{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EULVQMR737T4EFKDY55VNUPFN4","short_pith_number":"pith:EULVQMR7","canonical_record":{"source":{"id":"1205.4738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-05-21T20:22:52Z","cross_cats_sorted":[],"title_canon_sha256":"02901c02183465a32bcc5241db174066c6a12ad9eb7a1480036fd743a582b82b","abstract_canon_sha256":"612baa6b5cf1f435a0690b064db2bbb99fc31ab61357acb25877d1bef324b7be"},"schema_version":"1.0"},"canonical_sha256":"251758323fdfe7c21543c77b56d1e56f3e1577dff85e06fb0c8de7be7a7f4caf","source":{"kind":"arxiv","id":"1205.4738","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4738","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4738v1","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4738","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"pith_short_12","alias_value":"EULVQMR737T4","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EULVQMR737T4EFKD","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EULVQMR7","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EULVQMR737T4EFKDY55VNUPFN4","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-05-21T20:22:52Z","cross_cats_sorted":[],"title_canon_sha256":"02901c02183465a32bcc5241db174066c6a12ad9eb7a1480036fd743a582b82b","abstract_canon_sha256":"612baa6b5cf1f435a0690b064db2bbb99fc31ab61357acb25877d1bef324b7be"},"schema_version":"1.0"},"canonical_sha256":"251758323fdfe7c21543c77b56d1e56f3e1577dff85e06fb0c8de7be7a7f4caf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:52.555243Z","signature_b64":"tMqXuxPVk084LhKWktD3Py6Mbg/qZDLJMt9R9El0TUbp0BTYqzUCCadnxd0y1iFfoMBaJ9V1DzTPfluXPlPYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"251758323fdfe7c21543c77b56d1e56f3e1577dff85e06fb0c8de7be7a7f4caf","last_reissued_at":"2026-05-18T03:47:52.554878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:52.554878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4738","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":"2026-05-18T03:47:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vhz+c4u0F5+oRM7CkrtjFwCdviDun22vq7ZLfG7vOiAfItZZCI5hYm2kj1RpP0XyYX+mt7lDkUO6cfdwDegTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:51:17.105898Z"},"content_sha256":"bff5b0ff12f20025ab56a32284898cd215f58b3c6420fcd557f908bca19f519f","schema_version":"1.0","event_id":"sha256:bff5b0ff12f20025ab56a32284898cd215f58b3c6420fcd557f908bca19f519f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EULVQMR737T4EFKDY55VNUPFN4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangulating the Square and Squaring the Triangle: Quadtrees and Delaunay Triangulations are Equivalent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Maarten L\\\"offler, Wolfgang Mulzer","submitted_at":"2012-05-21T20:22:52Z","abstract_excerpt":"We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms run in deterministic linear time on a pointer machine. Our work builds on and extends previous results by Krznaric and Levcopolous and Buchin and Mulzer. Our main tool for the second algorithm is the well-separated pair decomposition(WSPD), a structure that has been used previously"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4738","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":""},"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":"2026-05-18T03:47:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G9V1jaS0PlmzVROUeqLugn2kIWQp4lEGG+igqKBKJBAq/cctYRWP1fHsqfiqbSCmUs5mewh1urVmH05qJTtmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:51:17.106234Z"},"content_sha256":"ff93a85cc0d0ed3f8c57dae4e21fb1afbe13f65a393396fb2cb6b8aa2ec863ad","schema_version":"1.0","event_id":"sha256:ff93a85cc0d0ed3f8c57dae4e21fb1afbe13f65a393396fb2cb6b8aa2ec863ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EULVQMR737T4EFKDY55VNUPFN4/bundle.json","state_url":"https://pith.science/pith/EULVQMR737T4EFKDY55VNUPFN4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EULVQMR737T4EFKDY55VNUPFN4/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":"2026-05-30T07:51:17Z","links":{"resolver":"https://pith.science/pith/EULVQMR737T4EFKDY55VNUPFN4","bundle":"https://pith.science/pith/EULVQMR737T4EFKDY55VNUPFN4/bundle.json","state":"https://pith.science/pith/EULVQMR737T4EFKDY55VNUPFN4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EULVQMR737T4EFKDY55VNUPFN4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EULVQMR737T4EFKDY55VNUPFN4","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":"612baa6b5cf1f435a0690b064db2bbb99fc31ab61357acb25877d1bef324b7be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-05-21T20:22:52Z","title_canon_sha256":"02901c02183465a32bcc5241db174066c6a12ad9eb7a1480036fd743a582b82b"},"schema_version":"1.0","source":{"id":"1205.4738","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4738","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4738v1","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4738","created_at":"2026-05-18T03:47:52Z"},{"alias_kind":"pith_short_12","alias_value":"EULVQMR737T4","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EULVQMR737T4EFKD","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EULVQMR7","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:ff93a85cc0d0ed3f8c57dae4e21fb1afbe13f65a393396fb2cb6b8aa2ec863ad","target":"graph","created_at":"2026-05-18T03:47:52Z","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"},"paper":{"abstract_excerpt":"We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms run in deterministic linear time on a pointer machine. Our work builds on and extends previous results by Krznaric and Levcopolous and Buchin and Mulzer. Our main tool for the second algorithm is the well-separated pair decomposition(WSPD), a structure that has been used previously","authors_text":"Maarten L\\\"offler, Wolfgang Mulzer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-05-21T20:22:52Z","title":"Triangulating the Square and Squaring the Triangle: Quadtrees and Delaunay Triangulations are Equivalent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4738","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:bff5b0ff12f20025ab56a32284898cd215f58b3c6420fcd557f908bca19f519f","target":"record","created_at":"2026-05-18T03:47:52Z","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":"612baa6b5cf1f435a0690b064db2bbb99fc31ab61357acb25877d1bef324b7be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-05-21T20:22:52Z","title_canon_sha256":"02901c02183465a32bcc5241db174066c6a12ad9eb7a1480036fd743a582b82b"},"schema_version":"1.0","source":{"id":"1205.4738","kind":"arxiv","version":1}},"canonical_sha256":"251758323fdfe7c21543c77b56d1e56f3e1577dff85e06fb0c8de7be7a7f4caf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"251758323fdfe7c21543c77b56d1e56f3e1577dff85e06fb0c8de7be7a7f4caf","first_computed_at":"2026-05-18T03:47:52.554878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:52.554878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tMqXuxPVk084LhKWktD3Py6Mbg/qZDLJMt9R9El0TUbp0BTYqzUCCadnxd0y1iFfoMBaJ9V1DzTPfluXPlPYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:52.555243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4738","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bff5b0ff12f20025ab56a32284898cd215f58b3c6420fcd557f908bca19f519f","sha256:ff93a85cc0d0ed3f8c57dae4e21fb1afbe13f65a393396fb2cb6b8aa2ec863ad"],"state_sha256":"bf2b7721200ea890270259f6579fa06a9615513dccc93af37b9c64a0a3fb2d19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zGGaT4dvL3kOhptU4K6q1S2/cRAHMbuGqsHnWd4ygzsNmMYy3Ns/GJRdD1W6z4tFHZ341wRnqU18kLHxPDkgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:51:17.108190Z","bundle_sha256":"64731a50d0d7b6ba415caed42a4daf45d0be47fde9b3456f2c482843f58785f4"}}