{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QP2KCEGFEUJATQ3T4V5DHFINR6","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":"8f83af4c487f31b6a2e5b1922f266b3a18ee4a7bb312dbe1485362117c24e53f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-06T14:22:52Z","title_canon_sha256":"88aef6c59b4a0cae2c054a8a79dbc7f189c75ee533895d3e00854f0bbc591f4e"},"schema_version":"1.0","source":{"id":"1809.02008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.02008","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"1809.02008v1","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02008","created_at":"2026-05-18T00:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"QP2KCEGFEUJA","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QP2KCEGFEUJATQ3T","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QP2KCEGF","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:1938094b4b253a0f059babbe66fa9f0b48ceb14317fb8506c8a9dfbeb1ff71ae","target":"graph","created_at":"2026-05-18T00:06:21Z","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":"Based on the work of A. Vershik, we introduce two new combinatorial identities. We show how these identities can be used to prove a new hook-content identity. The main motivation for deriving this identity was a particular optimization problem in the field of quantum information processing.","authors_text":"Alessandro Bisio, Michal Sedl\\'ak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-06T14:22:52Z","title":"On some new hook-content identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02008","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:a0c90ff1007f026263b59779f2b08d132a87272878262cc1bba58ecbcdbdda66","target":"record","created_at":"2026-05-18T00:06:21Z","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":"8f83af4c487f31b6a2e5b1922f266b3a18ee4a7bb312dbe1485362117c24e53f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-06T14:22:52Z","title_canon_sha256":"88aef6c59b4a0cae2c054a8a79dbc7f189c75ee533895d3e00854f0bbc591f4e"},"schema_version":"1.0","source":{"id":"1809.02008","kind":"arxiv","version":1}},"canonical_sha256":"83f4a110c5251209c373e57a33950d8fb7edc75b94b54fc85ffc01bbeffa7798","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83f4a110c5251209c373e57a33950d8fb7edc75b94b54fc85ffc01bbeffa7798","first_computed_at":"2026-05-18T00:06:21.530042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:21.530042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q5U8lzS/4RGq8zoshgPSV8amPjp7FMQdEnBglMB+sx2Kp46Fwtrz0zufy+WRC6YNxPYWVWoq/wujCNUHt0z2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:21.530436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.02008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0c90ff1007f026263b59779f2b08d132a87272878262cc1bba58ecbcdbdda66","sha256:1938094b4b253a0f059babbe66fa9f0b48ceb14317fb8506c8a9dfbeb1ff71ae"],"state_sha256":"839bd8e83ebc34db61d1c406591e161c615643e7aebdf9ea316308c9bbdd8f79"}