{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SKSIQUUYMP3R6FS24ERW73TEMO","short_pith_number":"pith:SKSIQUUY","canonical_record":{"source":{"id":"1705.09061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-05-25T06:24:25Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"80d8692e418c16759cf119f3b4e95aca0204f43ec9bdcc15ba1f7edbef63454a","abstract_canon_sha256":"fa5e8f8dcd3345847023b88253ae78fda1f2ca65aacff95965dd57f7a2c8fc85"},"schema_version":"1.0"},"canonical_sha256":"92a488529863f71f165ae1236fee6463b57aa211eb4fb2a6bc846106a3afd7e0","source":{"kind":"arxiv","id":"1705.09061","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09061","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09061v1","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09061","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"pith_short_12","alias_value":"SKSIQUUYMP3R","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"pith_short_16","alias_value":"SKSIQUUYMP3R6FS2","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"pith_short_8","alias_value":"SKSIQUUY","created_at":"2026-07-05T03:19:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SKSIQUUYMP3R6FS24ERW73TEMO","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09061","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-05-25T06:24:25Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"80d8692e418c16759cf119f3b4e95aca0204f43ec9bdcc15ba1f7edbef63454a","abstract_canon_sha256":"fa5e8f8dcd3345847023b88253ae78fda1f2ca65aacff95965dd57f7a2c8fc85"},"schema_version":"1.0"},"canonical_sha256":"92a488529863f71f165ae1236fee6463b57aa211eb4fb2a6bc846106a3afd7e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:19:37.079261Z","signature_b64":"E8d77tsv5HnBuAnLE6+6VGah81UiWwVbRmCkW+qk3kysUcrBD5qJzzPnp8AVq+OfXwQ9zWLc4i/55FHWuNOyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92a488529863f71f165ae1236fee6463b57aa211eb4fb2a6bc846106a3afd7e0","last_reissued_at":"2026-07-05T03:19:37.078858Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:19:37.078858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09061","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":"2026-07-05T03:19:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DgSqD/maVqd7ktkXHKFN1ey+oCTZ3/jrrNO4NrrY4H++Nn+ZEyFYJNt+uVOw7Sm7GFQbtlYcwG3hv4gc+YugCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:09:56.862236Z"},"content_sha256":"1ca1a7227f70c1cf9603ff48870e9b511ab10a0c3e7828cbe4ea1a96555aceaa","schema_version":"1.0","event_id":"sha256:1ca1a7227f70c1cf9603ff48870e9b511ab10a0c3e7828cbe4ea1a96555aceaa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SKSIQUUYMP3R6FS24ERW73TEMO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangle Finding and Listing in CONGEST Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Fran\\c{c}ois Le Gall, Taisuke Izumi","submitted_at":"2017-05-25T06:24:25Z","abstract_excerpt":"Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle finding) as well as triangle enumeration (triangle listing) play central roles in the field of graph algorithms. In distributed computing, algorithms with sublinear round complexity for triangle finding and listing have recently been developed in the powerful CONGEST clique model, where communication is allowed between any two nodes of the network. In this paper we present the first algorithms with sublinear complexity for triangle finding and triangle listing in the standard CONGEST model, where the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09061","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1705.09061/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":"2026-07-05T03:19:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6VUgOjgnh4Eouk8M5M5x7mKLUHg1oBcU/+nQIR6/qK5pBojv9LcK9+B8ROjNC9pFWUHSYLBCN3uiAhfToQwJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:09:56.862723Z"},"content_sha256":"34f8aef5a5e7825ab733bcada1820aa72de5229e3624d4737989532ee8ba4533","schema_version":"1.0","event_id":"sha256:34f8aef5a5e7825ab733bcada1820aa72de5229e3624d4737989532ee8ba4533"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKSIQUUYMP3R6FS24ERW73TEMO/bundle.json","state_url":"https://pith.science/pith/SKSIQUUYMP3R6FS24ERW73TEMO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKSIQUUYMP3R6FS24ERW73TEMO/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":"2026-08-08T03:09:56Z","links":{"resolver":"https://pith.science/pith/SKSIQUUYMP3R6FS24ERW73TEMO","bundle":"https://pith.science/pith/SKSIQUUYMP3R6FS24ERW73TEMO/bundle.json","state":"https://pith.science/pith/SKSIQUUYMP3R6FS24ERW73TEMO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKSIQUUYMP3R6FS24ERW73TEMO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SKSIQUUYMP3R6FS24ERW73TEMO","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":"fa5e8f8dcd3345847023b88253ae78fda1f2ca65aacff95965dd57f7a2c8fc85","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-05-25T06:24:25Z","title_canon_sha256":"80d8692e418c16759cf119f3b4e95aca0204f43ec9bdcc15ba1f7edbef63454a"},"schema_version":"1.0","source":{"id":"1705.09061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09061","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09061v1","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09061","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"pith_short_12","alias_value":"SKSIQUUYMP3R","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"pith_short_16","alias_value":"SKSIQUUYMP3R6FS2","created_at":"2026-07-05T03:19:37Z"},{"alias_kind":"pith_short_8","alias_value":"SKSIQUUY","created_at":"2026-07-05T03:19:37Z"}],"graph_snapshots":[{"event_id":"sha256:34f8aef5a5e7825ab733bcada1820aa72de5229e3624d4737989532ee8ba4533","target":"graph","created_at":"2026-07-05T03:19:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1705.09061/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle finding) as well as triangle enumeration (triangle listing) play central roles in the field of graph algorithms. In distributed computing, algorithms with sublinear round complexity for triangle finding and listing have recently been developed in the powerful CONGEST clique model, where communication is allowed between any two nodes of the network. In this paper we present the first algorithms with sublinear complexity for triangle finding and triangle listing in the standard CONGEST model, where the ","authors_text":"Fran\\c{c}ois Le Gall, Taisuke Izumi","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-05-25T06:24:25Z","title":"Triangle Finding and Listing in CONGEST Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09061","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":"sha256:1ca1a7227f70c1cf9603ff48870e9b511ab10a0c3e7828cbe4ea1a96555aceaa","target":"record","created_at":"2026-07-05T03:19:37Z","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":"fa5e8f8dcd3345847023b88253ae78fda1f2ca65aacff95965dd57f7a2c8fc85","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2017-05-25T06:24:25Z","title_canon_sha256":"80d8692e418c16759cf119f3b4e95aca0204f43ec9bdcc15ba1f7edbef63454a"},"schema_version":"1.0","source":{"id":"1705.09061","kind":"arxiv","version":1}},"canonical_sha256":"92a488529863f71f165ae1236fee6463b57aa211eb4fb2a6bc846106a3afd7e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92a488529863f71f165ae1236fee6463b57aa211eb4fb2a6bc846106a3afd7e0","first_computed_at":"2026-07-05T03:19:37.078858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:19:37.078858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E8d77tsv5HnBuAnLE6+6VGah81UiWwVbRmCkW+qk3kysUcrBD5qJzzPnp8AVq+OfXwQ9zWLc4i/55FHWuNOyAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:19:37.079261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ca1a7227f70c1cf9603ff48870e9b511ab10a0c3e7828cbe4ea1a96555aceaa","sha256:34f8aef5a5e7825ab733bcada1820aa72de5229e3624d4737989532ee8ba4533"],"state_sha256":"7e12e136e6ac1cb0db0dd95394425e5d4ee90d51de4287e38752c282b0a97be2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vz84wTVu2ig7xTbzk85nd40r16S1hAdQqPzuaESHpyeLqBu02IBpOVUQbvuuGk63WlrwKFBLBiCZNzyXWyYAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T03:09:56.868088Z","bundle_sha256":"23010ba0b4e92a2acc8d9dd77f9ffde8924694450dcbd1a17e19b26d5eb63584"}}