{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4XCNVQURGGKMC2T4QFS5KNQNZB","short_pith_number":"pith:4XCNVQUR","canonical_record":{"source":{"id":"1910.06963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-15T17:59:55Z","cross_cats_sorted":[],"title_canon_sha256":"3262e4e6fb9cf44bb624265390f48f49792c15e68f0769e4b2bbf2f4421c6656","abstract_canon_sha256":"fe7579644bfde060666327b7995c7a7141d8cb1ab5778b355fd78f0d043c6f48"},"schema_version":"1.0"},"canonical_sha256":"e5c4dac2913194c16a7c8165d5360dc8540bc46c7675c23114993915384b3ca0","source":{"kind":"arxiv","id":"1910.06963","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.06963","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"arxiv_version","alias_value":"1910.06963v2","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.06963","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"pith_short_12","alias_value":"4XCNVQURGGKM","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4XCNVQURGGKMC2T4","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4XCNVQUR","created_at":"2026-07-05T06:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4XCNVQURGGKMC2T4QFS5KNQNZB","target":"record","payload":{"canonical_record":{"source":{"id":"1910.06963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-15T17:59:55Z","cross_cats_sorted":[],"title_canon_sha256":"3262e4e6fb9cf44bb624265390f48f49792c15e68f0769e4b2bbf2f4421c6656","abstract_canon_sha256":"fe7579644bfde060666327b7995c7a7141d8cb1ab5778b355fd78f0d043c6f48"},"schema_version":"1.0"},"canonical_sha256":"e5c4dac2913194c16a7c8165d5360dc8540bc46c7675c23114993915384b3ca0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:25:56.143606Z","signature_b64":"PkRY8g+uPnf9Bg50zKag0elObWTWuBFSQbYydG66cn9RguwARs2ngA5uQa1lINOnSQ6c2sU9mMpKPzqIe0WnBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5c4dac2913194c16a7c8165d5360dc8540bc46c7675c23114993915384b3ca0","last_reissued_at":"2026-07-05T06:25:56.143080Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:25:56.143080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.06963","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":"2026-07-05T06:25:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l08NUwrT56E+bVxNCfRiw/f9R/14pULSqNniEeMp+wr8eZh+STOmmKziDOoePKvEGSyjaXdR8qBYSKcLm6K1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:55:50.104366Z"},"content_sha256":"ce9223becc50deb12bb45ec740483ecaf661b687f477c0f49a4e8a4337d72235","schema_version":"1.0","event_id":"sha256:ce9223becc50deb12bb45ec740483ecaf661b687f477c0f49a4e8a4337d72235"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4XCNVQURGGKMC2T4QFS5KNQNZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounding the tripartite-circle crossing number of complete tripartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Charles Camacho, Elizabeth Bailey Matson, Jennifer White, Linda Kleist, Marija Jeli\\'c Milutinovi\\'c, Rachel Kirsch, Silvia Fern\\'andez-Merchant","submitted_at":"2019-10-15T17:59:55Z","abstract_excerpt":"A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not cross the circles. We present upper and lower bounds on the minimum number of crossings in tripartite-circle drawings of $K_{m,n,p}$. In contrast to 1- and 2-circle drawings, which may attain the Harary-Hill bound, our results imply that balanced restricted 3-circle drawings of the complete graph are not optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.06963","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/1910.06963/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":"2026-07-05T06:25:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNzERKU+3f4trpKc9E4o9RBiy9tHi8i3IGQ36eqLXy/Y4vkBa5cv365AgoPL8drClOAhqoF1CkbT1v+nlRyyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T15:55:50.104935Z"},"content_sha256":"889ffd8ab588266949ca280d8dabd19d3f9d627d1e3219fca752363d4d601057","schema_version":"1.0","event_id":"sha256:889ffd8ab588266949ca280d8dabd19d3f9d627d1e3219fca752363d4d601057"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XCNVQURGGKMC2T4QFS5KNQNZB/bundle.json","state_url":"https://