{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:NXEQN4GZNEH4DGZ7VAIQC5FHJY","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":"6c423d52e9a461300e52a1b6a2f0a369bb856ed31988e38dffb5adf8d4d0a1e4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-25T11:58:11Z","title_canon_sha256":"ab13aac50ca3db179dac6172aba2a433a924d4ff2c95e405f672fb8e40914431"},"schema_version":"1.0","source":{"id":"2310.16571","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.16571","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"arxiv_version","alias_value":"2310.16571v3","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.16571","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"pith_short_12","alias_value":"NXEQN4GZNEH4","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"pith_short_16","alias_value":"NXEQN4GZNEH4DGZ7","created_at":"2026-06-23T03:13:42Z"},{"alias_kind":"pith_short_8","alias_value":"NXEQN4GZ","created_at":"2026-06-23T03:13:42Z"}],"graph_snapshots":[{"event_id":"sha256:d47d5b62ffc29f72d9e9bc1912bfaf8a86c19889dcf734058ee778b53cd9fc1c","target":"graph","created_at":"2026-06-23T03:13:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.16571/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we give exact formulas for the average hitting times of random walks from one vertex to any other vertex on certain weighted Cayley graphs.","authors_text":"Yuuho Tanaka","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-25T11:58:11Z","title":"On the average hitting times of weighted Cayley graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.16571","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":"sha256:3a88dc46eec971e592f4ffb1f1c43841537d8a5fd07cc484f2780059a26e0427","target":"record","created_at":"2026-06-23T03:13:42Z","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":"6c423d52e9a461300e52a1b6a2f0a369bb856ed31988e38dffb5adf8d4d0a1e4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-25T11:58:11Z","title_canon_sha256":"ab13aac50ca3db179dac6172aba2a433a924d4ff2c95e405f672fb8e40914431"},"schema_version":"1.0","source":{"id":"2310.16571","kind":"arxiv","version":3}},"canonical_sha256":"6dc906f0d9690fc19b3fa8110174a74e0f086ffa0c5a625a5420e3befe93d925","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dc906f0d9690fc19b3fa8110174a74e0f086ffa0c5a625a5420e3befe93d925","first_computed_at":"2026-06-23T03:13:42.916283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:42.916283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UmDxLKw9tRnsBAqJh+uczHdA/hgK590wOAA2OOswZqEIX0+WaiePhreYaTkMro7LoSvtJMUaKZ1SEx9qFTj1AQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:42.916716Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.16571","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a88dc46eec971e592f4ffb1f1c43841537d8a5fd07cc484f2780059a26e0427","sha256:d47d5b62ffc29f72d9e9bc1912bfaf8a86c19889dcf734058ee778b53cd9fc1c"],"state_sha256":"10b5f0e7d1b26436add0e47f57bf12e66dbe0653e2f87e052d6ecc03f8fde26e"}