{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UFPF7ALRHNDTNQ2SX3A2DMAFSQ","short_pith_number":"pith:UFPF7ALR","canonical_record":{"source":{"id":"1101.4372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-01-23T13:44:38Z","cross_cats_sorted":["cs.DC","cs.NI","math.IT"],"title_canon_sha256":"0b47c46c9d1ed661c94bb4b97828a14c27f1bdd54ffc243718568f5258749ccc","abstract_canon_sha256":"3c5650249d97ba0ae4a5975c517dd37ae150fdcf19f879c85eed2a53afc4b4cf"},"schema_version":"1.0"},"canonical_sha256":"a15e5f81713b4736c352bec1a1b00594156ad660aa53ca15d3a00d7092a3eb30","source":{"kind":"arxiv","id":"1101.4372","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4372","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4372v1","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4372","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"pith_short_12","alias_value":"UFPF7ALRHNDT","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UFPF7ALRHNDTNQ2S","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UFPF7ALR","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UFPF7ALRHNDTNQ2SX3A2DMAFSQ","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-01-23T13:44:38Z","cross_cats_sorted":["cs.DC","cs.NI","math.IT"],"title_canon_sha256":"0b47c46c9d1ed661c94bb4b97828a14c27f1bdd54ffc243718568f5258749ccc","abstract_canon_sha256":"3c5650249d97ba0ae4a5975c517dd37ae150fdcf19f879c85eed2a53afc4b4cf"},"schema_version":"1.0"},"canonical_sha256":"a15e5f81713b4736c352bec1a1b00594156ad660aa53ca15d3a00d7092a3eb30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:11.151769Z","signature_b64":"lRcpX6ZbDxEmrB1rvuAQwI3jv3o0GtkK+6nBrcteH4/Z5lGYT19Q+ood3oQIQq45zVqjaWdcECOzYje9pWO5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a15e5f81713b4736c352bec1a1b00594156ad660aa53ca15d3a00d7092a3eb30","last_reissued_at":"2026-05-18T04:31:11.151301Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:11.151301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4372","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":"2026-05-18T04:31:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UiSzIzc0fHvpjHwBCqxZef2zeruIUVXrtxpFJ6E2otZKOHFERxsxdrJjRrvCa6btBjnrh10KLr4Vo2m5U2FCBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:16:28.265810Z"},"content_sha256":"3700845f6c532b98c9133153f61877d7d2e3cd2f4c34912010051da5108a4799","schema_version":"1.0","event_id":"sha256:3700845f6c532b98c9133153f61877d7d2e3cd2f4c34912010051da5108a4799"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UFPF7ALRHNDTNQ2SX3A2DMAFSQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order Optimal Information Spreading Using Algebraic Gossip","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.NI","math.IT"],"primary_cat":"cs.IT","authors_text":"Chen Avin, Keren Censor-Hillel, Michael Borokhovich, Zvi Lotker","submitted_at":"2011-01-23T13:44:38Z","abstract_excerpt":"In this paper we study gossip based information spreading with bounded message sizes. We use algebraic gossip to disseminate $k$ distinct messages to all $n$ nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of $O((k+\\log n + D)\\Delta)$ rounds with high probability, where $D$ and $\\Delta$ are the diameter and the maximum degree in the network, respectively. For many topologies and selections of $k$ this bound improves previous results, in particular, for graphs with a constant maximum degree it implies that uniform gossip is \\emph{order optima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4372","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":"2026-05-18T04:31:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kN7V0KgiKBWOy4ZxFYN2mxA8zr5GuFsF7nfMn1V7XwNxs/emfEEpY3lrzC5ezHUt65DRWpH4T/6jSjEMxTtnAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:16:28.266394Z"},"content_sha256":"28680fe3904b1c488cd54f2e15a8c3bb9af09b9da5d981909573e94c96bf5425","schema_version":"1.0","event_id":"sha256:28680fe3904b1c488cd54f2e15a8c3bb9af09b9da5d981909573e94c96bf5425"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UFPF7ALRHNDTNQ2SX3A2DMAFSQ/bundle.json","state_url":"https://pith.science/pith/