{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:K3SEKO2NAIY2ZNJQGDZCLM66AI","short_pith_number":"pith:K3SEKO2N","canonical_record":{"source":{"id":"1701.07946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T05:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"85f3c68c3bdd43ed553dae0723221c425115ba0555ab428b71149e78ab5adc28","abstract_canon_sha256":"a58015a4ee82d9bdea919eb5895afb371a0cb99ae920bfb32edecf44a4aaba3c"},"schema_version":"1.0"},"canonical_sha256":"56e4453b4d0231acb53030f225b3de02333ec3bfba0519070557c18922ee68f7","source":{"kind":"arxiv","id":"1701.07946","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07946","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07946v1","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07946","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"K3SEKO2NAIY2","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K3SEKO2NAIY2ZNJQ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K3SEKO2N","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:K3SEKO2NAIY2ZNJQGDZCLM66AI","target":"record","payload":{"canonical_record":{"source":{"id":"1701.07946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T05:17:48Z","cross_cats_sorted":[],"title_canon_sha256":"85f3c68c3bdd43ed553dae0723221c425115ba0555ab428b71149e78ab5adc28","abstract_canon_sha256":"a58015a4ee82d9bdea919eb5895afb371a0cb99ae920bfb32edecf44a4aaba3c"},"schema_version":"1.0"},"canonical_sha256":"56e4453b4d0231acb53030f225b3de02333ec3bfba0519070557c18922ee68f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:59.335130Z","signature_b64":"te3CUKX/2+pjl0At0l3eEef/gzj2vdeZ8OCnP0lX8R78ngp0o2fb694mmHAjHxEV6RZ2iVMI5JN94SXJl6LIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56e4453b4d0231acb53030f225b3de02333ec3bfba0519070557c18922ee68f7","last_reissued_at":"2026-05-18T00:51:59.334347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:59.334347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.07946","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":"2026-05-18T00:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oXK+OyNfuPUDXSazANQGLAvJovy3ZR8Y5Hn1SUIIiul7+Gq2XDTcFzukunI/mcWnRWHTh3JFv4kAvcjOPsnnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:17:32.415257Z"},"content_sha256":"3ef3d11632ca4ad5824fb7f16c52f53c49ef5af9e93b0ba574cbae5ce1b203ff","schema_version":"1.0","event_id":"sha256:3ef3d11632ca4ad5824fb7f16c52f53c49ef5af9e93b0ba574cbae5ce1b203ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:K3SEKO2NAIY2ZNJQGDZCLM66AI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a property of the simple random walk on $\\mathbb{Z}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hayato Saigo, Hiroki Sako, Norio Konno","submitted_at":"2017-01-27T05:17:48Z","abstract_excerpt":"The subject of this paper is the simple random walk on $\\mathbb{Z}$. We give a very simple answer to the following problem: under the condition that a random walk has already spent $\\alpha$-percent of the traveling time on the positive side $\\mathbb{Z}_{\\ge 0}$, what is the probability that the random walk is now on the positive side?\n  The symmetric random walks which step $2n$-times can be decomposed in the following two ways: (1) how many times the walk steps on the positive side, (2) whether the last step is on the positive side or on the negative side. To answer the problem above, we clar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07946","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":"2026-05-18T00:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KE1jMLeGpNLUNQQ0wrZg9V1UoB3Pd2mQ31Y00DpJMy5aZcSRwk6W1sH3bpgb1/pbk1JsJMIcOfPHxx0HCPP/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:17:32.415637Z"},"content_sha256":"76e731cea4f1c59e3c62c61a3e9e484e16f0a398b41c55bb117be68026b65e9a","schema_version":"1.0","event_id":"sha256:76e731cea4f1c59e3c62c61a3e9e484e16f0a398b41c55bb117be68026b65e9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K3SEKO2NAIY2ZNJQGDZCLM66AI/bundle.json","state_url":"https://pith.science/pith