{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:AZPVABVJEBPAS6E6TDJWOLFCGS","short_pith_number":"pith:AZPVABVJ","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"},"canonical_sha256":"065f5006a9205e09789e98d3672ca2349bf0b7b60ad7d1e69b850ce7e76c5ad0","source":{"kind":"arxiv","id":"2311.01922","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.01922","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"arxiv_version","alias_value":"2311.01922v2","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.01922","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"pith_short_12","alias_value":"AZPVABVJEBPA","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"pith_short_16","alias_value":"AZPVABVJEBPAS6E6","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"pith_short_8","alias_value":"AZPVABVJ","created_at":"2026-07-05T11:43:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:AZPVABVJEBPAS6E6TDJWOLFCGS","target":"record","payload":{"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"},"canonical_sha256":"065f5006a9205e09789e98d3672ca2349bf0b7b60ad7d1e69b850ce7e76c5ad0","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"},"source_kind":"arxiv","source_id":"2311.01922","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:43:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jAZLeR/TwHrL+B4uLO2aINOWwHMoQKNX/zOfPqlb1DC2hQxyRBF5fyHu/OFW38jFcxQC9BLQfCadGlyTh96WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:49:58.180095Z"},"content_sha256":"74530573a1a8830920e36c7225dc6067eb77594bd24cdf549f256732b69fcf27","schema_version":"1.0","event_id":"sha256:74530573a1a8830920e36c7225dc6067eb77594bd24cdf549f256732b69fcf27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:AZPVABVJEBPAS6E6TDJWOLFCGS","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:43:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fuyXiIJe7qOsy32tYqk7Bx05AuhHxpLV66ZTAEKFwVSdeTlTcyAR+cxqSab0I2ccQypZku6reUfAuE2zRBdXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:49:58.180471Z"},"content_sha256":"14d4fd8239fb0b9fb57479902a51e9e422f74f696da0494e450f40e7e7c146dc","schema_version":"1.0","event_id":"sha256:14d4fd8239fb0b9fb57479902a51e9e422f74f696da0494e450f40e7e7c146dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/bundle.json","state_url":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T13:49:58Z","links":{"resolver":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS","bundle":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/bundle.json","state":"https://pith.science/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AZPVABVJEBPAS6E6TDJWOLFCGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AZPVABVJEBPAS6E6TDJWOLFCGS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"499a03b769975c1cccaa6c8a356556af6997d10b6621cb7bd0ea5e5966830424","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-11-03T14:01:00Z","title_canon_sha256":"92873c22e3b4501ad80b9f7bcd4aeefa2b8916f79bbc020fa9ffd67966929f06"},"schema_version":"1.0","source":{"id":"2311.01922","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.01922","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"arxiv_version","alias_value":"2311.01922v2","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.01922","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"pith_short_12","alias_value":"AZPVABVJEBPA","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"pith_short_16","alias_value":"AZPVABVJEBPAS6E6","created_at":"2026-07-05T11:43:53Z"},{"alias_kind":"pith_short_8","alias_value":"AZPVABVJ","created_at":"2026-07-05T11:43:53Z"}],"graph_snapshots":[{"event_id":"sha256:14d4fd8239fb0b9fb57479902a51e9e422f74f696da0494e450f40e7e7c146dc","target":"graph","created_at":"2026-07-05T11:43:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.01922/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Akira Yasuhara, Benjamin Audoux, Jean-Baptiste Meilhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-11-03T14:01:00Z","title":"Welded graphs, Wirtinger groups and knotted punctured spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.01922","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:74530573a1a8830920e36c7225dc6067eb77594bd24cdf549f256732b69fcf27","target":"record","created_at":"2026-07-05T11:43:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"499a03b769975c1cccaa6c8a356556af6997d10b6621cb7bd0ea5e5966830424","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-11-03T14:01:00Z","title_canon_sha256":"92873c22e3b4501ad80b9f7bcd4aeefa2b8916f79bbc020fa9ffd67966929f06"},"schema_version":"1.0","source":{"id":"2311.01922","kind":"arxiv","version":2}},"canonical_sha256":"065f5006a9205e09789e98d3672ca2349bf0b7b60ad7d1e69b850ce7e76c5ad0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"065f5006a9205e09789e98d3672ca2349bf0b7b60ad7d1e69b850ce7e76c5ad0","first_computed_at":"2026-07-05T11:43:53.351818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:53.351818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tzYQ/NZoR9nocA5IOgOFz8xnU4ES2XDfxIpPbqW71lT/33/Y+EBF4z5a0zFO2IsiVOo6qOHeXwAT6J79Ow/wCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:53.352333Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.01922","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74530573a1a8830920e36c7225dc6067eb77594bd24cdf549f256732b69fcf27","sha256:14d4fd8239fb0b9fb57479902a51e9e422f74f696da0494e450f40e7e7c146dc"],"state_sha256":"0e91a1b96f8f72497958e0cfa59b0da1968ffb4b019719a1cbdabc37a9ddcf80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1YqpXVmlexCDGaw4u8QY7blWG9M1vSbQhypxUNkaKVyzqviQvnqiAgKG4RtVXsA8Vf+mcEPAWoCw1BefrA9QAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:49:58.182435Z","bundle_sha256":"a3fe31aa6f5e5317d789835aba55d897beb5caa503e516b0e7a91dd36699563f"}}