{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:II2KLQAUXK7QAWUBJS5GFK27JX","short_pith_number":"pith:II2KLQAU","canonical_record":{"source":{"id":"1701.02653","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T15:59:27Z","cross_cats_sorted":[],"title_canon_sha256":"c1b1e05de3f9fb7d81db6139650b88930d0c4c27d4b1351f7efe90fecc07da2f","abstract_canon_sha256":"cbb131eefa469e7637dfa66af9661314ee2b39e3943c77437859840ba770f01a"},"schema_version":"1.0"},"canonical_sha256":"4234a5c014babf005a814cba62ab5f4ddcbf17da3cd9180a3210169c3f03a049","source":{"kind":"arxiv","id":"1701.02653","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02653","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02653v3","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02653","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"II2KLQAUXK7Q","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"II2KLQAUXK7QAWUB","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"II2KLQAU","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:II2KLQAUXK7QAWUBJS5GFK27JX","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02653","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T15:59:27Z","cross_cats_sorted":[],"title_canon_sha256":"c1b1e05de3f9fb7d81db6139650b88930d0c4c27d4b1351f7efe90fecc07da2f","abstract_canon_sha256":"cbb131eefa469e7637dfa66af9661314ee2b39e3943c77437859840ba770f01a"},"schema_version":"1.0"},"canonical_sha256":"4234a5c014babf005a814cba62ab5f4ddcbf17da3cd9180a3210169c3f03a049","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:14.162205Z","signature_b64":"ZD6g7lVIjIuAng1BlFA8mViCB7c4a1DfVsVSPP2db/xZVoqmEoVizcN7EccX/WPcuoXmEgycpAP/0kaKmdoUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4234a5c014babf005a814cba62ab5f4ddcbf17da3cd9180a3210169c3f03a049","last_reissued_at":"2026-05-18T00:19:14.161440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:14.161440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02653","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NZGmf496aKpW2/t6xZfD8uQ/XFvDu11AuMlh9QrgPe+xNh24OW9s2C3uDJUZCGeigRmsewmSKVwi+nA6+IT7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:34:05.758782Z"},"content_sha256":"c56baaf21dc8e6ceec6d81b646f8f79087f0c8b8f282a16f08b5d7647c4d34aa","schema_version":"1.0","event_id":"sha256:c56baaf21dc8e6ceec6d81b646f8f79087f0c8b8f282a16f08b5d7647c4d34aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:II2KLQAUXK7QAWUBJS5GFK27JX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coalescing random walk on unimodular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Foxall, Matthew Junge, Tom Hutchcroft","submitted_at":"2017-01-10T15:59:27Z","abstract_excerpt":"Coalescing random walk on a unimodular random rooted graph for which the root has finite expected degree visits each site infinitely often almost surely. A corollary is that an opinion in the voter model on such graphs has infinite expected lifetime. Additionally, we deduce an adaptation of our main theorem that holds uniformly for coalescing random walk on finite random unimodular graphs with degree distribution stochastically dominated by a probability measure with finite mean."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02653","kind":"arxiv","version":3},"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":"2026-05-18T00:19:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f8wej76r/NdbbpJEKIppEm4tspGe32ajUurk4+xgv0MXALpLuPaVD5PEB1h+ea4eAn8KGSl0uT6AO6rqfzjbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:34:05.759132Z"},"content_sha256":"4495539546ee67109ab13e98ddf30d481cb2ae17c748a3118c4fa62a48c0af20","schema_version":"1.0","event_id":"sha256:4495539546ee67109ab13e98ddf30d481cb2ae17c748a3118c4fa62a48c0af20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/II2KLQAUXK7QAWUBJS5GFK27JX/bundle.json","state_url":"https://pith.science/pith/II2KLQAUXK7QAWUBJS5GFK27JX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/II2KLQAUXK7QAWUBJS5GFK27JX/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":"2026-05-22T18:34:05Z","links":{"resolver":"https://pith.science/pith/II2KLQAUXK7QAWUBJS5GFK27JX","bundle":"https://pith.science/pith/II2KLQAUXK7QAWUBJS5GFK27JX/bundle.json","state":"https://pith.science/pith/II2KLQAUXK7QAWUBJS5GFK27JX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/II2KLQAUXK7QAWUBJS5GFK27JX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:II2KLQAUXK7QAWUBJS5GFK27JX","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":"cbb131eefa469e7637dfa66af9661314ee2b39e3943c77437859840ba770f01a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T15:59:27Z","title_canon_sha256":"c1b1e05de3f9fb7d81db6139650b88930d0c4c27d4b1351f7efe90fecc07da2f"},"schema_version":"1.0","source":{"id":"1701.02653","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02653","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02653v3","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02653","created_at":"2026-05-18T00:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"II2KLQAUXK7Q","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"II2KLQAUXK7QAWUB","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"II2KLQAU","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:4495539546ee67109ab13e98ddf30d481cb2ae17c748a3118c4fa62a48c0af20","target":"graph","created_at":"2026-05-18T00:19:14Z","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":"Coalescing random walk on a unimodular random rooted graph for which the root has finite expected degree visits each site infinitely often almost surely. A corollary is that an opinion in the voter model on such graphs has infinite expected lifetime. Additionally, we deduce an adaptation of our main theorem that holds uniformly for coalescing random walk on finite random unimodular graphs with degree distribution stochastically dominated by a probability measure with finite mean.","authors_text":"Eric Foxall, Matthew Junge, Tom Hutchcroft","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T15:59:27Z","title":"Coalescing random walk on unimodular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02653","kind":"arxiv","version":3},"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:c56baaf21dc8e6ceec6d81b646f8f79087f0c8b8f282a16f08b5d7647c4d34aa","target":"record","created_at":"2026-05-18T00:19:14Z","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":"cbb131eefa469e7637dfa66af9661314ee2b39e3943c77437859840ba770f01a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T15:59:27Z","title_canon_sha256":"c1b1e05de3f9fb7d81db6139650b88930d0c4c27d4b1351f7efe90fecc07da2f"},"schema_version":"1.0","source":{"id":"1701.02653","kind":"arxiv","version":3}},"canonical_sha256":"4234a5c014babf005a814cba62ab5f4ddcbf17da3cd9180a3210169c3f03a049","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4234a5c014babf005a814cba62ab5f4ddcbf17da3cd9180a3210169c3f03a049","first_computed_at":"2026-05-18T00:19:14.161440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:14.161440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZD6g7lVIjIuAng1BlFA8mViCB7c4a1DfVsVSPP2db/xZVoqmEoVizcN7EccX/WPcuoXmEgycpAP/0kaKmdoUAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:14.162205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02653","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c56baaf21dc8e6ceec6d81b646f8f79087f0c8b8f282a16f08b5d7647c4d34aa","sha256:4495539546ee67109ab13e98ddf30d481cb2ae17c748a3118c4fa62a48c0af20"],"state_sha256":"f01116e66b9ef03c4e1ddfb45fe57eb884df072547918b3b334611c17a003d36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stNaWDJlA5nPYrEzXetrnyJv55cgalorlml8YgGs9eBq/5dmf8V2OTI385XTfRWzz4aCjN3LuSzOJEGVI4uSCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T18:34:05.761113Z","bundle_sha256":"9d644c79dcd866e6fffbcf91f7775f854881fd247a3c77b78024fa86be72837d"}}