{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GINIFI5EBENOZKIPVCQO4ALN2Q","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":"7119e7271d665c74ab65b74c9273ce9bf4b7c665e211d688cfc6cbfc155c3829","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-20T11:01:03Z","title_canon_sha256":"8e6ff0e60b2f24346afc83503fa8c9e7eab4286a842c4e1823eab4cbf21b8b8a"},"schema_version":"1.0","source":{"id":"1312.5884","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5884","created_at":"2026-05-18T02:28:23Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5884v2","created_at":"2026-05-18T02:28:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5884","created_at":"2026-05-18T02:28:23Z"},{"alias_kind":"pith_short_12","alias_value":"GINIFI5EBENO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GINIFI5EBENOZKIP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GINIFI5E","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:f3c4d1d96bc18953b37eb30cdf84ae9154cbeef4717635632924137adc33bd97","target":"graph","created_at":"2026-05-18T02:28:23Z","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":"In this short paper, we give a $p$-adic analogue of the Hard Leftschetz Theorem.","authors_text":"Daniel Caro","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-20T11:01:03Z","title":"Hard Lefschetz Theorem in $p$-adic cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5884","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":"sha256:6416f04d519e7336fbddc1bb8b71b2e1d5390a148c5ebc7afc0302042c20c4c6","target":"record","created_at":"2026-05-18T02:28:23Z","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":"7119e7271d665c74ab65b74c9273ce9bf4b7c665e211d688cfc6cbfc155c3829","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-12-20T11:01:03Z","title_canon_sha256":"8e6ff0e60b2f24346afc83503fa8c9e7eab4286a842c4e1823eab4cbf21b8b8a"},"schema_version":"1.0","source":{"id":"1312.5884","kind":"arxiv","version":2}},"canonical_sha256":"321a82a3a4091aeca90fa8a0ee016dd4158df831dc3ea5ef4b55fda6d1c6f790","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"321a82a3a4091aeca90fa8a0ee016dd4158df831dc3ea5ef4b55fda6d1c6f790","first_computed_at":"2026-05-18T02:28:23.207687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:23.207687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LITEoIZcenlhJDU4yKsHUsvSsmTzUz9skfsKS4I05Q0NHPq1PFViLoXN5Fj25oA3ht+qIzIFzreO2rctLtYAAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:23.208278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5884","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6416f04d519e7336fbddc1bb8b71b2e1d5390a148c5ebc7afc0302042c20c4c6","sha256:f3c4d1d96bc18953b37eb30cdf84ae9154cbeef4717635632924137adc33bd97"],"state_sha256":"f9866e9eaee93c25a8a16153c1d00b632a3e140e1b4830ce1089402be40b68f4"}