{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WMEMYJALADDO3FSOAK6MVJQ7QD","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":"b8934d0df0ab6e2e6a40c3e32ba56cdcda7d6c6496c6fa9b1b54850e6f83b551","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-02T07:15:14Z","title_canon_sha256":"1acb283ac6f577ad5cac96b59aab36dfc9dce97b385d4d89b09e3a26a8a15f1f"},"schema_version":"1.0","source":{"id":"1808.00691","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.00691","created_at":"2026-07-05T01:23:52Z"},{"alias_kind":"arxiv_version","alias_value":"1808.00691v3","created_at":"2026-07-05T01:23:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00691","created_at":"2026-07-05T01:23:52Z"},{"alias_kind":"pith_short_12","alias_value":"WMEMYJALADDO","created_at":"2026-07-05T01:23:52Z"},{"alias_kind":"pith_short_16","alias_value":"WMEMYJALADDO3FSO","created_at":"2026-07-05T01:23:52Z"},{"alias_kind":"pith_short_8","alias_value":"WMEMYJAL","created_at":"2026-07-05T01:23:52Z"}],"graph_snapshots":[{"event_id":"sha256:712be0addda5bd50ed96387448f9508f05c92a9fe62ecad1065441e05c7406dd","target":"graph","created_at":"2026-07-05T01:23:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1808.00691/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Estimating the number of triangles in a graph is one of the most fundamental problems in sublinear algorithms. In this work, we provide an algorithm that approximately counts the number of triangles in a graph using only polylogarithmic queries when \\emph{the number of triangles on any edge in the graph is polylogarithmically bounded}. Our query oracle {\\em Tripartite Independent Set} (TIS) takes three disjoint sets of vertices $A$, $B$ and $C$ as inputs, and answers whether there exists a triangle having one endpoint in each of these three sets. Our query model generally belongs to the class ","authors_text":"Anup Bhattacharya, Arijit Bishnu, Arijit Ghosh, Gopinath Mishra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-02T07:15:14Z","title":"On Triangle Estimation using Tripartite Independent Set Queries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00691","kind":"arxiv","version":3},"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":"sha256:865e772c6c9d3172244562a0234c97a649e076905d4746f260437596f9abb61f","target":"record","created_at":"2026-07-05T01:23:52Z","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":"b8934d0df0ab6e2e6a40c3e32ba56cdcda7d6c6496c6fa9b1b54850e6f83b551","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-02T07:15:14Z","title_canon_sha256":"1acb283ac6f577ad5cac96b59aab36dfc9dce97b385d4d89b09e3a26a8a15f1f"},"schema_version":"1.0","source":{"id":"1808.00691","kind":"arxiv","version":3}},"canonical_sha256":"b308cc240b00c6ed964e02bccaa61f80e7b9f4af14317539aa0d094c68d65066","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b308cc240b00c6ed964e02bccaa61f80e7b9f4af14317539aa0d094c68d65066","first_computed_at":"2026-07-05T01:23:52.848071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:23:52.848071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V8AxmuOwipOqUUwGAHCjCyvq+AP+Fe0JQCrPrVUe1VHCrapTC/QWjwa3usRwj0VXHslD9DP4aP0rHYGVRB89CA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:23:52.848435Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.00691","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:865e772c6c9d3172244562a0234c97a649e076905d4746f260437596f9abb61f","sha256:712be0addda5bd50ed96387448f9508f05c92a9fe62ecad1065441e05c7406dd"],"state_sha256":"4bd523e2e140513d67242fe51a8f80e77c68a51ffc1123c806b500c3453812a9"}