{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WMEMYJALADDO3FSOAK6MVJQ7QD","short_pith_number":"pith:WMEMYJAL","canonical_record":{"source":{"id":"1808.00691","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-02T07:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"1acb283ac6f577ad5cac96b59aab36dfc9dce97b385d4d89b09e3a26a8a15f1f","abstract_canon_sha256":"b8934d0df0ab6e2e6a40c3e32ba56cdcda7d6c6496c6fa9b1b54850e6f83b551"},"schema_version":"1.0"},"canonical_sha256":"b308cc240b00c6ed964e02bccaa61f80e7b9f4af14317539aa0d094c68d65066","source":{"kind":"arxiv","id":"1808.00691","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WMEMYJALADDO3FSOAK6MVJQ7QD","target":"record","payload":{"canonical_record":{"source":{"id":"1808.00691","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-02T07:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"1acb283ac6f577ad5cac96b59aab36dfc9dce97b385d4d89b09e3a26a8a15f1f","abstract_canon_sha256":"b8934d0df0ab6e2e6a40c3e32ba56cdcda7d6c6496c6fa9b1b54850e6f83b551"},"schema_version":"1.0"},"canonical_sha256":"b308cc240b00c6ed964e02bccaa61f80e7b9f4af14317539aa0d094c68d65066","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:23:52.848435Z","signature_b64":"V8AxmuOwipOqUUwGAHCjCyvq+AP+Fe0JQCrPrVUe1VHCrapTC/QWjwa3usRwj0VXHslD9DP4aP0rHYGVRB89CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b308cc240b00c6ed964e02bccaa61f80e7b9f4af14317539aa0d094c68d65066","last_reissued_at":"2026-07-05T01:23:52.848071Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:23:52.848071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.00691","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ViiJzTzJewrdKM+8FZ+JSIeAXyN3N/uZT+0LYgBc+T+g477A7w/gxVu8XzcqxyBke/NpFnxkh7IHxHie0ZOpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:15:03.823815Z"},"content_sha256":"865e772c6c9d3172244562a0234c97a649e076905d4746f260437596f9abb61f","schema_version":"1.0","event_id":"sha256:865e772c6c9d3172244562a0234c97a649e076905d4746f260437596f9abb61f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WMEMYJALADDO3FSOAK6MVJQ7QD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Triangle Estimation using Tripartite Independent Set Queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anup Bhattacharya, Arijit Bishnu, Arijit Ghosh, Gopinath Mishra","submitted_at":"2018-08-02T07:15:14Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00691","kind":"arxiv","version":3},"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/1808.00691/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":"2026-07-05T01:23:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ZY9woaxYY7eAxqkxntqRuLJxFTei90MMyLs8yRnnfKILezI+JZJJ7r4igtf1h9kyY4iOHLWrACt/0rsJltPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T11:15:03.824337Z"},"content_sha256":"712be0addda5bd50ed96387448f9508f05c92a9fe62ecad1065441e05c7406dd","schema_version":"1.0","event_id":"sha256:712be0addda5bd50ed96387448f9508f05c92a9fe62ecad1065441e05c7406dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMEMYJALADDO3FSOAK6MVJQ7QD/bundle.json","state_url":"https://pith.science/pith/WMEMYJALADDO3FSOAK6MVJQ7QD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMEMYJALADDO3FSOAK6MVJQ7QD/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":"2026-08-16T11:15:03Z","links":{"resolver":"https://pith.science/pith/WMEMYJALADDO3FSOAK6MVJQ7QD","bundle":"https://pith.science/pith/WMEMYJALADDO3FSOAK6MVJQ7QD/bundle.json","state":"https://pith.science/pith/WMEMYJALADDO3FSOAK6MVJQ7QD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMEMYJALADDO3FSOAK6MVJQ7QD/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/tK4UEnuX6ZHZC4ZSQWYnOHhu6sWFOgWDY+z1G6kI6GHKOw77Y5wHs/gQvq/wxTTTCGPqSy8SakLtFjJ+gjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T11:15:03.828936Z","bundle_sha256":"8ed2a89b7245970a7ab3347c1ca6b276a33f9b333227096f5ced8165458c1964"}}