{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:WQOTIPACDPEE3XXCQJYA5GA2DI","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":"d11a2784d36d8765c36196a7a72e7799083c59952e79e1ec11d6976d8a9394d3","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.CO","submitted_at":"2004-04-26T19:14:46Z","title_canon_sha256":"d7add673d30a35b302b30390ae1f7632ede25e84739f91ffbe1198916f589d43"},"schema_version":"1.0","source":{"id":"math/0404467","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404467","created_at":"2026-07-04T14:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404467v1","created_at":"2026-07-04T14:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404467","created_at":"2026-07-04T14:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"WQOTIPACDPEE","created_at":"2026-07-04T14:38:33Z"},{"alias_kind":"pith_short_16","alias_value":"WQOTIPACDPEE3XXC","created_at":"2026-07-04T14:38:33Z"},{"alias_kind":"pith_short_8","alias_value":"WQOTIPAC","created_at":"2026-07-04T14:38:33Z"}],"graph_snapshots":[{"event_id":"sha256:3b24c13a68e0b275804cb48f8f144d52a3318dd439722023e858b3101fae93fd","target":"graph","created_at":"2026-07-04T14:38:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0404467/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The article provides an explicit algebraic expression for the generating function of walks on graphs. Its proof is based on the scattering theory for the differential Laplace operator on non-compact graphs.","authors_text":"Robert Schrader, Vadim Kostrykin","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2004-04-26T19:14:46Z","title":"Generating Functions of Random Walks on Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404467","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":"sha256:0b352a92bda5b98a38720f841cb1ba5cefd10744390ec27d63c6cf43ddbeac60","target":"record","created_at":"2026-07-04T14:38:33Z","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":"d11a2784d36d8765c36196a7a72e7799083c59952e79e1ec11d6976d8a9394d3","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.CO","submitted_at":"2004-04-26T19:14:46Z","title_canon_sha256":"d7add673d30a35b302b30390ae1f7632ede25e84739f91ffbe1198916f589d43"},"schema_version":"1.0","source":{"id":"math/0404467","kind":"arxiv","version":1}},"canonical_sha256":"b41d343c021bc84ddee282700e981a1a23163fe002dbdc097a6681d2386490ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b41d343c021bc84ddee282700e981a1a23163fe002dbdc097a6681d2386490ff","first_computed_at":"2026-07-04T14:38:33.821453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:33.821453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FhRpoa7vRyKBR1ccFQYq79PCDFKW3iyI30h9D9kgQsR0wKzifyXZf6JaaLJka+QzAfVHAsw/1XZ8pdiyUEi1Aw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:33.821823Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0404467","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b352a92bda5b98a38720f841cb1ba5cefd10744390ec27d63c6cf43ddbeac60","sha256:3b24c13a68e0b275804cb48f8f144d52a3318dd439722023e858b3101fae93fd"],"state_sha256":"c1edd294548a6b04b5a1835366a1b10d8f8043258232f59976ac41711310c354"}