{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CCLNVFHLEOOCXRYE5MPNAIJLPN","short_pith_number":"pith:CCLNVFHL","canonical_record":{"source":{"id":"1608.01766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-08-05T05:36:45Z","cross_cats_sorted":["cond-mat.dis-nn","cs.SI"],"title_canon_sha256":"b0a1e6fc207ed99bd2b97fd707b355905943dc8a275230d1371585863578e43c","abstract_canon_sha256":"ee46d665aee6cbff1fa9321f35119c681b069271690651f13696140eb3e2ea1b"},"schema_version":"1.0"},"canonical_sha256":"1096da94eb239c2bc704eb1ed0212b7b7717039e382d269d10ad052829b77057","source":{"kind":"arxiv","id":"1608.01766","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01766","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01766v1","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01766","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"CCLNVFHLEOOC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CCLNVFHLEOOCXRYE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CCLNVFHL","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CCLNVFHLEOOCXRYE5MPNAIJLPN","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-08-05T05:36:45Z","cross_cats_sorted":["cond-mat.dis-nn","cs.SI"],"title_canon_sha256":"b0a1e6fc207ed99bd2b97fd707b355905943dc8a275230d1371585863578e43c","abstract_canon_sha256":"ee46d665aee6cbff1fa9321f35119c681b069271690651f13696140eb3e2ea1b"},"schema_version":"1.0"},"canonical_sha256":"1096da94eb239c2bc704eb1ed0212b7b7717039e382d269d10ad052829b77057","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:44.652796Z","signature_b64":"s8mCRI4u81mQ0HIJ5jENhD7QUGLBWZHC4+o96CpsOUBrUkwzheXRgsou2fcMM+z//JLom+XCwbWNFUEdTYQgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1096da94eb239c2bc704eb1ed0212b7b7717039e382d269d10ad052829b77057","last_reissued_at":"2026-05-18T01:09:44.652263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:44.652263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01766","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":"2026-05-18T01:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F/fXmX1B4IFlTtUv4vAfqXp2FCKtucjrDc4R3EXUg5jpZjCMuKPTOyvlmwFy/1t9cKhztHv9qAqSFm7swnF1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:55:13.216568Z"},"content_sha256":"8533fbcf43ebf19ffe9f315fb5cc5bc93d30dd2a28bae15f27b6ce6888bea45c","schema_version":"1.0","event_id":"sha256:8533fbcf43ebf19ffe9f315fb5cc5bc93d30dd2a28bae15f27b6ce6888bea45c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CCLNVFHLEOOCXRYE5MPNAIJLPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asynchronous Rumor Spreading on Random Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Konstantinos Panagiotou, Leo Speidel","submitted_at":"2016-08-05T05:36:45Z","abstract_excerpt":"We perform a thorough study of various characteristics of the asynchronous push-pull protocol for spreading a rumor on Erd\\H{o}s-R\\'enyi random graphs $G_{n,p}$, for any $p>c\\ln(n)/n$ with $c>1$. In particular, we provide a simple strategy for analyzing the asynchronous push-pull protocol on arbitrary graph topologies and apply this strategy to $G_{n,p}$. We prove tight bounds of logarithmic order for the total time that is needed until the information has spread to all nodes. Surprisingly, the time required by the asynchronous push-pull protocol is asymptotically almost unaffected by the aver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01766","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":""},"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":"2026-05-18T01:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lMl3XAqDtz1o2dYj5gogkek9sszwUIB5t5YOyfx6JtNF+aZkGZMtBKe5LReLqYxiiRJ48nttzYhH6Tl46E1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:55:13.216941Z"},"content_sha256":"2c3c99005df44472ccb1b55c148011c4dfaefdefd05529237de642cb9920b4d4","schema_version":"1.0","event_id":"sha256:2c3c99005df44472ccb1b55c148011c4dfaefdefd05529237de642cb9920b4d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CCLNVFHLEOOCXRYE5MPNAIJLPN/bundle.json","state_url":"https://pith.science/pith/CCLNVFHLEOOCXRYE5MPNAIJLPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CCLNVFHLEOOCXRYE5MPNAIJLPN/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":"2026-06-06T18:55:13Z","links":{"resolver":"https://pith.science/pith/CCLNVFHLEOOCXRYE5MPNAIJLPN","bundle":"https://pith.science/pith/CCLNVFHLEOOCXRYE5MPNAIJLPN/bundle.json","state":"https://pith.science/pith/CCLNVFHLEOOCXRYE5MPNAIJLPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CCLNVFHLEOOCXRYE5MPNAIJLPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CCLNVFHLEOOCXRYE5MPNAIJLPN","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":"ee46d665aee6cbff1fa9321f35119c681b069271690651f13696140eb3e2ea1b","cross_cats_sorted":["cond-mat.dis-nn","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-08-05T05:36:45Z","title_canon_sha256":"b0a1e6fc207ed99bd2b97fd707b355905943dc8a275230d1371585863578e43c"},"schema_version":"1.0","source":{"id":"1608.01766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01766","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01766v1","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01766","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"CCLNVFHLEOOC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CCLNVFHLEOOCXRYE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CCLNVFHL","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:2c3c99005df44472ccb1b55c148011c4dfaefdefd05529237de642cb9920b4d4","target":"graph","created_at":"2026-05-18T01:09:44Z","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 perform a thorough study of various characteristics of the asynchronous push-pull protocol for spreading a rumor on Erd\\H{o}s-R\\'enyi random graphs $G_{n,p}$, for any $p>c\\ln(n)/n$ with $c>1$. In particular, we provide a simple strategy for analyzing the asynchronous push-pull protocol on arbitrary graph topologies and apply this strategy to $G_{n,p}$. We prove tight bounds of logarithmic order for the total time that is needed until the information has spread to all nodes. Surprisingly, the time required by the asynchronous push-pull protocol is asymptotically almost unaffected by the aver","authors_text":"Konstantinos Panagiotou, Leo Speidel","cross_cats":["cond-mat.dis-nn","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-08-05T05:36:45Z","title":"Asynchronous Rumor Spreading on Random Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01766","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":"sha256:8533fbcf43ebf19ffe9f315fb5cc5bc93d30dd2a28bae15f27b6ce6888bea45c","target":"record","created_at":"2026-05-18T01:09:44Z","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":"ee46d665aee6cbff1fa9321f35119c681b069271690651f13696140eb3e2ea1b","cross_cats_sorted":["cond-mat.dis-nn","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2016-08-05T05:36:45Z","title_canon_sha256":"b0a1e6fc207ed99bd2b97fd707b355905943dc8a275230d1371585863578e43c"},"schema_version":"1.0","source":{"id":"1608.01766","kind":"arxiv","version":1}},"canonical_sha256":"1096da94eb239c2bc704eb1ed0212b7b7717039e382d269d10ad052829b77057","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1096da94eb239c2bc704eb1ed0212b7b7717039e382d269d10ad052829b77057","first_computed_at":"2026-05-18T01:09:44.652263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:44.652263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s8mCRI4u81mQ0HIJ5jENhD7QUGLBWZHC4+o96CpsOUBrUkwzheXRgsou2fcMM+z//JLom+XCwbWNFUEdTYQgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:44.652796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8533fbcf43ebf19ffe9f315fb5cc5bc93d30dd2a28bae15f27b6ce6888bea45c","sha256:2c3c99005df44472ccb1b55c148011c4dfaefdefd05529237de642cb9920b4d4"],"state_sha256":"be3f687702b9dccaf910c71347ba69de38870f4feaf86497224e119a48f06f71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DZTlRlC5Nq1x94NVXib5w8YeUeycUcMsqfKOMehtrhw1V6vdSJpMnuvXRhW9igkCfOTvpTE2Q3yLdkya8W87BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:55:13.219177Z","bundle_sha256":"1f5fa292c6c1178da44cea78004980ce312feb44c5520aa61c6950d867e8a514"}}