{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IHC732YG6OO63IQPXL27OOLWBP","short_pith_number":"pith:IHC732YG","canonical_record":{"source":{"id":"1802.04789","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-13T18:47:15Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"e4f291ab5007b44880bcd52dc4e1a29cb6e34461a64cb0039c8c998f9d308791","abstract_canon_sha256":"efe031eb54a3c8e6042ddec90ae70a52a74041962f868bcd3e3caf2ffd94bd9c"},"schema_version":"1.0"},"canonical_sha256":"41c5fdeb06f39deda20fbaf5f739760bf209099a78e763f2cc9eb2013880d8e7","source":{"kind":"arxiv","id":"1802.04789","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04789","created_at":"2026-05-17T23:50:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04789v4","created_at":"2026-05-17T23:50:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04789","created_at":"2026-05-17T23:50:45Z"},{"alias_kind":"pith_short_12","alias_value":"IHC732YG6OO6","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IHC732YG6OO63IQP","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IHC732YG","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IHC732YG6OO63IQPXL27OOLWBP","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04789","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-13T18:47:15Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"e4f291ab5007b44880bcd52dc4e1a29cb6e34461a64cb0039c8c998f9d308791","abstract_canon_sha256":"efe031eb54a3c8e6042ddec90ae70a52a74041962f868bcd3e3caf2ffd94bd9c"},"schema_version":"1.0"},"canonical_sha256":"41c5fdeb06f39deda20fbaf5f739760bf209099a78e763f2cc9eb2013880d8e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:45.178956Z","signature_b64":"hePsJ6xoyybmGqn3Z7aIwpqSnbHqTwT1SUyapiFU/k846xJgK/XXjrmWh8Se7GdlmUqyjBhMQEqQJos3czdKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41c5fdeb06f39deda20fbaf5f739760bf209099a78e763f2cc9eb2013880d8e7","last_reissued_at":"2026-05-17T23:50:45.178574Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:45.178574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04789","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6g2Ec3ohIwUbHhaz0Z3eN0Tul0EiiZijTLldxR8OxinP9Ks9ZpRDqZKrdsWBXkikuWj6OoOU8TWARxleZmOWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:02:34.824736Z"},"content_sha256":"24c61772fbe6d1bee77e37a3e9cc183356fa623a2d5627500f92c2cc9aa6336f","schema_version":"1.0","event_id":"sha256:24c61772fbe6d1bee77e37a3e9cc183356fa623a2d5627500f92c2cc9aa6336f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IHC732YG6OO63IQPXL27OOLWBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Matrix Multiplication and Triangle Listing in the Congested Clique Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.DS","authors_text":"Dean Leitersdorf, Elia Turner, Keren Censor-Hillel","submitted_at":"2018-02-13T18:47:15Z","abstract_excerpt":"We multiply two $n \\times n$ matrices $S,T$ over semirings in the Congested Clique model, where $n$ fully connected nodes communicate synchronously using $O(\\log n)$-bit messages, within $O(nz(S)^{1/3} nz(T)^{1/3}/n + 1)$ rounds of communication, where $nz(A)$ denotes the number of non-zero elements in a matrix $A$. By leveraging the sparsity of the input matrices, our algorithm greatly reduces communication compared with general algorithms [Censor-Hillel et al., PODC 2015], improving upon the state-of-the-art for matrices with $o(n^2)$ non-zero elements. Our algorithm exhibits the additional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04789","kind":"arxiv","version":4},"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":"2026-05-17T23:50:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5AW6+7Yng/A2+pXH5yjWSdp5+lg69XVD0HDNrMzM9lQRvxDBjTm96P3gxKv6MD/iZlYu1bO5YPCi5WZ8MsTjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:02:34.825262Z"},"content_sha256":"f786cf334da697a2faf57bde5099807edaaf9397771f67dbc448d4fecb0e14c4","schema_version":"1.0","event_id":"sha256:f786cf334da697a2faf57bde5099807edaaf9397771f67dbc448d4fecb0e14c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHC732YG6OO63IQPXL27OOLWBP/bundle.json","state_url":"https://pith.science/pith/IHC732YG6OO63IQPXL27OOLWBