{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:CYMSU4ZLSSU5X2VZIDSJOWR5IZ","short_pith_number":"pith:CYMSU4ZL","schema_version":"1.0","canonical_sha256":"16192a732b94a9dbeab940e4975a3d466a1ff3ee045be9cf1cec36487195eac3","source":{"kind":"arxiv","id":"2009.13951","version":1},"attestation_state":"computed","paper":{"title":"Collisions of Random Walks in Dynamic Random Environments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Noah Halberstam, Tom Hutchcroft","submitted_at":"2020-09-29T12:14:50Z","abstract_excerpt":"We study dynamic random conductance models on $\\mathbb{Z}^2$ in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove under a second moment assumption that two conditionally independent random walks in the same environment collide infinitely often almost surely. These results apply in particular to random walks on dynamical percolation."},"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":"2009.13951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-09-29T12:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"efab708fac122418074794f11f135057a93dcdf651de8fd599f77626d4c8caf7","abstract_canon_sha256":"5242c111f4b781f341d8f28740d679621f40909f5d1b6aadf0bb46e02c60ee57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:38:46.748262Z","signature_b64":"wjBpoHfHj7ncgK9TJH70gcLHVU95xHo59kEzxteAMHZO929Nnl3TvLx9luFY0zaE+nGGsUenpHy2x9o8PLxSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16192a732b94a9dbeab940e4975a3d466a1ff3ee045be9cf1cec36487195eac3","last_reissued_at":"2026-07-05T01:38:46.747871Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:38:46.747871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Collisions of Random Walks in Dynamic Random Environments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Noah Halberstam, Tom Hutchcroft","submitted_at":"2020-09-29T12:14:50Z","abstract_excerpt":"We study dynamic random conductance models on $\\mathbb{Z}^2$ in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove under a second moment assumption that two conditionally independent random walks in the same environment collide infinitely often almost surely. These results apply in particular to random walks on dynamical percolation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.13951","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/2009.13951/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":"2009.13951","created_at":"2026-07-05T01:38:46.747932+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.13951v1","created_at":"2026-07-05T01:38:46.747932+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.13951","created_at":"2026-07-05T01:38:46.747932+00:00"},{"alias_kind":"pith_short_12","alias_value":"CYMSU4ZLSSU5","created_at":"2026-07-05T01:38:46.747932+00:00"},{"alias_kind":"pith_short_16","alias_value":"CYMSU4ZLSSU5X2VZ","created_at":"2026-07-05T01:38:46.747932+00:00"},{"alias_kind":"pith_short_8","alias_value":"CYMSU4ZL","created_at":"2026-07-05T01:38:46.747932+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/CYMSU4ZLSSU5X2VZIDSJOWR5IZ","json":"https://pith.science/pith/CYMSU4ZLSSU5X2VZIDSJOWR5IZ.json","graph_json":"https://pith.science/api/pith-number/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/graph.json","events_json":"https://pith.science/api/pith-number/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/events.json","paper":"https://pith.science/paper/CYMSU4ZL"},"agent_actions":{"view_html":"https://pith.science/pith/CYMSU4ZLSSU5X2VZIDSJOWR5IZ","download_json":"https://pith.science/pith/CYMSU4ZLSSU5X2VZIDSJOWR5IZ.json","view_paper":"https://pith.science/paper/CYMSU4ZL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.13951&json=true","fetch_graph":"https://pith.science/api/pith-number/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/action/storage_attestation","attest_author":"https://pith.science/pith/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/action/author_attestation","sign_citation":"https://pith.science/pith/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/action/citation_signature","submit_replication":"https://pith.science/pith/CYMSU4ZLSSU5X2VZIDSJOWR5IZ/action/replication_record"}},"created_at":"2026-07-05T01:38:46.747932+00:00","updated_at":"2026-07-05T01:38:46.747932+00:00"}