{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2QIF5TBZSJQKBCDG4YJFKBWOIK","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":"bf691e005cfc7f0ef2f6f8cbde8c425389f3eda4f19133d69034b2c69ee4b2d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T21:07:20Z","title_canon_sha256":"c77262d8abd69458c6fe7ba2ba6ebe3be49ee89c1955ca4f2250c5263111aa73"},"schema_version":"1.0","source":{"id":"1405.3686","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3686","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3686v1","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3686","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"pith_short_12","alias_value":"2QIF5TBZSJQK","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2QIF5TBZSJQKBCDG","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2QIF5TBZ","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:af9d71711dc2e036a0e3496e982705667fdaa4abfd6d8c7065fe5c609540f83d","target":"graph","created_at":"2026-05-18T02:51:50Z","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":"A group valued function on a graph is called balanced if the product of its values along any cycle is equal to the identity element of the group. We compute the number of balanced functions from edges and vertices of a directed graph to a finite group.","authors_text":"Avraham Goldstein, Robert Shwartz, Vadim E. Levit, Yonah Cherniavsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T21:07:20Z","title":"Enumeration of balanced finite group valued functions on directed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3686","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":"sha256:30a71733292b65738d2878462993f3763970e39bfe14eadd825b435bbe0d5b68","target":"record","created_at":"2026-05-18T02:51:50Z","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":"bf691e005cfc7f0ef2f6f8cbde8c425389f3eda4f19133d69034b2c69ee4b2d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T21:07:20Z","title_canon_sha256":"c77262d8abd69458c6fe7ba2ba6ebe3be49ee89c1955ca4f2250c5263111aa73"},"schema_version":"1.0","source":{"id":"1405.3686","kind":"arxiv","version":1}},"canonical_sha256":"d4105ecc399260a08866e6125506ce428fae89a1a7be6b40747cb75f70a8d18d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4105ecc399260a08866e6125506ce428fae89a1a7be6b40747cb75f70a8d18d","first_computed_at":"2026-05-18T02:51:50.056283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:50.056283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"obKcAWqf1Ac4WMJ5HNaVYdyJzCsQH1+sI+/JmpBKNOZ/3L1t9MHOuA6m4u88Yon5Nj572NQYZN0HVurqPxmZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:50.056731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3686","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30a71733292b65738d2878462993f3763970e39bfe14eadd825b435bbe0d5b68","sha256:af9d71711dc2e036a0e3496e982705667fdaa4abfd6d8c7065fe5c609540f83d"],"state_sha256":"8526fb1c437ab4cae3a6ce2fb328b7c1da44f3fc5677f356cab605d433a2189c"}