{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:R7PDW6GLRVPXC43WYH66MHCJJP","short_pith_number":"pith:R7PDW6GL","schema_version":"1.0","canonical_sha256":"8fde3b78cb8d5f717376c1fde61c494bc15b8b7e82f847cc59d3921ad728314e","source":{"kind":"arxiv","id":"2606.06381","version":1},"attestation_state":"computed","paper":{"title":"Discrete Incremental Voting: New Bounds for General Graphs and Expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Colin Cooper, Lukas Hintze, Petra Berenbrink, Thorsten G\\\"otte, Tomasz Radzik","submitted_at":"2026-06-04T16:47:45Z","abstract_excerpt":"We analyze the discrete incremental voting process (DIV) introduced by Cooper, Radzik, and Shiraga [OPODIS '23]. In this process, we consider a set $V$ of $n$ nodes connected in an undirected graph $G = (V, E)$ where each node has an integer opinion. In one step a randomly selected node interacts with its randomly selected neighbor and changes its opinion by $1$ in the direction of the neighbour's opinion. The process converges to a unique opinion that, in expectation, is the degree-weighted average of the initial opinions.\n  We show that if the graph has conductance $\\Phi(G)$, the ratio of th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.06381","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2026-06-04T16:47:45Z","cross_cats_sorted":[],"title_canon_sha256":"06ba8661c3025b5a2d951a884c324908596b680f7d939e6f881d8847182d14e3","abstract_canon_sha256":"ae5d06c6fe5372ae54236c1c33817b240c1e4fac5fb874bf4ee374e75e0dec16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:43.888276Z","signature_b64":"CAFm/HROSlPsAReKTq2onBEVkJ5FqB26D8uh4Sj3xMW6InIw02Kps/rUJsUaiYMRuUXo8XAV7cTPMkaCbAd6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fde3b78cb8d5f717376c1fde61c494bc15b8b7e82f847cc59d3921ad728314e","last_reissued_at":"2026-06-05T01:15:43.887869Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:43.887869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete Incremental Voting: New Bounds for General Graphs and Expanders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DC","authors_text":"Colin Cooper, Lukas Hintze, Petra Berenbrink, Thorsten G\\\"otte, Tomasz Radzik","submitted_at":"2026-06-04T16:47:45Z","abstract_excerpt":"We analyze the discrete incremental voting process (DIV) introduced by Cooper, Radzik, and Shiraga [OPODIS '23]. In this process, we consider a set $V$ of $n$ nodes connected in an undirected graph $G = (V, E)$ where each node has an integer opinion. In one step a randomly selected node interacts with its randomly selected neighbor and changes its opinion by $1$ in the direction of the neighbour's opinion. The process converges to a unique opinion that, in expectation, is the degree-weighted average of the initial opinions.\n  We show that if the graph has conductance $\\Phi(G)$, the ratio of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06381","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06381/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.06381","created_at":"2026-06-05T01:15:43.887933+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06381v1","created_at":"2026-06-05T01:15:43.887933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06381","created_at":"2026-06-05T01:15:43.887933+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7PDW6GLRVPX","created_at":"2026-06-05T01:15:43.887933+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7PDW6GLRVPXC43W","created_at":"2026-06-05T01:15:43.887933+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7PDW6GL","created_at":"2026-06-05T01:15:43.887933+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP","json":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP.json","graph_json":"https://pith.science/api/pith-number/R7PDW6GLRVPXC43WYH66MHCJJP/graph.json","events_json":"https://pith.science/api/pith-number/R7PDW6GLRVPXC43WYH66MHCJJP/events.json","paper":"https://pith.science/paper/R7PDW6GL"},"agent_actions":{"view_html":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP","download_json":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP.json","view_paper":"https://pith.science/paper/R7PDW6GL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06381&json=true","fetch_graph":"https://pith.science/api/pith-number/R7PDW6GLRVPXC43WYH66MHCJJP/graph.json","fetch_events":"https://pith.science/api/pith-number/R7PDW6GLRVPXC43WYH66MHCJJP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP/action/storage_attestation","attest_author":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP/action/author_attestation","sign_citation":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP/action/citation_signature","submit_replication":"https://pith.science/pith/R7PDW6GLRVPXC43WYH66MHCJJP/action/replication_record"}},"created_at":"2026-06-05T01:15:43.887933+00:00","updated_at":"2026-06-05T01:15:43.887933+00:00"}