pith.science/pith/4XCNVQURGGKMC2T4QFS5KNQNZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XCNVQURGGKMC2T4QFS5KNQNZB/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":"2026-08-03T15:55:50Z","links":{"resolver":"https://pith.science/pith/4XCNVQURGGKMC2T4QFS5KNQNZB","bundle":"https://pith.science/pith/4XCNVQURGGKMC2T4QFS5KNQNZB/bundle.json","state":"https://pith.science/pith/4XCNVQURGGKMC2T4QFS5KNQNZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XCNVQURGGKMC2T4QFS5KNQNZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4XCNVQURGGKMC2T4QFS5KNQNZB","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":"fe7579644bfde060666327b7995c7a7141d8cb1ab5778b355fd78f0d043c6f48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-15T17:59:55Z","title_canon_sha256":"3262e4e6fb9cf44bb624265390f48f49792c15e68f0769e4b2bbf2f4421c6656"},"schema_version":"1.0","source":{"id":"1910.06963","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.06963","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"arxiv_version","alias_value":"1910.06963v2","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.06963","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"pith_short_12","alias_value":"4XCNVQURGGKM","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"4XCNVQURGGKMC2T4","created_at":"2026-07-05T06:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"4XCNVQUR","created_at":"2026-07-05T06:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:889ffd8ab588266949ca280d8dabd19d3f9d627d1e3219fca752363d4d601057","target":"graph","created_at":"2026-07-05T06:25:56Z","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/1910.06963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not cross the circles. We present upper and lower bounds on the minimum number of crossings in tripartite-circle drawings of $K_{m,n,p}$. In contrast to 1- and 2-circle drawings, which may attain the Harary-Hill bound, our results imply that balanced restricted 3-circle drawings of the complete graph are not optimal.","authors_text":"Charles Camacho, Elizabeth Bailey Matson, Jennifer White, Linda Kleist, Marija Jeli\\'c Milutinovi\\'c, Rachel Kirsch, Silvia Fern\\'andez-Merchant","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-15T17:59:55Z","title":"Bounding the tripartite-circle crossing number of complete tripartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.06963","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:ce9223becc50deb12bb45ec740483ecaf661b687f477c0f49a4e8a4337d72235","target":"record","created_at":"2026-07-05T06:25:56Z","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":"fe7579644bfde060666327b7995c7a7141d8cb1ab5778b355fd78f0d043c6f48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-10-15T17:59:55Z","title_canon_sha256":"3262e4e6fb9cf44bb624265390f48f49792c15e68f0769e4b2bbf2f4421c6656"},"schema_version":"1.0","source":{"id":"1910.06963","kind":"arxiv","version":2}},"canonical_sha256":"e5c4dac2913194c16a7c8165d5360dc8540bc46c7675c23114993915384b3ca0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5c4dac2913194c16a7c8165d5360dc8540bc46c7675c23114993915384b3ca0","first_computed_at":"2026-07-05T06:25:56.143080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:25:56.143080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PkRY8g+uPnf9Bg50zKag0elObWTWuBFSQbYydG66cn9RguwARs2ngA5uQa1lINOnSQ6c2sU9mMpKPzqIe0WnBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:25:56.143606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.06963","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce9223becc50deb12bb45ec740483ecaf661b687f477c0f49a4e8a4337d72235","sha256:889ffd8ab588266949ca280d8dabd19d3f9d627d1e3219fca752363d4d601057"],"state_sha256":"4f1138064c3b79e63dd2d00a4417c8b0a70c93ac70d8acce1cfbb6cc8756af17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l2muje2zTIHi6Kz01+euzU93Ty4KGKERcmCG3F/jSHVI6G8ATfDC2kKJWpJj5voV6i+80YgAG04Kdd4jsLMeDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T15:55:50.108053Z","bundle_sha256":"499256e0911e838e630b4f691ec6ce095f424216382762417037b302a07b47f0"}}