{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YKK4SJUNFC46ODAA3LYHYUY4SP","short_pith_number":"pith:YKK4SJUN","canonical_record":{"source":{"id":"2412.18959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-25T18:20:44Z","cross_cats_sorted":[],"title_canon_sha256":"f00a97b041913a7b447d6c3d0b46d62993da519f96d491d6971b39d89b067cc5","abstract_canon_sha256":"aff088124b85e40e2b8eab90338c48e4396e330741f92162b4fd06352bde95bf"},"schema_version":"1.0"},"canonical_sha256":"c295c9268d28b9e70c00daf07c531c93cbabc7902f7a69e3d3f89aef38cdee5d","source":{"kind":"arxiv","id":"2412.18959","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18959","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18959v1","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18959","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"YKK4SJUNFC46","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"pith_short_16","alias_value":"YKK4SJUNFC46ODAA","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"pith_short_8","alias_value":"YKK4SJUN","created_at":"2026-07-05T09:54:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YKK4SJUNFC46ODAA3LYHYUY4SP","target":"record","payload":{"canonical_record":{"source":{"id":"2412.18959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-25T18:20:44Z","cross_cats_sorted":[],"title_canon_sha256":"f00a97b041913a7b447d6c3d0b46d62993da519f96d491d6971b39d89b067cc5","abstract_canon_sha256":"aff088124b85e40e2b8eab90338c48e4396e330741f92162b4fd06352bde95bf"},"schema_version":"1.0"},"canonical_sha256":"c295c9268d28b9e70c00daf07c531c93cbabc7902f7a69e3d3f89aef38cdee5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:13.885032Z","signature_b64":"ro1bYQvRpgYGAONsHx+a3z09OgkWh41Ga1UeHt6a7VGZNufF+mK0g5Z60q1L1vF+2TxETVcU86IoMu9RzgjsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c295c9268d28b9e70c00daf07c531c93cbabc7902f7a69e3d3f89aef38cdee5d","last_reissued_at":"2026-07-05T09:54:13.884656Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:13.884656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.18959","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:54:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pt/MLp1N1iYd8pLOl7Q9HlEvexJq2w+JNcZGvSg2jqgTvQ4PhFUaYFn2Pb4A0AsUUQDGUYHTCelv/hql0HhTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:03:56.632071Z"},"content_sha256":"73e5863b3ecd8d7eb1647fb2bd1c0156150d20a5d7ddcfd4f728efe44a1ea597","schema_version":"1.0","event_id":"sha256:73e5863b3ecd8d7eb1647fb2bd1c0156150d20a5d7ddcfd4f728efe44a1ea597"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YKK4SJUNFC46ODAA3LYHYUY4SP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Skew-symmetric augmented matrices and a characterization of virtual doodles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jos\\'e Gregorio Rodr\\'iguez-Nieto, Olga Patricia Salazar-D\\'iaz, Oscar Ocampo","submitted_at":"2024-12-25T18:20:44Z","abstract_excerpt":"In this paper, we present a brief overview of the concept of doodles from the perspective of J.S. Carter's work on classifying immersed curves and the work of J.S. Carter, S. Kamada, and M. Saito on stable equivalence of knots on surfaces and virtual knot cobordisms. We use the homology intersection number and the work of G. Cairns and D. Elton on the Gauss word problem to introduce the concept of skew-symmetric augmented matrices for determining whether a virtual doodle is non-classical. We also provide a characterization of the virtualization of classical doodles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18959","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/2412.18959/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":"2026-07-05T09:54:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8VSgjUOlYbfa6E0UXuNR74YjLP2d/LLua8D9DuPKuUQT0O4dVfUSzAbohYt1HnGreyp775BdtrLTxfpFKaZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:03:56.632590Z"},"content_sha256":"2c28519d1a5816f7be37fb1559789f22e4067b9446112082fcf02b3c5c989b50","schema_version":"1.0","event_id":"sha256:2c28519d1a5816f7be37fb1559789f22e4067b9446112082fcf02b3c5c989b50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKK4SJUNFC46ODAA3LYHYUY4SP/bundle.json","state_url":"https://pith.science/pith/YKK