{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:PGHZI3Q4UMX7L5ZVK5LUKQE2SO","short_pith_number":"pith:PGHZI3Q4","canonical_record":{"source":{"id":"2304.05318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-04-11T16:23:42Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3593388131badf75d08bab5874b69bfe0a1f331b3af2e1f8ac14bbccfead2417","abstract_canon_sha256":"31b6bf8acadc33e869fca8c886c97472c56a489286796862fe08033ed9de67d0"},"schema_version":"1.0"},"canonical_sha256":"798f946e1ca32ff5f735575745409a939d2e1a0ef15e8a1b3adb238ea35ad927","source":{"kind":"arxiv","id":"2304.05318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.05318","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"arxiv_version","alias_value":"2304.05318v1","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.05318","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"pith_short_12","alias_value":"PGHZI3Q4UMX7","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"pith_short_16","alias_value":"PGHZI3Q4UMX7L5ZV","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"pith_short_8","alias_value":"PGHZI3Q4","created_at":"2026-07-05T06:00:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:PGHZI3Q4UMX7L5ZVK5LUKQE2SO","target":"record","payload":{"canonical_record":{"source":{"id":"2304.05318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-04-11T16:23:42Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3593388131badf75d08bab5874b69bfe0a1f331b3af2e1f8ac14bbccfead2417","abstract_canon_sha256":"31b6bf8acadc33e869fca8c886c97472c56a489286796862fe08033ed9de67d0"},"schema_version":"1.0"},"canonical_sha256":"798f946e1ca32ff5f735575745409a939d2e1a0ef15e8a1b3adb238ea35ad927","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:00:17.952997Z","signature_b64":"DJFUhiWn/e3GE2zc1hvwMzWfqr2jehdZDQyN2rYP4Uk0YNOztGQtMydV123wh0qw9ECjYmRI5ezi02XPN4TxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"798f946e1ca32ff5f735575745409a939d2e1a0ef15e8a1b3adb238ea35ad927","last_reissued_at":"2026-07-05T06:00:17.952469Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:00:17.952469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.05318","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":"2026-07-05T06:00:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VpNa1pX1u0/sY0vNtlf794UZfRmWpfERtiainVQNrhFAWVQmfIW4Pq0dzrlHtTmmYH3QvSwX/naChal0VL2LDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T09:14:42.299812Z"},"content_sha256":"78edb55acfe3e3ae38184c83c57a0542ecf4b7a58a1a33a6e31a6afa9c9b4c42","schema_version":"1.0","event_id":"sha256:78edb55acfe3e3ae38184c83c57a0542ecf4b7a58a1a33a6e31a6afa9c9b4c42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:PGHZI3Q4UMX7L5ZVK5LUKQE2SO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sampling planar tanglegrams and pairs of disjoint triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Alexander E. Black, Alex McDonough, Garrett Nelson, Kevin Liu, Mei Yin, Michael C. Wigal, Youngho Yoo","submitted_at":"2023-04-11T16:23:42Z","abstract_excerpt":"A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that the problem of generating planar tanglegrams uniformly at random reduces to the corresponding problem for irreducible planar tanglegram layouts, which are known to be in bijection with pairs of disjoint triangulations of a convex polygon. We extend the flip operation on a single triangulation to a flip operation on pairs of disjoint triangulations. Interestingly, the resulting flip graph is both connected and regular, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.05318","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/2304.05318/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":"2026-07-05T06:00:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6+CRsF0O1+2ETdg5zqbC5LCYKgUhfDou1En/f7NL9XHkhrbGZMKPLjCoHnO9qMUgb+6H739RU+gB0sE6XnEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T09:14:42.300175Z"},"content_sha256":"d5231ec2edf7eeafc9a4663f48f73e1bc7ee74d7ef9c8ab2a5883ecf5a803822","schema_version":"1.0","event_id":"sha256:d5231ec2edf7eeafc9a4663f48f73e1bc7ee74d7ef9c8ab2a5883ecf5a803822"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PGHZI3Q4UMX7L5ZVK5LUKQE2SO/bundle.json