{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EK77CZNZPEKPAABZHVCVE5JAK4","short_pith_number":"pith:EK77CZNZ","canonical_record":{"source":{"id":"1608.03313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-08-10T23:57:44Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"d358856637d500edb21ed7803cef199e89b0722dcc0777e44e747212e0b2883d","abstract_canon_sha256":"69d3c661a696b1ea9741971b4c66534f7ab033d0fc024f0f0c7051139cf8d466"},"schema_version":"1.0"},"canonical_sha256":"22bff165b97914f000393d45527520572fe82a966a33bd066f52bd721392096e","source":{"kind":"arxiv","id":"1608.03313","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03313","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03313v2","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03313","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"pith_short_12","alias_value":"EK77CZNZPEKP","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EK77CZNZPEKPAABZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EK77CZNZ","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EK77CZNZPEKPAABZHVCVE5JAK4","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03313","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-08-10T23:57:44Z","cross_cats_sorted":["cs.DC"],"title_canon_sha256":"d358856637d500edb21ed7803cef199e89b0722dcc0777e44e747212e0b2883d","abstract_canon_sha256":"69d3c661a696b1ea9741971b4c66534f7ab033d0fc024f0f0c7051139cf8d466"},"schema_version":"1.0"},"canonical_sha256":"22bff165b97914f000393d45527520572fe82a966a33bd066f52bd721392096e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:45.087641Z","signature_b64":"NQ3KldGNZIU29wewWk8YjqTZ5vBRBuXxYaLw9uy3yMozPUs2ix8Y6T1Z9NL64gjb/LVSUKa1WPx5hO2pEECGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22bff165b97914f000393d45527520572fe82a966a33bd066f52bd721392096e","last_reissued_at":"2026-05-18T01:00:45.087205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:45.087205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03313","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":"2026-05-18T01:00:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"009ZeS23GCgvD3ezxTMnYHN10OEo8w/W49E3YcIT3goLR0HdY8L834Lw7aS3gu6NwvnUjQ2ZGJSNu7tEBR+kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:20:12.547990Z"},"content_sha256":"f74975b3860c518c02f34902765ee32d1a2d9ccea177f9a149850d1de1626921","schema_version":"1.0","event_id":"sha256:f74975b3860c518c02f34902765ee32d1a2d9ccea177f9a149850d1de1626921"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EK77CZNZPEKPAABZHVCVE5JAK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight Network Topology Dependent Bounds on Rounds of Communication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC"],"primary_cat":"cs.CC","authors_text":"Arkadev Chattopadhyay, Atri Rudra, Michael Langberg, Shi Li","submitted_at":"2016-08-10T23:57:44Z","abstract_excerpt":"We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we fix the function and then vary the underlying network topology. This complements the recent such results on total communication that have received some attention. We also present some applications to distributed graph computation problems.\n  Our main contribution is a proof technique that allows us to reduce the problem on a general graph topology to a rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03313","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":"2026-05-18T01:00:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IrTPOQMbaWvcTWiYDSbkHwM4rZe+AgdwYkZEL4V3dCji/Y5RQLQjlEE3INNqRscLzSPwDg5nj6KILQgUxiO2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:20:12.548355Z"},"content_sha256":"948fec4d66ddf82a864ed65530c737e35f96b3c2c686367b2f023525e63894d5","schema_version":"1.0","event_id":"sha256:948fec4d66ddf82a864ed65530c737e35f96b3c2c686367b2f023525e63894d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EK77CZNZPEKPAABZHVCVE5JAK4/bundle.json","state_url":"https://pith.science/pith/EK77CZNZPEKPAABZHVCVE5JAK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EK77CZNZPEKPAABZHVCVE5JAK4/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":"2026-06-22T22:20:12Z","links":{"resolver":"https://pith.science/pith/EK77CZNZPEKPAABZHVCVE5JAK4","bundle":"https://pith.science/pith/EK77CZNZPEKPAABZHVCVE5JAK4/bundle.json","state":"https://pith.science/pith/EK77CZNZPEKPAABZHVCVE5JAK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EK77CZNZPEKPAABZHVCVE5JAK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EK77CZNZPEKPAABZHVCVE5JAK4","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":"69d3c661a696b1ea9741971b4c66534f7ab033d0fc024f0f0c7051139cf8d466","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-08-10T23:57:44Z","title_canon_sha256":"d358856637d500edb21ed7803cef199e89b0722dcc0777e44e747212e0b2883d"},"schema_version":"1.0","source":{"id":"1608.03313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03313","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03313v2","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03313","created_at":"2026-05-18T01:00:45Z"},{"alias_kind":"pith_short_12","alias_value":"EK77CZNZPEKP","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EK77CZNZPEKPAABZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EK77CZNZ","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:948fec4d66ddf82a864ed65530c737e35f96b3c2c686367b2f023525e63894d5","target":"graph","created_at":"2026-05-18T01:00:45Z","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 prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing, we fix the function and then vary the underlying network topology. This complements the recent such results on total communication that have received some attention. We also present some applications to distributed graph computation problems.\n  Our main contribution is a proof technique that allows us to reduce the problem on a general graph topology to a rel","authors_text":"Arkadev Chattopadhyay, Atri Rudra, Michael Langberg, Shi Li","cross_cats":["cs.DC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-08-10T23:57:44Z","title":"Tight Network Topology Dependent Bounds on Rounds of Communication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03313","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:f74975b3860c518c02f34902765ee32d1a2d9ccea177f9a149850d1de1626921","target":"record","created_at":"2026-05-18T01:00:45Z","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":"69d3c661a696b1ea9741971b4c66534f7ab033d0fc024f0f0c7051139cf8d466","cross_cats_sorted":["cs.DC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-08-10T23:57:44Z","title_canon_sha256":"d358856637d500edb21ed7803cef199e89b0722dcc0777e44e747212e0b2883d"},"schema_version":"1.0","source":{"id":"1608.03313","kind":"arxiv","version":2}},"canonical_sha256":"22bff165b97914f000393d45527520572fe82a966a33bd066f52bd721392096e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22bff165b97914f000393d45527520572fe82a966a33bd066f52bd721392096e","first_computed_at":"2026-05-18T01:00:45.087205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:45.087205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NQ3KldGNZIU29wewWk8YjqTZ5vBRBuXxYaLw9uy3yMozPUs2ix8Y6T1Z9NL64gjb/LVSUKa1WPx5hO2pEECGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:45.087641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f74975b3860c518c02f34902765ee32d1a2d9ccea177f9a149850d1de1626921","sha256:948fec4d66ddf82a864ed65530c737e35f96b3c2c686367b2f023525e63894d5"],"state_sha256":"2ec85cdc4204bb4a186351bd92133f2c5a5afb6c08570105459d114b37c0bf54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygPcXYCUo8X+GiTljOLF0SkvDw9pFoSMxcDpI5mVAWmjJamIzgZmxB4wQPYFRxCb3UNur46EMx024ltJ2tmlDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:20:12.550307Z","bundle_sha256":"e8d872ff134c3998c7286d1f5522cf58863272c21f6990a0d154a79f8cef3767"}}