{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:LFTCKC6JOTHA2LIBN4K5CRHX6V","short_pith_number":"pith:LFTCKC6J","canonical_record":{"source":{"id":"1907.04645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-07-10T12:10:09Z","cross_cats_sorted":["cs.CC","cs.DM","cs.DS","math.CO"],"title_canon_sha256":"763cd4659b7d35f3e663cbb09d1ef4b31648a879cdfb23bad368a795501aea87","abstract_canon_sha256":"e0ab955a232320a02d47d00d1ecf09ed119702783d70078be62a91ec95a3cee4"},"schema_version":"1.0"},"canonical_sha256":"5966250bc974ce0d2d016f15d144f7f54ae1a492a920c7735e0395648b0c97ed","source":{"kind":"arxiv","id":"1907.04645","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04645","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04645v1","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04645","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"pith_short_12","alias_value":"LFTCKC6JOTHA","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LFTCKC6JOTHA2LIB","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LFTCKC6J","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:LFTCKC6JOTHA2LIBN4K5CRHX6V","target":"record","payload":{"canonical_record":{"source":{"id":"1907.04645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-07-10T12:10:09Z","cross_cats_sorted":["cs.CC","cs.DM","cs.DS","math.CO"],"title_canon_sha256":"763cd4659b7d35f3e663cbb09d1ef4b31648a879cdfb23bad368a795501aea87","abstract_canon_sha256":"e0ab955a232320a02d47d00d1ecf09ed119702783d70078be62a91ec95a3cee4"},"schema_version":"1.0"},"canonical_sha256":"5966250bc974ce0d2d016f15d144f7f54ae1a492a920c7735e0395648b0c97ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:57.243939Z","signature_b64":"zXL1/lxKlQopG9HgHnVBLQl0ym8E0mQMU0rlLd+QvDoRMgvq5jIeMoTa6Y3on9rucB51w4bzU8jMXOgl/C5UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5966250bc974ce0d2d016f15d144f7f54ae1a492a920c7735e0395648b0c97ed","last_reissued_at":"2026-05-17T23:40:57.243343Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:57.243343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.04645","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":"2026-05-17T23:40:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lCq5UaCQhsCaNUoeSSaYELyRJouwTwLduGdKtroUETEAtIETUc33DQ6g7auGWzjaVa4sK/Cdf2JiiHDh1WWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:33:02.223461Z"},"content_sha256":"cf5b97d6df4fe6fd4ef98db9621891f4eda4fbe4e4baef2e497814a855c54583","schema_version":"1.0","event_id":"sha256:cf5b97d6df4fe6fd4ef98db9621891f4eda4fbe4e4baef2e497814a855c54583"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:LFTCKC6JOTHA2LIBN4K5CRHX6V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothed Analysis of Order Types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.DS","math.CO"],"primary_cat":"cs.CG","authors_text":"Ivor van der Hoog, Martijn van Schaik, Tillmann Miltzow","submitted_at":"2019-07-10T12:10:09Z","abstract_excerpt":"Consider an ordered point set $P = (p_1,\\ldots,p_n)$, its order type (denoted by $\\chi_P$) is a map which assigns to every triple of points a value in $\\{+,-,0\\}$ based on whether the points are collinear(0), oriented clockwise(-) or counter-clockwise(+). An abstract order type is a map $\\chi : \\left[\\substack{n\\\\3}\\right] \\rightarrow \\{+,-,0\\}$ (where $\\left[\\substack{n\\\\3}\\right]$ is the collection of all triples of a set of $n$ elements) that satisfies the following condition: for every set of five elements $S\\subset [n]$ its induced order type $\\chi_{|S}$ is realizable by a point set. To b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04645","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":"2026-05-17T23:40:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBwylBRLSmeUIq1HGB3EyTfdC8hZG7O9/atER4CTFat7W28rOx5e6nVu2Ly10H5kgZmxXLiFlJS39CFMGtwhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:33:02.224189Z"},"content_sha256":"622691a5de3d82f0656ba3763f22b71f32b950f87b2edd1a402c3aac6c71eed6","schema_version":"1.0","event_id":"sha256:622691a5de3d82f0656ba3763f22b71f32b950f87b2edd1a402c3aac6c71eed6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFTCKC6JOTHA2LIBN4K5CRHX6V/bundle.json","state_url":"https://