-11-03T14:01:00Z","cross_cats_sorted":[],"title_canon_sha256":"92873c22e3b4501ad80b9f7bcd4aeefa2b8916f79bbc020fa9ffd67966929f06","abstract_canon_sha256":"499a03b769975c1cccaa6c8a356556af6997d10b6621cb7bd0ea5e5966830424"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:53.352333Z","signature_b64":"tzYQ/NZoR9nocA5IOgOFz8xnU4ES2XDfxIpPbqW71lT/33/Y+EBF4z5a0zFO2IsiVOo6qOHeXwAT6J79Ow/wCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"065f5006a9205e09789e98d3672ca2349bf0b7b60ad7d1e69b850ce7e76c5ad0","last_reissued_at":"2026-07-05T11:43:53.351818Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:53.351818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Welded graphs, Wirtinger groups and knotted punctured spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Akira Yasuhara, Benjamin Audoux, Jean-Baptiste Meilhan","submitted_at":"2023-11-03T14:01:00Z","abstract_excerpt":"We develop a general diagrammatic theory of welded graphs, and provide an extension of Satoh's Tube map from welded graphs to ribbon surface-links. As a topological application, we obtain a complete link-homotopy classification of so-called knotted punctured spheres in $4$-space, by means of the $4$-dimensional Milnor invariants introduced previously by the authors. On the algebraic side, we show that the theory of welded graphs can be reinterpreted as a theory of Wirtinger group presentations, up to a natural set of transformations; these groups arise as the fundamental group of the exterior "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.01922","kind":"arxiv","version":2},"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/2311.01922/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":"2311.01922","created_at":"2026-07-05T11:43:53.351871+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.01922v2","created_at":"2026-07-05T11:43:53.351871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.01922","created_at":"2026-07-05T11:43:53.351871+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZPVABVJEBPA","created_at":"2026-07-05T11:43:53.351871+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZPVABVJEBPAS6E6","created_at":"2026-07-05T11:43:53.351871+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZPVABVJ","created_at":"2026-07-05T11:43:53.351871+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/AZPVABVJEBPAS6E6TDJWOLFCGS","json":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS.json","graph_json":"https://pith.science/api/pith-number/AZPVABVJEBPAS6E6TDJWOLFCGS/graph.json","events_json":"https://pith.science/api/pith-number/AZPVABVJEBPAS6E6TDJWOLFCGS/events.json","paper":"https://pith.science/paper/AZPVABVJ"},"agent_actions":{"view_html":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS","download_json":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS.json","view_paper":"https://pith.science/paper/AZPVABVJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.01922&json=true","fetch_graph":"https://pith.science/api/pith-number/AZPVABVJEBPAS6E6TDJWOLFCGS/graph.json","fetch_events":"https://pith.science/api/pith-number/AZPVABVJEBPAS6E6TDJWOLFCGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/action/storage_attestation","attest_author":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/action/author_attestation","sign_citation":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/action/citation_signature","submit_replication":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/action/replication_record"}},"created_at":"2026-07-05T11:43:53.351871+00:00","updated_at":"2026-07-05T11:43:53.351871+00:00"}