{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WYPLR6EJCFTQORD3O64CNZKEIZ","short_pith_number":"pith:WYPLR6EJ","canonical_record":{"source":{"id":"1412.2667","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2014-12-08T17:08:11Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"5c65a9a271bc3d4652209a0458bcd28e48f3fdaabcfc388f9df2b963e15e1f33","abstract_canon_sha256":"9f65a071928820452c749862f7df6fb0c210316cc115d03a1b1dc78d7aa6f749"},"schema_version":"1.0"},"canonical_sha256":"b61eb8f889116707447b77b826e54446715ff13ad3c2fc10e446357ea0bf0011","source":{"kind":"arxiv","id":"1412.2667","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2667","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2667v2","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2667","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"WYPLR6EJCFTQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WYPLR6EJCFTQORD3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WYPLR6EJ","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WYPLR6EJCFTQORD3O64CNZKEIZ","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2667","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2014-12-08T17:08:11Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"5c65a9a271bc3d4652209a0458bcd28e48f3fdaabcfc388f9df2b963e15e1f33","abstract_canon_sha256":"9f65a071928820452c749862f7df6fb0c210316cc115d03a1b1dc78d7aa6f749"},"schema_version":"1.0"},"canonical_sha256":"b61eb8f889116707447b77b826e54446715ff13ad3c2fc10e446357ea0bf0011","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:39.663941Z","signature_b64":"/1Le2cpCQyeUOK1TJ1uegHFHJZrXQ64osTLU1Q9JFLyaJNB3zTv4yoQSFtiYxuDbpdQ+C+iNSV0WiOKFBUcTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b61eb8f889116707447b77b826e54446715ff13ad3c2fc10e446357ea0bf0011","last_reissued_at":"2026-05-18T02:20:39.663200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:39.663200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2667","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dUNjDKFZn8N0346VB88jZOA/RaEUwVoW2vwSUrdzIVsrfzdIriDPUbQ9a2L3ichwrk07hz3uXqlnxX2y7tK2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:50:36.261823Z"},"content_sha256":"b7715696cba6d3f217ab816be972d1020a7be433ac6ca066a9cc6594685585ee","schema_version":"1.0","event_id":"sha256:b7715696cba6d3f217ab816be972d1020a7be433ac6ca066a9cc6594685585ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WYPLR6EJCFTQORD3O64CNZKEIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing Exact Distances in the Congested Clique","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DC","authors_text":"Ami Paz, Keren Censor-Hillel","submitted_at":"2014-12-08T17:08:11Z","abstract_excerpt":"This paper gives simple distributed algorithms for the fundamental problem of computing graph distances in the Congested Clique model. One of the main components of our algorithms is fast matrix multiplication, for which we show an $O(n^{1/3})$-round algorithm when the multiplication needs to be performed over a semi-ring, and an $O(n^{0.157})$-round algorithm when the computation can be performed over a field. We propose to denote by $\\kappa$ the exponent of matrix multiplication in this model, which gives $\\kappa < 0.157$.\n  We show how to compute all-pairs-shortest-paths (APSP) in $O(n^{1/3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2667","kind":"arxiv","version":2},"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":"2026-05-18T02:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+fONCXNW5E2DaS213wEiTMdxpCmhBXZMGoG6F8r/ly/f/EJzNL/l2tZlQLy5jQjB8LJomMjU6z7B0Sedi1mXAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:50:36.262235Z"},"content_sha256":"98ed3ec4f44d333fc09328121b5d12287bfab4a532fcb54ebb1bccbdfe5b76d0","schema_version":"1.0","event_id":"sha256:98ed3ec4f44d333fc09328121b5d12287bfab4a532fcb54ebb1bccbdfe5b76d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYPLR6EJCFTQORD3O64CNZKEIZ/bundle.json","state_url":"https://pith.science/pith/WYPLR6EJCFTQORD3O64CNZKEIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYPLR6EJCFTQORD3O64CNZKEIZ/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":"2026-06-01T02:50:36Z","links":{"resolver":"https://pith.science/pith/WYPLR6EJCFTQORD3O64CNZKEIZ","bundle":"https://pith.science/pith/WYPLR6EJCFTQORD3O64CNZKEIZ/bundle.json","state":"https://pith.science/pith/WYPLR6EJCFTQORD3O64CNZKEIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYPLR6EJCFTQORD3O64CNZKEIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WYPLR6EJCFTQORD3O64CNZKEIZ","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":"9f65a071928820452c749862f7df6fb0c210316cc115d03a1b1dc78d7aa6f749","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2014-12-08T17:08:11Z","title_canon_sha256":"5c65a9a271bc3d4652209a0458bcd28e48f3fdaabcfc388f9df2b963e15e1f33"},"schema_version":"1.0","source":{"id":"1412.2667","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2667","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2667v2","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2667","created_at":"2026-05-18T02:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"WYPLR6EJCFTQ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WYPLR6EJCFTQORD3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WYPLR6EJ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:98ed3ec4f44d333fc09328121b5d12287bfab4a532fcb54ebb1bccbdfe5b76d0","target":"graph","created_at":"2026-05-18T02:20:39Z","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":"This paper gives simple distributed algorithms for the fundamental problem of computing graph distances in the Congested Clique model. One of the main components of our algorithms is fast matrix multiplication, for which we show an $O(n^{1/3})$-round algorithm when the multiplication needs to be performed over a semi-ring, and an $O(n^{0.157})$-round algorithm when the computation can be performed over a field. We propose to denote by $\\kappa$ the exponent of matrix multiplication in this model, which gives $\\kappa < 0.157$.\n  We show how to compute all-pairs-shortest-paths (APSP) in $O(n^{1/3","authors_text":"Ami Paz, Keren Censor-Hillel","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2014-12-08T17:08:11Z","title":"Computing Exact Distances in the Congested Clique"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2667","kind":"arxiv","version":2},"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:b7715696cba6d3f217ab816be972d1020a7be433ac6ca066a9cc6594685585ee","target":"record","created_at":"2026-05-18T02:20:39Z","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":"9f65a071928820452c749862f7df6fb0c210316cc115d03a1b1dc78d7aa6f749","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2014-12-08T17:08:11Z","title_canon_sha256":"5c65a9a271bc3d4652209a0458bcd28e48f3fdaabcfc388f9df2b963e15e1f33"},"schema_version":"1.0","source":{"id":"1412.2667","kind":"arxiv","version":2}},"canonical_sha256":"b61eb8f889116707447b77b826e54446715ff13ad3c2fc10e446357ea0bf0011","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b61eb8f889116707447b77b826e54446715ff13ad3c2fc10e446357ea0bf0011","first_computed_at":"2026-05-18T02:20:39.663200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:39.663200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/1Le2cpCQyeUOK1TJ1uegHFHJZrXQ64osTLU1Q9JFLyaJNB3zTv4yoQSFtiYxuDbpdQ+C+iNSV0WiOKFBUcTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:39.663941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2667","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7715696cba6d3f217ab816be972d1020a7be433ac6ca066a9cc6594685585ee","sha256:98ed3ec4f44d333fc09328121b5d12287bfab4a532fcb54ebb1bccbdfe5b76d0"],"state_sha256":"d0a190a7c5af605eb0bda6ef700f884dc9bb713309aee81baa17ebd8268eb9c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6W9zCNaGSnpc5u43NiyBRODVEFEZ+Rmw6mDBt4jvk0i/4pVM2888XSELeAVgvi3086+5tflNDNXjJmnmVFOAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:50:36.264531Z","bundle_sha256":"8549982452a99555320c0bb589f1d186d4e08dc418ac9d92d3896ee07ce13e84"}}