/K3SEKO2NAIY2ZNJQGDZCLM66AI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K3SEKO2NAIY2ZNJQGDZCLM66AI/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":"2026-06-04T19:17:32Z","links":{"resolver":"https://pith.science/pith/K3SEKO2NAIY2ZNJQGDZCLM66AI","bundle":"https://pith.science/pith/K3SEKO2NAIY2ZNJQGDZCLM66AI/bundle.json","state":"https://pith.science/pith/K3SEKO2NAIY2ZNJQGDZCLM66AI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K3SEKO2NAIY2ZNJQGDZCLM66AI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:K3SEKO2NAIY2ZNJQGDZCLM66AI","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":"a58015a4ee82d9bdea919eb5895afb371a0cb99ae920bfb32edecf44a4aaba3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T05:17:48Z","title_canon_sha256":"85f3c68c3bdd43ed553dae0723221c425115ba0555ab428b71149e78ab5adc28"},"schema_version":"1.0","source":{"id":"1701.07946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.07946","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1701.07946v1","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07946","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"K3SEKO2NAIY2","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K3SEKO2NAIY2ZNJQ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K3SEKO2N","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:76e731cea4f1c59e3c62c61a3e9e484e16f0a398b41c55bb117be68026b65e9a","target":"graph","created_at":"2026-05-18T00:51:59Z","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":"The subject of this paper is the simple random walk on $\\mathbb{Z}$. We give a very simple answer to the following problem: under the condition that a random walk has already spent $\\alpha$-percent of the traveling time on the positive side $\\mathbb{Z}_{\\ge 0}$, what is the probability that the random walk is now on the positive side?\n  The symmetric random walks which step $2n$-times can be decomposed in the following two ways: (1) how many times the walk steps on the positive side, (2) whether the last step is on the positive side or on the negative side. To answer the problem above, we clar","authors_text":"Hayato Saigo, Hiroki Sako, Norio Konno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T05:17:48Z","title":"On a property of the simple random walk on $\\mathbb{Z}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07946","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":"sha256:3ef3d11632ca4ad5824fb7f16c52f53c49ef5af9e93b0ba574cbae5ce1b203ff","target":"record","created_at":"2026-05-18T00:51:59Z","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":"a58015a4ee82d9bdea919eb5895afb371a0cb99ae920bfb32edecf44a4aaba3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-27T05:17:48Z","title_canon_sha256":"85f3c68c3bdd43ed553dae0723221c425115ba0555ab428b71149e78ab5adc28"},"schema_version":"1.0","source":{"id":"1701.07946","kind":"arxiv","version":1}},"canonical_sha256":"56e4453b4d0231acb53030f225b3de02333ec3bfba0519070557c18922ee68f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56e4453b4d0231acb53030f225b3de02333ec3bfba0519070557c18922ee68f7","first_computed_at":"2026-05-18T00:51:59.334347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:59.334347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"te3CUKX/2+pjl0At0l3eEef/gzj2vdeZ8OCnP0lX8R78ngp0o2fb694mmHAjHxEV6RZ2iVMI5JN94SXJl6LIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:59.335130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.07946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ef3d11632ca4ad5824fb7f16c52f53c49ef5af9e93b0ba574cbae5ce1b203ff","sha256:76e731cea4f1c59e3c62c61a3e9e484e16f0a398b41c55bb117be68026b65e9a"],"state_sha256":"75cd67133e2642e7fd776dafc4fa3f74f63ae02976bc7a97f22b24fba9fa3f49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6AzzY8Q2Pgd5rRJkf1mywnz8BJ4YsJ5XxXnooBHGxdjBdsc7c9IbV+fDUCPV96bMajaXZ73yiOGvR4fVOVFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:17:32.417593Z","bundle_sha256":"3364ed57825abaabc0e9af0eab65d9f39e031f988c4637dadbd1441fed0b7fdb"}}