{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SVTIEQCHEIFYYVEVTZFWHNUGHK","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":"4705f2c6e281ec001f76d817d150c96a7ae0f2b5a520790656c070c3e2ab6319","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-15T04:05:14Z","title_canon_sha256":"bf9a1dc7860f3be1c6767ee8e7ca004dad9181a7bb438fd7d791ee31c9e08d70"},"schema_version":"1.0","source":{"id":"1203.3264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3264","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3264v2","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3264","created_at":"2026-05-18T01:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"SVTIEQCHEIFY","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SVTIEQCHEIFYYVEV","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SVTIEQCH","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:532cad792b1199a192556f25e83bdab632aee82cec1d055186eb0dab2ee4a1cb","target":"graph","created_at":"2026-05-18T01:33:40Z","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 provide bijective proofs of two classic identities that are very simple to prove using generating functions, but surprisingly difficult to prove combinatorially. The problem of finding a bijective proof for the first identity was first raised in the 1930s. The second, more involved identity takes the first one a step further.","authors_text":"Miklos Bona","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-15T04:05:14Z","title":"A Bijective Proof of and Identity Extending a Classic Result of Hajos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3264","kind":"arxiv","version":2},"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":"sha256:95edd0e3ff39139ebf5e0cd34e5c3e882fa4efc0e1afd33befa87af9f4778bbe","target":"record","created_at":"2026-05-18T01:33:40Z","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":"4705f2c6e281ec001f76d817d150c96a7ae0f2b5a520790656c070c3e2ab6319","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-03-15T04:05:14Z","title_canon_sha256":"bf9a1dc7860f3be1c6767ee8e7ca004dad9181a7bb438fd7d791ee31c9e08d70"},"schema_version":"1.0","source":{"id":"1203.3264","kind":"arxiv","version":2}},"canonical_sha256":"9566824047220b8c54959e4b63b6863a86f07c971c73df4b0f2b5231f1150804","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9566824047220b8c54959e4b63b6863a86f07c971c73df4b0f2b5231f1150804","first_computed_at":"2026-05-18T01:33:40.647752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:40.647752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H0kGxdZywoXXkYYJc9b/YCU8TxquwF6SBkIz6OVcpd9yIpG0oHNnYVDBUqhSmscquRVUSisru06u3lA+yr0LCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:40.648159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95edd0e3ff39139ebf5e0cd34e5c3e882fa4efc0e1afd33befa87af9f4778bbe","sha256:532cad792b1199a192556f25e83bdab632aee82cec1d055186eb0dab2ee4a1cb"],"state_sha256":"6d68bf8d0946a77262d5204f736211100ea8b0ee03d66968c359cd1f49ae810b"}