{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZBCKOCWA6TB4TMHP7OAC5UJD64","short_pith_number":"pith:ZBCKOCWA","canonical_record":{"source":{"id":"1302.3069","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T12:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"c07442e5856dd2d5fc19beca79a94a386590731ca7ed4d1c4cc474683e09f5b5","abstract_canon_sha256":"3a5210c31052018d5ecc8a3b38e8f691109eeed12c41efbde535c24b060a3c1e"},"schema_version":"1.0"},"canonical_sha256":"c844a70ac0f4c3c9b0effb802ed123f71156538ed67d69dcad11d56fa70c0b6c","source":{"kind":"arxiv","id":"1302.3069","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3069","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3069v3","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3069","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZBCKOCWA6TB4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBCKOCWA6TB4TMHP","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBCKOCWA","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZBCKOCWA6TB4TMHP7OAC5UJD64","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3069","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T12:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"c07442e5856dd2d5fc19beca79a94a386590731ca7ed4d1c4cc474683e09f5b5","abstract_canon_sha256":"3a5210c31052018d5ecc8a3b38e8f691109eeed12c41efbde535c24b060a3c1e"},"schema_version":"1.0"},"canonical_sha256":"c844a70ac0f4c3c9b0effb802ed123f71156538ed67d69dcad11d56fa70c0b6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:31.053133Z","signature_b64":"mT/KeW+eMNGBrKCVSreNXAesYO6ctvC5YKSAlyhdxpsHR0dR+1jfV9yIjERVoFXf805xjAQpVqGeHkPKyUGoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c844a70ac0f4c3c9b0effb802ed123f71156538ed67d69dcad11d56fa70c0b6c","last_reissued_at":"2026-05-18T03:32:31.052228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:31.052228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3069","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":"2026-05-18T03:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/L3yyusJIrWUK7R6BdDBn5S0kPZjftgpnHw99/J9iLkA87/15beCqZAqA+NF4ttCg1FyniNs6Uhc6FxL6MWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:25:27.522691Z"},"content_sha256":"f1d4ffc044a02bec364a1157b0aa69df18138d45a98a50daa8d73d90578e262e","schema_version":"1.0","event_id":"sha256:f1d4ffc044a02bec364a1157b0aa69df18138d45a98a50daa8d73d90578e262e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZBCKOCWA6TB4TMHP7OAC5UJD64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tail asymptotic of the stationary distribution for the state dependent (1,R)-reflecting random walk: near critical","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ke Zhou, Wenming Hong","submitted_at":"2013-02-13T12:50:29Z","abstract_excerpt":"In this paper, we consider the $(1,R)$ state-dependent reflecting random walk (RW) on the half line, allowing the size of jumps to the right at maximal $R$ and to the left only 1. We provide an explicit criterion for positive recurrence and the explicit expression of the stationary distribution based on the intrinsic branching structure within the walk. As an application, we obtain the tail asymptotic of the stationary distribution in the \"near critical\" situation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3069","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":"2026-05-18T03:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vfFA6PdK1M2DseOmFWlxSEFVDBJ/E7Wq4lzM3gV5L+uFZ8bvdgB5Vq9ueL/5tLXWv66n6Uk2LAEjL5/o/s3bBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:25:27.523026Z"},"content_sha256":"19ac19d051125663424f003390659b7bbe91c57ad0440ea631054baf7c1a3ce1","schema_version":"1.0","event_id":"sha256:19ac19d051125663424f003390659b7bbe91c57ad0440ea631054baf7c1a3ce1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBCKOCWA6TB4TMHP7OAC5UJD64/bundle.json","state_url":"https://pith.science/pith/ZBCKOCWA6TB4TMHP7OAC5UJD64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBCKOCWA6TB4TMHP7OAC5UJD64/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":"2026-06-02T05:25:27Z","links":{"resolver":"https://pith.science/pith/ZBCKOCWA6TB4TMHP7OAC5UJD64","bundle":"https://pith.science/pith/ZBCKOCWA6TB4TMHP7OAC5UJD64/bundle.json","state":"https://pith.science/pith/ZBCKOCWA6TB4TMHP7OAC5UJD64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBCKOCWA6TB4TMHP7OAC5UJD64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZBCKOCWA6TB4TMHP7OAC5UJD64","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":"3a5210c31052018d5ecc8a3b38e8f691109eeed12c41efbde535c24b060a3c1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T12:50:29Z","title_canon_sha256":"c07442e5856dd2d5fc19beca79a94a386590731ca7ed4d1c4cc474683e09f5b5"},"schema_version":"1.0","source":{"id":"1302.3069","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3069","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3069v3","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3069","created_at":"2026-05-18T03:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZBCKOCWA6TB4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBCKOCWA6TB4TMHP","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBCKOCWA","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:19ac19d051125663424f003390659b7bbe91c57ad0440ea631054baf7c1a3ce1","target":"graph","created_at":"2026-05-18T03:32:31Z","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":"In this paper, we consider the $(1,R)$ state-dependent reflecting random walk (RW) on the half line, allowing the size of jumps to the right at maximal $R$ and to the left only 1. We provide an explicit criterion for positive recurrence and the explicit expression of the stationary distribution based on the intrinsic branching structure within the walk. As an application, we obtain the tail asymptotic of the stationary distribution in the \"near critical\" situation.","authors_text":"Ke Zhou, Wenming Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T12:50:29Z","title":"Tail asymptotic of the stationary distribution for the state dependent (1,R)-reflecting random walk: near critical"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3069","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:f1d4ffc044a02bec364a1157b0aa69df18138d45a98a50daa8d73d90578e262e","target":"record","created_at":"2026-05-18T03:32:31Z","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":"3a5210c31052018d5ecc8a3b38e8f691109eeed12c41efbde535c24b060a3c1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-02-13T12:50:29Z","title_canon_sha256":"c07442e5856dd2d5fc19beca79a94a386590731ca7ed4d1c4cc474683e09f5b5"},"schema_version":"1.0","source":{"id":"1302.3069","kind":"arxiv","version":3}},"canonical_sha256":"c844a70ac0f4c3c9b0effb802ed123f71156538ed67d69dcad11d56fa70c0b6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c844a70ac0f4c3c9b0effb802ed123f71156538ed67d69dcad11d56fa70c0b6c","first_computed_at":"2026-05-18T03:32:31.052228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:31.052228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mT/KeW+eMNGBrKCVSreNXAesYO6ctvC5YKSAlyhdxpsHR0dR+1jfV9yIjERVoFXf805xjAQpVqGeHkPKyUGoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:31.053133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3069","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1d4ffc044a02bec364a1157b0aa69df18138d45a98a50daa8d73d90578e262e","sha256:19ac19d051125663424f003390659b7bbe91c57ad0440ea631054baf7c1a3ce1"],"state_sha256":"09dbfbb4684f20b7ab2ac6c1a13bc02eb00b0a6de48be60cf9d4fb718e1ba9cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6FHyNYedstO7t71ABIr3y0Tx3rLHRl22od6F3SZBr1rm/uY21EIw8WT8iC6UTH8m1qsD6YfjowdON2dEisSeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:25:27.524995Z","bundle_sha256":"bb3f1be189ce3626fae007542ed085afb66e325cbc8d82932e1aa76295d734ba"}}