{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PVFRWW25N5X5XAOBLJNKYESRU4","short_pith_number":"pith:PVFRWW25","canonical_record":{"source":{"id":"1501.05066","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-21T06:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"ea6707536ddf69c5e5abb7eae9ee253857dac6f76c8b893eea18ce64fb4cb2b4","abstract_canon_sha256":"164a2be87d69bd9331c03a7e73522ddf07aad677cb549dfad14e37440e80f3fc"},"schema_version":"1.0"},"canonical_sha256":"7d4b1b5b5d6f6fdb81c15a5aac1251a72eb4126c7c65828a206377e2ddba532d","source":{"kind":"arxiv","id":"1501.05066","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05066","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05066v3","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05066","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"PVFRWW25N5X5","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PVFRWW25N5X5XAOB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PVFRWW25","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PVFRWW25N5X5XAOBLJNKYESRU4","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05066","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-21T06:16:27Z","cross_cats_sorted":[],"title_canon_sha256":"ea6707536ddf69c5e5abb7eae9ee253857dac6f76c8b893eea18ce64fb4cb2b4","abstract_canon_sha256":"164a2be87d69bd9331c03a7e73522ddf07aad677cb549dfad14e37440e80f3fc"},"schema_version":"1.0"},"canonical_sha256":"7d4b1b5b5d6f6fdb81c15a5aac1251a72eb4126c7c65828a206377e2ddba532d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:33.721634Z","signature_b64":"zINHNcdkkN5/igk4h/Z8S9zUDthkpLypuyUGGOp2zk1BI83Hg6tpxOE6H1lGJkRZjM6gs/teGz9pZmJU57/5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d4b1b5b5d6f6fdb81c15a5aac1251a72eb4126c7c65828a206377e2ddba532d","last_reissued_at":"2026-05-18T02:25:33.721182Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:33.721182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05066","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":"2026-05-18T02:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zADXbyWL+VoFrKTdoPyscbtvR9qSzNW3VNI1JdBRLnBYIsJQ6IdtPIMMyzQlqnGdWZsNWOpF/7Hse48H1aodBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:59:21.353197Z"},"content_sha256":"80bd348a62f34e2124c6aa9ba5c359727792c3a280b1a0e33888ca85a387f59e","schema_version":"1.0","event_id":"sha256:80bd348a62f34e2124c6aa9ba5c359727792c3a280b1a0e33888ca85a387f59e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PVFRWW25N5X5XAOBLJNKYESRU4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Property of Random Walks on a Cycle Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yasunari Fukai, Yoshihiro Mizoguchi, Yuki Ikeda","submitted_at":"2015-01-21T06:16:27Z","abstract_excerpt":"We analyze the Hunter vs Rabbit game on graph, which is a kind of model of communication in an adhoc mobile network. Let $G$ be a cycle graph with $N$ nodes. The hunter can move from a vertex to another vertex on the graph along an edge. The rabbit can move to any vertex on graph at once. We formalized the game using the random walk framework. The strategy of the rabbit is formalized using a one dimensional random walk over $\\mathbb{Z}$. We classify strategies using the order $O(k^{-\\beta-1})$ of their Fourier transformation. We investigate lower bounds and upper bounds of a probability that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05066","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":"2026-05-18T02:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3XSlIe0B1hbEsv9SQwRXsG3uToawQfYPQ9PI+i9EDrzU1t/xa6w1FVWslHH5pJZhQQZkl1dOf6zkvtSLvJclAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:59:21.353908Z"},"content_sha256":"bb2cc45e103b1faccd48e4f5a382e0aabfbb60df82f2f6b4c0575ded6c0d7b24","schema_version":"1.0","event_id":"sha256:bb2cc45e103b1faccd48e4f5a382e0aabfbb60df82f2f6b4c0575ded6c0d7b24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVFRWW25N5X5XAOBLJNKYESRU4/bundle.json","state_url":"https://pith.science/pith/PVFRWW25N5X5XAOBLJNKYESRU4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVFRWW25N5X5XAOBLJNKYESRU4/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":"2026-06-09T06:59:21Z","links":{"resolver":"https://pith.science/pith/PVFRWW25N5X5XAOBLJNKYESRU4","bundle":"https://pith.science/pith/PVFRWW25N5X5XAOBLJNKYESRU4/bundle.json","state":"https://pith.science/pith/PVFRWW25N5X5XAOBLJNKYESRU4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVFRWW25N5X5XAOBLJNKYESRU4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PVFRWW25N5X5XAOBLJNKYESRU4","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":"164a2be87d69bd9331c03a7e73522ddf07aad677cb549dfad14e37440e80f3fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-21T06:16:27Z","title_canon_sha256":"ea6707536ddf69c5e5abb7eae9ee253857dac6f76c8b893eea18ce64fb4cb2b4"},"schema_version":"1.0","source":{"id":"1501.05066","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05066","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05066v3","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05066","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"PVFRWW25N5X5","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PVFRWW25N5X5XAOB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PVFRWW25","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:bb2cc45e103b1faccd48e4f5a382e0aabfbb60df82f2f6b4c0575ded6c0d7b24","target":"graph","created_at":"2026-05-18T02:25:33Z","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 analyze the Hunter vs Rabbit game on graph, which is a kind of model of communication in an adhoc mobile network. Let $G$ be a cycle graph with $N$ nodes. The hunter can move from a vertex to another vertex on the graph along an edge. The rabbit can move to any vertex on graph at once. We formalized the game using the random walk framework. The strategy of the rabbit is formalized using a one dimensional random walk over $\\mathbb{Z}$. We classify strategies using the order $O(k^{-\\beta-1})$ of their Fourier transformation. We investigate lower bounds and upper bounds of a probability that t","authors_text":"Yasunari Fukai, Yoshihiro Mizoguchi, Yuki Ikeda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-21T06:16:27Z","title":"A Property of Random Walks on a Cycle Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05066","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":"sha256:80bd348a62f34e2124c6aa9ba5c359727792c3a280b1a0e33888ca85a387f59e","target":"record","created_at":"2026-05-18T02:25:33Z","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":"164a2be87d69bd9331c03a7e73522ddf07aad677cb549dfad14e37440e80f3fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-21T06:16:27Z","title_canon_sha256":"ea6707536ddf69c5e5abb7eae9ee253857dac6f76c8b893eea18ce64fb4cb2b4"},"schema_version":"1.0","source":{"id":"1501.05066","kind":"arxiv","version":3}},"canonical_sha256":"7d4b1b5b5d6f6fdb81c15a5aac1251a72eb4126c7c65828a206377e2ddba532d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d4b1b5b5d6f6fdb81c15a5aac1251a72eb4126c7c65828a206377e2ddba532d","first_computed_at":"2026-05-18T02:25:33.721182Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:33.721182Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zINHNcdkkN5/igk4h/Z8S9zUDthkpLypuyUGGOp2zk1BI83Hg6tpxOE6H1lGJkRZjM6gs/teGz9pZmJU57/5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:33.721634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05066","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80bd348a62f34e2124c6aa9ba5c359727792c3a280b1a0e33888ca85a387f59e","sha256:bb2cc45e103b1faccd48e4f5a382e0aabfbb60df82f2f6b4c0575ded6c0d7b24"],"state_sha256":"a4b9149b139eeab724e34bf0648d83e06fd87b720b172e779aa239b0190b6615"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kH7W0oPc5jpOz/DTWbmESiUlZ8dQZMKhYtBMJv3aigeYZixlmXP4O9OoGuY7xj9rN+Ofwlq9h9e1CAOcV/zwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:59:21.358081Z","bundle_sha256":"feab4a058fa938cd8883012c9e5f5f019fa20f993fe64de325b2bf4961879ef8"}}