{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:56DV5NFO7NY3WQTXKBIF2Y5A5W","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":"f6fa307ae4294f2dab8afad7630d2ce928f0251894e0cb2bf3616f7045382d2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-25T10:02:29Z","title_canon_sha256":"76271c8b10ff0d86455fb8ea2f3a6d40b87018632197758f882b1e9df595383e"},"schema_version":"1.0","source":{"id":"1105.4983","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4983","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4983v2","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4983","created_at":"2026-05-18T03:38:02Z"},{"alias_kind":"pith_short_12","alias_value":"56DV5NFO7NY3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"56DV5NFO7NY3WQTX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"56DV5NFO","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:92d3ca47ea2a24077b73012112d6f2f6fb11614dae1155300fb6ac87a00506fc","target":"graph","created_at":"2026-05-18T03:38:02Z","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 minimal surfaces $S$ of general type with $p_g=q=2$ and $K_S^2=6$ whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth, irreducible components $\\mathcal{M}_{Ia}$, $\\mathcal{M}_{Ib}$, $\\mathcal{M}_{II}$ of dimension 4, 4, 3, respectively. The general surface $S$ contains a smooth elliptic curve $Z$ such that $Z^2=-2$, which is contracted by the Albanese map and which is preserved by any first-order deformation.","authors_text":"Francesco Polizzi, Matteo Penegini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-25T10:02:29Z","title":"Surfaces with p_g=q=2, K^2=6 and Albanese map of degree 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4983","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:cf07f2f358197e1dcddd0e4fcb83c2dfd0a7bb964d0f27ab926a77b8ca956223","target":"record","created_at":"2026-05-18T03:38:02Z","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":"f6fa307ae4294f2dab8afad7630d2ce928f0251894e0cb2bf3616f7045382d2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-25T10:02:29Z","title_canon_sha256":"76271c8b10ff0d86455fb8ea2f3a6d40b87018632197758f882b1e9df595383e"},"schema_version":"1.0","source":{"id":"1105.4983","kind":"arxiv","version":2}},"canonical_sha256":"ef875eb4aefb71bb427750505d63a0edad333b1cba3bd724e882afd308adeb57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef875eb4aefb71bb427750505d63a0edad333b1cba3bd724e882afd308adeb57","first_computed_at":"2026-05-18T03:38:02.976483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:02.976483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rg6oGM5uv2gyGQSyh85cxP7WOUqdyepGv/isBr/62LBy9d7qly3PjiVz80YkQVxryYWA0WKyEV31Gvd7zYmQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:02.976991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4983","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf07f2f358197e1dcddd0e4fcb83c2dfd0a7bb964d0f27ab926a77b8ca956223","sha256:92d3ca47ea2a24077b73012112d6f2f6fb11614dae1155300fb6ac87a00506fc"],"state_sha256":"3cbb784ebd60d79e860505d1b2a312e9254aad5b1a4e85df00f551b9653f0d24"}