{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IBSHMLMIKYD43XYGQZEFAUBGEH","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":"58466b004f43cf87da701f29a67bf1c71c9a7992a1c7e3f63b2549650a65f7a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-24T21:11:01Z","title_canon_sha256":"fa5e672d8a98327592ad57470c11389853a6153707ede2d2bbb5280e5c6d3a25"},"schema_version":"1.0","source":{"id":"1904.11071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11071","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11071v1","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11071","created_at":"2026-05-17T23:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"IBSHMLMIKYD4","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IBSHMLMIKYD43XYG","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IBSHMLMI","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:f43c1d2db8130344cace6f299a4c5d7fa4578a5a1b4d81d201da48e9c7de293a","target":"graph","created_at":"2026-05-17T23:47:45Z","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 recall that a smooth ample surface $\\mathcal{S}$ in a general $(1,2,2)$-polarized abelian threefold, which is the pullback of the Theta divisor of a smooth plane quartic curve $\\mathcal{D}$, is a surface isogenous to the product $\\mathcal{C} \\times \\mathcal{C}$, where $\\mathcal{C}$ is a genus $9$ curve embedded in $\\mathbb{P}^3$ as complete intersection of a smooth quadric and a smooth quartic. We show that the space of global holomorhic sections of the canonical bundle of this surface is generated by certain determinantal bihomogeneous polynomials of bidegree $(2,2)$ on $\\mathbb{P}^3$, whi","authors_text":"Luca Cesarano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-24T21:11:01Z","title":"Biquadratic addition laws on elliptic curves in $\\mathbb{P}^3$ and the canonical map of the $(1,2,2)$-Theta divisor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11071","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":"sha256:72d4fba8b954383457c2981cd73d4388f82f7eec4db789312f63c7831aa04f81","target":"record","created_at":"2026-05-17T23:47:45Z","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":"58466b004f43cf87da701f29a67bf1c71c9a7992a1c7e3f63b2549650a65f7a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-24T21:11:01Z","title_canon_sha256":"fa5e672d8a98327592ad57470c11389853a6153707ede2d2bbb5280e5c6d3a25"},"schema_version":"1.0","source":{"id":"1904.11071","kind":"arxiv","version":1}},"canonical_sha256":"4064762d885607cddf06864850502621cd401ba1443ef46cea1220f4487fa866","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4064762d885607cddf06864850502621cd401ba1443ef46cea1220f4487fa866","first_computed_at":"2026-05-17T23:47:45.902171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:45.902171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I3+dJjedOqbQFSmiJ9JUmZraoDWBeSmeSWbCV6FTIBT7BTFGSSGnp8ZqsduPjSQ9zSvSK7EBJKcQ+Zzux9DIDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:45.902713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72d4fba8b954383457c2981cd73d4388f82f7eec4db789312f63c7831aa04f81","sha256:f43c1d2db8130344cace6f299a4c5d7fa4578a5a1b4d81d201da48e9c7de293a"],"state_sha256":"f84be07030a784e4cb0f664727f7c5c01f6285d081fab99d1ff6acff1a5aa480"}