pith.science/pith/LFTCKC6JOTHA2LIBN4K5CRHX6V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFTCKC6JOTHA2LIBN4K5CRHX6V/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":"2026-05-25T19:33:02Z","links":{"resolver":"https://pith.science/pith/LFTCKC6JOTHA2LIBN4K5CRHX6V","bundle":"https://pith.science/pith/LFTCKC6JOTHA2LIBN4K5CRHX6V/bundle.json","state":"https://pith.science/pith/LFTCKC6JOTHA2LIBN4K5CRHX6V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFTCKC6JOTHA2LIBN4K5CRHX6V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LFTCKC6JOTHA2LIBN4K5CRHX6V","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":"e0ab955a232320a02d47d00d1ecf09ed119702783d70078be62a91ec95a3cee4","cross_cats_sorted":["cs.CC","cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-07-10T12:10:09Z","title_canon_sha256":"763cd4659b7d35f3e663cbb09d1ef4b31648a879cdfb23bad368a795501aea87"},"schema_version":"1.0","source":{"id":"1907.04645","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04645","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04645v1","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04645","created_at":"2026-05-17T23:40:57Z"},{"alias_kind":"pith_short_12","alias_value":"LFTCKC6JOTHA","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LFTCKC6JOTHA2LIB","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LFTCKC6J","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:622691a5de3d82f0656ba3763f22b71f32b950f87b2edd1a402c3aac6c71eed6","target":"graph","created_at":"2026-05-17T23:40:57Z","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":"Consider an ordered point set $P = (p_1,\\ldots,p_n)$, its order type (denoted by $\\chi_P$) is a map which assigns to every triple of points a value in $\\{+,-,0\\}$ based on whether the points are collinear(0), oriented clockwise(-) or counter-clockwise(+). An abstract order type is a map $\\chi : \\left[\\substack{n\\\\3}\\right] \\rightarrow \\{+,-,0\\}$ (where $\\left[\\substack{n\\\\3}\\right]$ is the collection of all triples of a set of $n$ elements) that satisfies the following condition: for every set of five elements $S\\subset [n]$ its induced order type $\\chi_{|S}$ is realizable by a point set. To b","authors_text":"Ivor van der Hoog, Martijn van Schaik, Tillmann Miltzow","cross_cats":["cs.CC","cs.DM","cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-07-10T12:10:09Z","title":"Smoothed Analysis of Order Types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04645","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:cf5b97d6df4fe6fd4ef98db9621891f4eda4fbe4e4baef2e497814a855c54583","target":"record","created_at":"2026-05-17T23:40:57Z","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":"e0ab955a232320a02d47d00d1ecf09ed119702783d70078be62a91ec95a3cee4","cross_cats_sorted":["cs.CC","cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-07-10T12:10:09Z","title_canon_sha256":"763cd4659b7d35f3e663cbb09d1ef4b31648a879cdfb23bad368a795501aea87"},"schema_version":"1.0","source":{"id":"1907.04645","kind":"arxiv","version":1}},"canonical_sha256":"5966250bc974ce0d2d016f15d144f7f54ae1a492a920c7735e0395648b0c97ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5966250bc974ce0d2d016f15d144f7f54ae1a492a920c7735e0395648b0c97ed","first_computed_at":"2026-05-17T23:40:57.243343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:57.243343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zXL1/lxKlQopG9HgHnVBLQl0ym8E0mQMU0rlLd+QvDoRMgvq5jIeMoTa6Y3on9rucB51w4bzU8jMXOgl/C5UCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:57.243939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04645","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf5b97d6df4fe6fd4ef98db9621891f4eda4fbe4e4baef2e497814a855c54583","sha256:622691a5de3d82f0656ba3763f22b71f32b950f87b2edd1a402c3aac6c71eed6"],"state_sha256":"90ad9be77c947722882bd222a21442247795168e281fbe5740f8811486dfbd93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xBfU51SI4I7CitF5N+J734YvLseTvmovQPJIw6D1nh10NLD6r+UQMV/8NIf6LwDlo4u9OXLz6YINCfpPYA0tAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:33:02.228273Z","bundle_sha256":"44682b101da3bdebd3c8e58391f4a80c756251a9dcf4cdb8d9c9f1ce75f1fb61"}}