{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JJ5NZTSMAU5VG7ANJPROMDKTAY","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":"91164832ce1565bebbe56dd43e225babb8fd7068a183d99c4035b708aa97406c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T21:52:58Z","title_canon_sha256":"a47ccb039b59fa9c7fa05bf41509a76e03663c0fabad44556e35f0ac49529e62"},"schema_version":"1.0","source":{"id":"1111.0047","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0047","created_at":"2026-05-18T03:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0047v4","created_at":"2026-05-18T03:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0047","created_at":"2026-05-18T03:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"JJ5NZTSMAU5V","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JJ5NZTSMAU5VG7AN","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JJ5NZTSM","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:ffb623c4b0b1e6e6f1cf9085736b185f14bb818a879a6db25836a62dda4951ab","target":"graph","created_at":"2026-05-18T03:15:06Z","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 classify the cohomology classes of Lagrangian 4-planes $\\P^4$ in a smooth manifold $X$ deformation equivalent to a Hilbert scheme of 4 points on a $K3$ surface, up to the monodromy action. Classically, the cone of effective curves on a $K3$ surface $S$ is generated by nonegative classes $C$, for which $(C,C)\\geq0$, and nodal classes $C$, for which $(C,C)=-2$; Hassett and Tschinkel conjecture that the cone of effective curves on a holomorphic symplectic variety $X$ is similarly controlled by \"nodal\" classes $C$ such that $(C,C)=-\\gamma$, for $(\\cdot,\\cdot)$ now the Beauville-Bogomolov form, ","authors_text":"Andrei Jorza, Benjamin Bakker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T21:52:58Z","title":"Lagrangian 4-planes in holomorphic symplectic varieties of K3^[4] type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0047","kind":"arxiv","version":4},"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":"sha256:04dbd4c1ee68a749aca67cad6935649f9d433f29b2c4ca70e2f11e76eefcf09b","target":"record","created_at":"2026-05-18T03:15:06Z","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":"91164832ce1565bebbe56dd43e225babb8fd7068a183d99c4035b708aa97406c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T21:52:58Z","title_canon_sha256":"a47ccb039b59fa9c7fa05bf41509a76e03663c0fabad44556e35f0ac49529e62"},"schema_version":"1.0","source":{"id":"1111.0047","kind":"arxiv","version":4}},"canonical_sha256":"4a7adcce4c053b537c0d4be2e60d53063ec866802c659bd1c39f6c0dc6da92d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a7adcce4c053b537c0d4be2e60d53063ec866802c659bd1c39f6c0dc6da92d8","first_computed_at":"2026-05-18T03:15:06.774620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:06.774620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"blAb5wPR2VQa7MGyKUQW/9KY35yAbAmqAMzjra8+i1gxRRThgQhnyVRtKv8COy04g6rBFIBEukbukKBjNMYLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:06.775592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0047","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04dbd4c1ee68a749aca67cad6935649f9d433f29b2c4ca70e2f11e76eefcf09b","sha256:ffb623c4b0b1e6e6f1cf9085736b185f14bb818a879a6db25836a62dda4951ab"],"state_sha256":"e08aed38e40888e194bf75674a6d336f804b802b89e64b0f739592cea00c8204"}