UFPF7ALRHNDTNQ2SX3A2DMAFSQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UFPF7ALRHNDTNQ2SX3A2DMAFSQ/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":"2026-05-25T14:16:28Z","links":{"resolver":"https://pith.science/pith/UFPF7ALRHNDTNQ2SX3A2DMAFSQ","bundle":"https://pith.science/pith/UFPF7ALRHNDTNQ2SX3A2DMAFSQ/bundle.json","state":"https://pith.science/pith/UFPF7ALRHNDTNQ2SX3A2DMAFSQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UFPF7ALRHNDTNQ2SX3A2DMAFSQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UFPF7ALRHNDTNQ2SX3A2DMAFSQ","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":"3c5650249d97ba0ae4a5975c517dd37ae150fdcf19f879c85eed2a53afc4b4cf","cross_cats_sorted":["cs.DC","cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-01-23T13:44:38Z","title_canon_sha256":"0b47c46c9d1ed661c94bb4b97828a14c27f1bdd54ffc243718568f5258749ccc"},"schema_version":"1.0","source":{"id":"1101.4372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4372","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4372v1","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4372","created_at":"2026-05-18T04:31:11Z"},{"alias_kind":"pith_short_12","alias_value":"UFPF7ALRHNDT","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UFPF7ALRHNDTNQ2S","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UFPF7ALR","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:28680fe3904b1c488cd54f2e15a8c3bb9af09b9da5d981909573e94c96bf5425","target":"graph","created_at":"2026-05-18T04:31:11Z","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":"In this paper we study gossip based information spreading with bounded message sizes. We use algebraic gossip to disseminate $k$ distinct messages to all $n$ nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of $O((k+\\log n + D)\\Delta)$ rounds with high probability, where $D$ and $\\Delta$ are the diameter and the maximum degree in the network, respectively. For many topologies and selections of $k$ this bound improves previous results, in particular, for graphs with a constant maximum degree it implies that uniform gossip is \\emph{order optima","authors_text":"Chen Avin, Keren Censor-Hillel, Michael Borokhovich, Zvi Lotker","cross_cats":["cs.DC","cs.NI","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-01-23T13:44:38Z","title":"Order Optimal Information Spreading Using Algebraic Gossip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4372","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":"sha256:3700845f6c532b98c9133153f61877d7d2e3cd2f4c34912010051da5108a4799","target":"record","created_at":"2026-05-18T04:31:11Z","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":"3c5650249d97ba0ae4a5975c517dd37ae150fdcf19f879c85eed2a53afc4b4cf","cross_cats_sorted":["cs.DC","cs.NI","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-01-23T13:44:38Z","title_canon_sha256":"0b47c46c9d1ed661c94bb4b97828a14c27f1bdd54ffc243718568f5258749ccc"},"schema_version":"1.0","source":{"id":"1101.4372","kind":"arxiv","version":1}},"canonical_sha256":"a15e5f81713b4736c352bec1a1b00594156ad660aa53ca15d3a00d7092a3eb30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a15e5f81713b4736c352bec1a1b00594156ad660aa53ca15d3a00d7092a3eb30","first_computed_at":"2026-05-18T04:31:11.151301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:11.151301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lRcpX6ZbDxEmrB1rvuAQwI3jv3o0GtkK+6nBrcteH4/Z5lGYT19Q+ood3oQIQq45zVqjaWdcECOzYje9pWO5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:11.151769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3700845f6c532b98c9133153f61877d7d2e3cd2f4c34912010051da5108a4799","sha256:28680fe3904b1c488cd54f2e15a8c3bb9af09b9da5d981909573e94c96bf5425"],"state_sha256":"dd1cc675ac8815e59a1effe49f7cc38ad22451843337dbdabce2053460630b92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NMNQf+DOfa4nv+zjvWYG+xlcmNfp0V64nfPQnxMVgoCCHHSEpWq457Q2PU5AN3zenwVkG7CqgVscsztJ5vsODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:16:28.269828Z","bundle_sha256":"f64f3b334b4c72ae1b7acf9134bd7ad2c3c5ec2bed5c214ffada756981293320"}}