{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JX5RYSO7HSVZM2S2FUKEPUNIBH","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":"b3bda3adea4ff93535096ceb2c7f2cfa6e6a11e80183ed1ad1f75f48e40921b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-06-10T15:17:26Z","title_canon_sha256":"bedaafbcb10eba4175178a462aeb4d15f1a8ea40c1c23c2ade4958b271ce0c3b"},"schema_version":"1.0","source":{"id":"1606.03357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03357","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03357v1","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03357","created_at":"2026-05-18T01:12:37Z"},{"alias_kind":"pith_short_12","alias_value":"JX5RYSO7HSVZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JX5RYSO7HSVZM2S2","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JX5RYSO7","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:215855bfca10b14e9e40807a286b602274f38e577a2cfef053e9b77a3e208d8e","target":"graph","created_at":"2026-05-18T01:12:37Z","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":"Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.) and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances ","authors_text":"Arnur Nigmetov, Dmitriy Morozov, Michael Kerber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-06-10T15:17:26Z","title":"Geometry Helps to Compare Persistence Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03357","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":"sha256:80d2db9370bbccacbabdfb31e05b71293312d6e1296e3cbae8e94a0914c8e9c7","target":"record","created_at":"2026-05-18T01:12:37Z","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":"b3bda3adea4ff93535096ceb2c7f2cfa6e6a11e80183ed1ad1f75f48e40921b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-06-10T15:17:26Z","title_canon_sha256":"bedaafbcb10eba4175178a462aeb4d15f1a8ea40c1c23c2ade4958b271ce0c3b"},"schema_version":"1.0","source":{"id":"1606.03357","kind":"arxiv","version":1}},"canonical_sha256":"4dfb1c49df3cab966a5a2d1447d1a809f85b048212a35ce0491dad40ad9658a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dfb1c49df3cab966a5a2d1447d1a809f85b048212a35ce0491dad40ad9658a5","first_computed_at":"2026-05-18T01:12:37.068803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:37.068803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1/tsezKHq0zM9SqXHLPqML59J9RpJHIlm7v34aeLGKuKMPW/vc9UZnfk+srpf1cRy7RvuHO6UW9EHmhMRUPICA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:37.069153Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80d2db9370bbccacbabdfb31e05b71293312d6e1296e3cbae8e94a0914c8e9c7","sha256:215855bfca10b14e9e40807a286b602274f38e577a2cfef053e9b77a3e208d8e"],"state_sha256":"e4da1237b8c914dd61b29dc7fb034fd88090b43a995115c6992bd5acb1861635"}