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHC732YG6OO63IQPXL27OOLWBP/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":"2026-06-01T02:02:34Z","links":{"resolver":"https://pith.science/pith/IHC732YG6OO63IQPXL27OOLWBP","bundle":"https://pith.science/pith/IHC732YG6OO63IQPXL27OOLWBP/bundle.json","state":"https://pith.science/pith/IHC732YG6OO63IQPXL27OOLWBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHC732YG6OO63IQPXL27OOLWBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IHC732YG6OO63IQPXL27OOLWBP","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":"efe031eb54a3c8e6042ddec90ae70a52a74041962f868bcd3e3caf2ffd94bd9c","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-13T18:47:15Z","title_canon_sha256":"e4f291ab5007b44880bcd52dc4e1a29cb6e34461a64cb0039c8c998f9d308791"},"schema_version":"1.0","source":{"id":"1802.04789","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04789","created_at":"2026-05-17T23:50:45Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04789v4","created_at":"2026-05-17T23:50:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04789","created_at":"2026-05-17T23:50:45Z"},{"alias_kind":"pith_short_12","alias_value":"IHC732YG6OO6","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IHC732YG6OO63IQP","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IHC732YG","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:f786cf334da697a2faf57bde5099807edaaf9397771f67dbc448d4fecb0e14c4","target":"graph","created_at":"2026-05-17T23:50:45Z","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":"We multiply two $n \\times n$ matrices $S,T$ over semirings in the Congested Clique model, where $n$ fully connected nodes communicate synchronously using $O(\\log n)$-bit messages, within $O(nz(S)^{1/3} nz(T)^{1/3}/n + 1)$ rounds of communication, where $nz(A)$ denotes the number of non-zero elements in a matrix $A$. By leveraging the sparsity of the input matrices, our algorithm greatly reduces communication compared with general algorithms [Censor-Hillel et al., PODC 2015], improving upon the state-of-the-art for matrices with $o(n^2)$ non-zero elements. Our algorithm exhibits the additional ","authors_text":"Dean Leitersdorf, Elia Turner, Keren Censor-Hillel","cross_cats":["cs.DC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-13T18:47:15Z","title":"Sparse Matrix Multiplication and Triangle Listing in the Congested Clique Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04789","kind":"arxiv","version":4},"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":"sha256:24c61772fbe6d1bee77e37a3e9cc183356fa623a2d5627500f92c2cc9aa6336f","target":"record","created_at":"2026-05-17T23:50:45Z","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":"efe031eb54a3c8e6042ddec90ae70a52a74041962f868bcd3e3caf2ffd94bd9c","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-13T18:47:15Z","title_canon_sha256":"e4f291ab5007b44880bcd52dc4e1a29cb6e34461a64cb0039c8c998f9d308791"},"schema_version":"1.0","source":{"id":"1802.04789","kind":"arxiv","version":4}},"canonical_sha256":"41c5fdeb06f39deda20fbaf5f739760bf209099a78e763f2cc9eb2013880d8e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41c5fdeb06f39deda20fbaf5f739760bf209099a78e763f2cc9eb2013880d8e7","first_computed_at":"2026-05-17T23:50:45.178574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:45.178574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hePsJ6xoyybmGqn3Z7aIwpqSnbHqTwT1SUyapiFU/k846xJgK/XXjrmWh8Se7GdlmUqyjBhMQEqQJos3czdKCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:45.178956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04789","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24c61772fbe6d1bee77e37a3e9cc183356fa623a2d5627500f92c2cc9aa6336f","sha256:f786cf334da697a2faf57bde5099807edaaf9397771f67dbc448d4fecb0e14c4"],"state_sha256":"5b4e5b06d6187a5ac7268e31f69e82d58a94d33c95585569d228fd2d69f15d48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"syBsG8wJpEFNpkT54SwFg+5A0hMal0TJvHJ+dfqtgGYDFqYkus97Wo/1wRKL99h/GfDbeR5cd/gQfXZ4kjHZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:02:34.828930Z","bundle_sha256":"55ce664e8dbf63a37a97b7935c8e3d9cde29e375e9d2c1a550fabc4b19fbc499"}}