{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6OW47UCFR5CH43YPWY6AN4JNUC","short_pith_number":"pith:6OW47UCF","canonical_record":{"source":{"id":"1707.06423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-20T09:24:08Z","cross_cats_sorted":[],"title_canon_sha256":"59d2cf4416fc41ac2be53b2a93362664d7694e898f5ed28e33db2e1c4d4165c6","abstract_canon_sha256":"552710358913d0779018ca5fd10f188158dd62c55175008d81c20624ae8d004f"},"schema_version":"1.0"},"canonical_sha256":"f3adcfd0458f447e6f0fb63c06f12da0a2495743c347040ac1b1547fbb90dabd","source":{"kind":"arxiv","id":"1707.06423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06423","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06423v1","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06423","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"6OW47UCFR5CH","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6OW47UCFR5CH43YP","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6OW47UCF","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6OW47UCFR5CH43YPWY6AN4JNUC","target":"record","payload":{"canonical_record":{"source":{"id":"1707.06423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-20T09:24:08Z","cross_cats_sorted":[],"title_canon_sha256":"59d2cf4416fc41ac2be53b2a93362664d7694e898f5ed28e33db2e1c4d4165c6","abstract_canon_sha256":"552710358913d0779018ca5fd10f188158dd62c55175008d81c20624ae8d004f"},"schema_version":"1.0"},"canonical_sha256":"f3adcfd0458f447e6f0fb63c06f12da0a2495743c347040ac1b1547fbb90dabd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:53.864562Z","signature_b64":"1sAb2RasOwzCsYe9tjRUCMEt9qyrksDNbyjgec5zIY9SL5nP18jfQ9CsPJcvYiaOFJJej1ZVVEPpTwCXd7+HCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3adcfd0458f447e6f0fb63c06f12da0a2495743c347040ac1b1547fbb90dabd","last_reissued_at":"2026-05-18T00:39:53.863873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:53.863873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.06423","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":"2026-05-18T00:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R2iAQCIxecZ6AMHWG+bvIjGeT4xBu4+um20itSB5Thcio6mX6DXKs9ic7/P1uX3bkstcPtEFsm8Pv97IpUVrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:42:15.647009Z"},"content_sha256":"d942af2e44fcab67ada27696f8c0cd885a9ef569cd3a590c7f4d04835046b3be","schema_version":"1.0","event_id":"sha256:d942af2e44fcab67ada27696f8c0cd885a9ef569cd3a590c7f4d04835046b3be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6OW47UCFR5CH43YPWY6AN4JNUC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the number of points skipped by a transient (1,2) random walk on the line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hua-Ming Wang","submitted_at":"2017-07-20T09:24:08Z","abstract_excerpt":"Consider a transient near-critical (1,2) random walk on the positive half line. We give a criteria for the finiteness of the number of the skipped points (the points never visited) by the random walk. This result generalizes (partially) the criteria for the finiteness of the number of cutpoingts of the nearest neighbor random walk on the line by Cs\\'aki, F\\\"olders, R\\'ev\\'esz [J Theor Probab (2010) 23: 624-638]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06423","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":"2026-05-18T00:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AVHNkH3g1wtDV1hCpZHYwwtRE7hF5mK1EyLBY7Q4VoxiN3GMkmkQJ5B0XZuUE35yTnOgO0YEDDd+Us2r2R0cCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:42:15.647737Z"},"content_sha256":"1b2b91fc08357ecad53bfc4ff008261d254135238ba15bd91a6cd3853ef8029e","schema_version":"1.0","event_id":"sha256:1b2b91fc08357ecad53bfc4ff008261d254135238ba15bd91a6cd3853ef8029e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6OW47UCFR5CH43YPWY6AN4JNUC/bundle.json","state_url":"https://pith.science/pith/6OW47UCFR5CH43YPWY6AN4JNUC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6OW47UCFR5CH43YPWY6AN4JNUC/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":"2026-06-09T08:42:15Z","links":{"resolver":"https://pith.science/pith/6OW47UCFR5CH43YPWY6AN4JNUC","bundle":"https://pith.science/pith/6OW47UCFR5CH43YPWY6AN4JNUC/bundle.json","state":"https://pith.science/pith/6OW47UCFR5CH43YPWY6AN4JNUC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6OW47UCFR5CH43YPWY6AN4JNUC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6OW47UCFR5CH43YPWY6AN4JNUC","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":"552710358913d0779018ca5fd10f188158dd62c55175008d81c20624ae8d004f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-20T09:24:08Z","title_canon_sha256":"59d2cf4416fc41ac2be53b2a93362664d7694e898f5ed28e33db2e1c4d4165c6"},"schema_version":"1.0","source":{"id":"1707.06423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06423","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06423v1","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06423","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"6OW47UCFR5CH","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6OW47UCFR5CH43YP","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6OW47UCF","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:1b2b91fc08357ecad53bfc4ff008261d254135238ba15bd91a6cd3853ef8029e","target":"graph","created_at":"2026-05-18T00:39:53Z","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":"Consider a transient near-critical (1,2) random walk on the positive half line. We give a criteria for the finiteness of the number of the skipped points (the points never visited) by the random walk. This result generalizes (partially) the criteria for the finiteness of the number of cutpoingts of the nearest neighbor random walk on the line by Cs\\'aki, F\\\"olders, R\\'ev\\'esz [J Theor Probab (2010) 23: 624-638].","authors_text":"Hua-Ming Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-20T09:24:08Z","title":"On the number of points skipped by a transient (1,2) random walk on the line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06423","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:d942af2e44fcab67ada27696f8c0cd885a9ef569cd3a590c7f4d04835046b3be","target":"record","created_at":"2026-05-18T00:39:53Z","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":"552710358913d0779018ca5fd10f188158dd62c55175008d81c20624ae8d004f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-20T09:24:08Z","title_canon_sha256":"59d2cf4416fc41ac2be53b2a93362664d7694e898f5ed28e33db2e1c4d4165c6"},"schema_version":"1.0","source":{"id":"1707.06423","kind":"arxiv","version":1}},"canonical_sha256":"f3adcfd0458f447e6f0fb63c06f12da0a2495743c347040ac1b1547fbb90dabd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3adcfd0458f447e6f0fb63c06f12da0a2495743c347040ac1b1547fbb90dabd","first_computed_at":"2026-05-18T00:39:53.863873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:53.863873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1sAb2RasOwzCsYe9tjRUCMEt9qyrksDNbyjgec5zIY9SL5nP18jfQ9CsPJcvYiaOFJJej1ZVVEPpTwCXd7+HCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:53.864562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d942af2e44fcab67ada27696f8c0cd885a9ef569cd3a590c7f4d04835046b3be","sha256:1b2b91fc08357ecad53bfc4ff008261d254135238ba15bd91a6cd3853ef8029e"],"state_sha256":"f10581e80df28b2ce258323d135d9d5cd7bc25fe5b1fef3db3ef872f0a5458be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqaSZb7MRdDOvR1stgWxqwZvK0v381FlNGPSAqGms1qI4CKi9F5k+4OZfNscbubSwOvjibB7pqiqgMcBQ8F0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:42:15.651670Z","bundle_sha256":"31cae73e25437ccd919822dd991f2341106cfdd0fe46a48c2bc9a271fe79fb10"}}