4SJUNFC46ODAA3LYHYUY4SP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKK4SJUNFC46ODAA3LYHYUY4SP/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":"2026-08-14T17:03:56Z","links":{"resolver":"https://pith.science/pith/YKK4SJUNFC46ODAA3LYHYUY4SP","bundle":"https://pith.science/pith/YKK4SJUNFC46ODAA3LYHYUY4SP/bundle.json","state":"https://pith.science/pith/YKK4SJUNFC46ODAA3LYHYUY4SP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKK4SJUNFC46ODAA3LYHYUY4SP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YKK4SJUNFC46ODAA3LYHYUY4SP","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":"aff088124b85e40e2b8eab90338c48e4396e330741f92162b4fd06352bde95bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-25T18:20:44Z","title_canon_sha256":"f00a97b041913a7b447d6c3d0b46d62993da519f96d491d6971b39d89b067cc5"},"schema_version":"1.0","source":{"id":"2412.18959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.18959","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"2412.18959v1","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.18959","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"YKK4SJUNFC46","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"pith_short_16","alias_value":"YKK4SJUNFC46ODAA","created_at":"2026-07-05T09:54:13Z"},{"alias_kind":"pith_short_8","alias_value":"YKK4SJUN","created_at":"2026-07-05T09:54:13Z"}],"graph_snapshots":[{"event_id":"sha256:2c28519d1a5816f7be37fb1559789f22e4067b9446112082fcf02b3c5c989b50","target":"graph","created_at":"2026-07-05T09:54:13Z","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/2412.18959/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a brief overview of the concept of doodles from the perspective of J.S. Carter's work on classifying immersed curves and the work of J.S. Carter, S. Kamada, and M. Saito on stable equivalence of knots on surfaces and virtual knot cobordisms. We use the homology intersection number and the work of G. Cairns and D. Elton on the Gauss word problem to introduce the concept of skew-symmetric augmented matrices for determining whether a virtual doodle is non-classical. We also provide a characterization of the virtualization of classical doodles.","authors_text":"Jos\\'e Gregorio Rodr\\'iguez-Nieto, Olga Patricia Salazar-D\\'iaz, Oscar Ocampo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-25T18:20:44Z","title":"Skew-symmetric augmented matrices and a characterization of virtual doodles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.18959","kind":"arxiv","version":1},"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":"sha256:73e5863b3ecd8d7eb1647fb2bd1c0156150d20a5d7ddcfd4f728efe44a1ea597","target":"record","created_at":"2026-07-05T09:54:13Z","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":"aff088124b85e40e2b8eab90338c48e4396e330741f92162b4fd06352bde95bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-12-25T18:20:44Z","title_canon_sha256":"f00a97b041913a7b447d6c3d0b46d62993da519f96d491d6971b39d89b067cc5"},"schema_version":"1.0","source":{"id":"2412.18959","kind":"arxiv","version":1}},"canonical_sha256":"c295c9268d28b9e70c00daf07c531c93cbabc7902f7a69e3d3f89aef38cdee5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c295c9268d28b9e70c00daf07c531c93cbabc7902f7a69e3d3f89aef38cdee5d","first_computed_at":"2026-07-05T09:54:13.884656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:13.884656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ro1bYQvRpgYGAONsHx+a3z09OgkWh41Ga1UeHt6a7VGZNufF+mK0g5Z60q1L1vF+2TxETVcU86IoMu9RzgjsBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:13.885032Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.18959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73e5863b3ecd8d7eb1647fb2bd1c0156150d20a5d7ddcfd4f728efe44a1ea597","sha256:2c28519d1a5816f7be37fb1559789f22e4067b9446112082fcf02b3c5c989b50"],"state_sha256":"fa2ebd05c4eb007eecd1021d26a9b80cfffe86b77a9d97b08d7919505cf579f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WCCtVT6f4ySDPnseqmatt+ZCra2sp3RPk/8i0ni1VA5+wTDCLuc6plScvjR5sykDo65FdxbEZ7wOg+Y106SdCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T17:03:56.637895Z","bundle_sha256":"068c7840a23bbde78dc7253894348722c94ade0f89d3aff1025c6cbf531d563e"}}