{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:H5S4Q3BHME22VKYNB3IZWBRSXZ","short_pith_number":"pith:H5S4Q3BH","schema_version":"1.0","canonical_sha256":"3f65c86c276135aaab0d0ed19b0632be59ee26a8df7370c5ad38da0ee72a9463","source":{"kind":"arxiv","id":"1011.3895","version":2},"attestation_state":"computed","paper":{"title":"Stochastic flows in the Brownian web and net","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Schertzer, Jan M. Swart, Rongfeng Sun","submitted_at":"2010-11-17T06:37:13Z","abstract_excerpt":"Certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments are known to have diffusive scaling limits. In the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was introduced by Le Jan and Raimond, who showed that each such flow is characterized by its n-point motions. We focus on a class of stochastic flows of kernels with Brownia"},"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":"1011.3895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-17T06:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"78bbe13b02e8282f4031da6ece9df61a77438a21906b2b9934d63b9f50912fd9","abstract_canon_sha256":"0a8fa4555e7456fca98c555d66e5a59221ac0b885f062db7d4d82ca858cd9b41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:42.176650Z","signature_b64":"0qIbrmag6Fvn1xCLD2+rQb2fcHMDyX4C0sxmkyetngGUmU8j3J6LCFM8XfkMNQrLXoBC1ssCAMyIxjHyFrpCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f65c86c276135aaab0d0ed19b0632be59ee26a8df7370c5ad38da0ee72a9463","last_reissued_at":"2026-05-18T03:24:42.175483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:42.175483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic flows in the Brownian web and net","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Schertzer, Jan M. Swart, Rongfeng Sun","submitted_at":"2010-11-17T06:37:13Z","abstract_excerpt":"Certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments are known to have diffusive scaling limits. In the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was introduced by Le Jan and Raimond, who showed that each such flow is characterized by its n-point motions. We focus on a class of stochastic flows of kernels with Brownia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3895","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.3895","created_at":"2026-05-18T03:24:42.176077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3895v2","created_at":"2026-05-18T03:24:42.176077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3895","created_at":"2026-05-18T03:24:42.176077+00:00"},{"alias_kind":"pith_short_12","alias_value":"H5S4Q3BHME22","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"H5S4Q3BHME22VKYN","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"H5S4Q3BH","created_at":"2026-05-18T12:26:07.630475+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/H5S4Q3BHME22VKYNB3IZWBRSXZ","json":"https://pith.science/pith/H5S4Q3BHME22VKYNB3IZWBRSXZ.json","graph_json":"https://pith.science/api/pith-number/H5S4Q3BHME22VKYNB3IZWBRSXZ/graph.json","events_json":"https://pith.science/api/pith-number/H5S4Q3BHME22VKYNB3IZWBRSXZ/events.json","paper":"https://pith.science/paper/H5S4Q3BH"},"agent_actions":{"view_html":"https://pith.science/pith/H5S4Q3BHME22VKYNB3IZWBRSXZ","download_json":"https://pith.science/pith/H5S4Q3BHME22VKYNB3IZWBRSXZ.json","view_paper":"https://pith.science/paper/H5S4Q3BH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3895&json=true","fetch_graph":"https://pith.science/api/pith-number/H5S4Q3BHME22VKYNB3IZWBRSXZ/graph.json","fetch_events":"https://pith.science/api/pith-number/H5S4Q3BHME22VKYNB3IZWBRSXZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H5S4Q3BHME22VKYNB3IZWBRSXZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H5S4Q3BHME22VKYNB3IZWBRSXZ/action/storage_attestation","attest_author":"https://pith.science/pith/H5S4Q3BHME22VKYNB3IZWBRSXZ/action/author_attestation","sign_citation":"https://pith.science/pith/H5S4Q3BHME22VKYNB3IZWBRSXZ/action/citation_signature","submit_replication":"https://pith.science/pith/H5S4Q3BHME22VKYNB3IZWBRSXZ/action/replication_record"}},"created_at":"2026-05-18T03:24:42.176077+00:00","updated_at":"2026-05-18T03:24:42.176077+00:00"}