","state_url":"https://pith.science/pith/PGHZI3Q4UMX7L5ZVK5LUKQE2SO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PGHZI3Q4UMX7L5ZVK5LUKQE2SO/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":"2026-07-06T09:14:42Z","links":{"resolver":"https://pith.science/pith/PGHZI3Q4UMX7L5ZVK5LUKQE2SO","bundle":"https://pith.science/pith/PGHZI3Q4UMX7L5ZVK5LUKQE2SO/bundle.json","state":"https://pith.science/pith/PGHZI3Q4UMX7L5ZVK5LUKQE2SO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PGHZI3Q4UMX7L5ZVK5LUKQE2SO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:PGHZI3Q4UMX7L5ZVK5LUKQE2SO","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":"31b6bf8acadc33e869fca8c886c97472c56a489286796862fe08033ed9de67d0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-04-11T16:23:42Z","title_canon_sha256":"3593388131badf75d08bab5874b69bfe0a1f331b3af2e1f8ac14bbccfead2417"},"schema_version":"1.0","source":{"id":"2304.05318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.05318","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"arxiv_version","alias_value":"2304.05318v1","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.05318","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"pith_short_12","alias_value":"PGHZI3Q4UMX7","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"pith_short_16","alias_value":"PGHZI3Q4UMX7L5ZV","created_at":"2026-07-05T06:00:17Z"},{"alias_kind":"pith_short_8","alias_value":"PGHZI3Q4","created_at":"2026-07-05T06:00:17Z"}],"graph_snapshots":[{"event_id":"sha256:d5231ec2edf7eeafc9a4663f48f73e1bc7ee74d7ef9c8ab2a5883ecf5a803822","target":"graph","created_at":"2026-07-05T06:00:17Z","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/2304.05318/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that the problem of generating planar tanglegrams uniformly at random reduces to the corresponding problem for irreducible planar tanglegram layouts, which are known to be in bijection with pairs of disjoint triangulations of a convex polygon. We extend the flip operation on a single triangulation to a flip operation on pairs of disjoint triangulations. Interestingly, the resulting flip graph is both connected and regular, ","authors_text":"Alexander E. Black, Alex McDonough, Garrett Nelson, Kevin Liu, Mei Yin, Michael C. Wigal, Youngho Yoo","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-04-11T16:23:42Z","title":"Sampling planar tanglegrams and pairs of disjoint triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.05318","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":"sha256:78edb55acfe3e3ae38184c83c57a0542ecf4b7a58a1a33a6e31a6afa9c9b4c42","target":"record","created_at":"2026-07-05T06:00:17Z","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":"31b6bf8acadc33e869fca8c886c97472c56a489286796862fe08033ed9de67d0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-04-11T16:23:42Z","title_canon_sha256":"3593388131badf75d08bab5874b69bfe0a1f331b3af2e1f8ac14bbccfead2417"},"schema_version":"1.0","source":{"id":"2304.05318","kind":"arxiv","version":1}},"canonical_sha256":"798f946e1ca32ff5f735575745409a939d2e1a0ef15e8a1b3adb238ea35ad927","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"798f946e1ca32ff5f735575745409a939d2e1a0ef15e8a1b3adb238ea35ad927","first_computed_at":"2026-07-05T06:00:17.952469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:00:17.952469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DJFUhiWn/e3GE2zc1hvwMzWfqr2jehdZDQyN2rYP4Uk0YNOztGQtMydV123wh0qw9ECjYmRI5ezi02XPN4TxCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:00:17.952997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.05318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78edb55acfe3e3ae38184c83c57a0542ecf4b7a58a1a33a6e31a6afa9c9b4c42","sha256:d5231ec2edf7eeafc9a4663f48f73e1bc7ee74d7ef9c8ab2a5883ecf5a803822"],"state_sha256":"a703682c36bf768dee955824283bbaf04f5c96fc27767fa4ef23df32f680abb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z4Dw1d+B07KHWPs4KLHD66TW1NUl5Xu4F+qJB+ON0o+ipb+ceTTl0bJisnWyjSrxIg+FDFTzFEa6jKRw4dyZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T09:14:42.302110Z","bundle_sha256":"79015bb1c458d906f636c0a0f867c5a8f9b8f20289dcb7569882ab77fc223f9f"}}