{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SCL56GKN4QQMC6RIM23EMZXNX5","short_pith_number":"pith:SCL56GKN","canonical_record":{"source":{"id":"1702.02754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-09T09:15:02Z","cross_cats_sorted":[],"title_canon_sha256":"b04416021531106b1820a57d4d8a4d22cafecff57ab1faa1da44c5024dc6d944","abstract_canon_sha256":"d5754c179319594c17bd6bfcabb1a3e1e23b218b38528164689c4de2411a9937"},"schema_version":"1.0"},"canonical_sha256":"9097df194de420c17a2866b64666edbf618ac2ffef6a4267eef3bfcf335ce0ac","source":{"kind":"arxiv","id":"1702.02754","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02754","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02754v1","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02754","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"SCL56GKN4QQM","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SCL56GKN4QQMC6RI","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SCL56GKN","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SCL56GKN4QQMC6RIM23EMZXNX5","target":"record","payload":{"canonical_record":{"source":{"id":"1702.02754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-09T09:15:02Z","cross_cats_sorted":[],"title_canon_sha256":"b04416021531106b1820a57d4d8a4d22cafecff57ab1faa1da44c5024dc6d944","abstract_canon_sha256":"d5754c179319594c17bd6bfcabb1a3e1e23b218b38528164689c4de2411a9937"},"schema_version":"1.0"},"canonical_sha256":"9097df194de420c17a2866b64666edbf618ac2ffef6a4267eef3bfcf335ce0ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:02.572383Z","signature_b64":"SArZSDkaCi4V4duYtJEtcjtiIGTDEwNHpic5JKutHRLCTUdR8bJRa35XC0Lauuu755EvpOVpN3k5raPS8UivDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9097df194de420c17a2866b64666edbf618ac2ffef6a4267eef3bfcf335ce0ac","last_reissued_at":"2026-05-18T00:51:02.571876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:02.571876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.02754","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":"2026-05-18T00:51:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WE4KwpfB81J5XAtdTA/fnf5VmlX5QbL1U8LPusdIniG+V5wzDOHYOtWlxJLfvMyDRoKpuzMapZDoxDmh1vEGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:47:36.311709Z"},"content_sha256":"2c705efc379a9eff1f586019e7a6deacb09a0faaa89d5dc8f310ddb892efe780","schema_version":"1.0","event_id":"sha256:2c705efc379a9eff1f586019e7a6deacb09a0faaa89d5dc8f310ddb892efe780"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SCL56GKN4QQMC6RIM23EMZXNX5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodicity of a system of interacting random walks with asymmetric interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amine Asselah, Luisa Andreis, Paolo Dai Pra","submitted_at":"2017-02-09T09:15:02Z","abstract_excerpt":"We study N interacting random walks on the positive integers. Each particle has drift {\\delta} towards infinity, a reflection at the origin, and a drift towards particles with lower positions. This inhomogeneous mean field system is shown to be ergodic only when the interaction is strong enough. We focus on this latter regime, and point out the effect of piles of particles, a phenomenon absent in models of interacting diffusion in continuous space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02754","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":"2026-05-18T00:51:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5DtDKkTCbvG2iysOMaqqYnw1rhasDmELBtOfbVSyoREEm5p/PEDiE+bMf71f3YiJNvxj5hByNDKzcnlG+P0HDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:47:36.312348Z"},"content_sha256":"2287fbdad0e8c0ff6f04bd99ecae8532923fa7fda468a55f0fb50ae8f6082af4","schema_version":"1.0","event_id":"sha256:2287fbdad0e8c0ff6f04bd99ecae8532923fa7fda468a55f0fb50ae8f6082af4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SCL56GKN4QQMC6RIM23EMZXNX5/bundle.json","state_url":"https://pith.science/pith/SCL56GKN4QQMC6RIM23EMZXNX5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SCL56GKN4QQMC6RIM23EMZXNX5/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":"2026-06-12T06:47:36Z","links":{"resolver":"https://pith.science/pith/SCL56GKN4QQMC6RIM23EMZXNX5","bundle":"https://pith.science/pith/SCL56GKN4QQMC6RIM23EMZXNX5/bundle.json","state":"https://pith.science/pith/SCL56GKN4QQMC6RIM23EMZXNX5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SCL56GKN4QQMC6RIM23EMZXNX5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SCL56GKN4QQMC6RIM23EMZXNX5","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":"d5754c179319594c17bd6bfcabb1a3e1e23b218b38528164689c4de2411a9937","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-09T09:15:02Z","title_canon_sha256":"b04416021531106b1820a57d4d8a4d22cafecff57ab1faa1da44c5024dc6d944"},"schema_version":"1.0","source":{"id":"1702.02754","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02754","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02754v1","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02754","created_at":"2026-05-18T00:51:02Z"},{"alias_kind":"pith_short_12","alias_value":"SCL56GKN4QQM","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SCL56GKN4QQMC6RI","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SCL56GKN","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:2287fbdad0e8c0ff6f04bd99ecae8532923fa7fda468a55f0fb50ae8f6082af4","target":"graph","created_at":"2026-05-18T00:51:02Z","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":"We study N interacting random walks on the positive integers. Each particle has drift {\\delta} towards infinity, a reflection at the origin, and a drift towards particles with lower positions. This inhomogeneous mean field system is shown to be ergodic only when the interaction is strong enough. We focus on this latter regime, and point out the effect of piles of particles, a phenomenon absent in models of interacting diffusion in continuous space.","authors_text":"Amine Asselah, Luisa Andreis, Paolo Dai Pra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-09T09:15:02Z","title":"Ergodicity of a system of interacting random walks with asymmetric interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02754","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":"sha256:2c705efc379a9eff1f586019e7a6deacb09a0faaa89d5dc8f310ddb892efe780","target":"record","created_at":"2026-05-18T00:51:02Z","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":"d5754c179319594c17bd6bfcabb1a3e1e23b218b38528164689c4de2411a9937","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-09T09:15:02Z","title_canon_sha256":"b04416021531106b1820a57d4d8a4d22cafecff57ab1faa1da44c5024dc6d944"},"schema_version":"1.0","source":{"id":"1702.02754","kind":"arxiv","version":1}},"canonical_sha256":"9097df194de420c17a2866b64666edbf618ac2ffef6a4267eef3bfcf335ce0ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9097df194de420c17a2866b64666edbf618ac2ffef6a4267eef3bfcf335ce0ac","first_computed_at":"2026-05-18T00:51:02.571876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:02.571876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SArZSDkaCi4V4duYtJEtcjtiIGTDEwNHpic5JKutHRLCTUdR8bJRa35XC0Lauuu755EvpOVpN3k5raPS8UivDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:02.572383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02754","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c705efc379a9eff1f586019e7a6deacb09a0faaa89d5dc8f310ddb892efe780","sha256:2287fbdad0e8c0ff6f04bd99ecae8532923fa7fda468a55f0fb50ae8f6082af4"],"state_sha256":"cb28ce744b8f9121607c0b03d7b6f80448c256ce164cf72e30efa97784a34a01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FVKQ+vSJt6jqYVm/uzeXU0dCEfNLarOM5u3RUBFvdjIeZmZtEXRZ1Y/B8IMa0vghYEX/8yTyt8rbMNQ9pPZoDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:47:36.315098Z","bundle_sha256":"399934c4aedcec3c008898dd08652c2d775a541e35ad6115b010d473cac98c69"}}