{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UK7EUNFNTC6WDVLJD4XI4MDRCZ","short_pith_number":"pith:UK7EUNFN","canonical_record":{"source":{"id":"1211.1648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-07T19:48:01Z","cross_cats_sorted":[],"title_canon_sha256":"7c12cad614df43baf641a070d0bda524e535cb98fbc0a9be4f67b2279ba4bb5d","abstract_canon_sha256":"6d97f99a3cd383089cfc3a90bccfe250b9bb80d93b587f2e2812e2645a2d1d10"},"schema_version":"1.0"},"canonical_sha256":"a2be4a34ad98bd61d5691f2e8e30711643bdfee61834476be540a54cc00f614b","source":{"kind":"arxiv","id":"1211.1648","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1648","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1648v1","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1648","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"UK7EUNFNTC6W","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UK7EUNFNTC6WDVLJ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UK7EUNFN","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UK7EUNFNTC6WDVLJD4XI4MDRCZ","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-07T19:48:01Z","cross_cats_sorted":[],"title_canon_sha256":"7c12cad614df43baf641a070d0bda524e535cb98fbc0a9be4f67b2279ba4bb5d","abstract_canon_sha256":"6d97f99a3cd383089cfc3a90bccfe250b9bb80d93b587f2e2812e2645a2d1d10"},"schema_version":"1.0"},"canonical_sha256":"a2be4a34ad98bd61d5691f2e8e30711643bdfee61834476be540a54cc00f614b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:53.196908Z","signature_b64":"Brw7p6wiIX0VGwBTuowtyPU81J/DYLRMSDqzxi+TDefzr3eGF8PqG1ie3kC4OTsnelcEbYcd/+F33Gkb2RLRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2be4a34ad98bd61d5691f2e8e30711643bdfee61834476be540a54cc00f614b","last_reissued_at":"2026-05-18T02:47:53.196437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:53.196437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1648","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l+cuUAjeLzntapVaLTz0XZ+tSmpz1gClnPxO10Qz17siC1b1hFouLlGGtfHNBsEI67Bbp3Q2CPojQpexoH9nBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:10:21.188679Z"},"content_sha256":"5afb6a197229700b3d55929c5fb740383505e8988fe314f6ef56785047d2adb6","schema_version":"1.0","event_id":"sha256:5afb6a197229700b3d55929c5fb740383505e8988fe314f6ef56785047d2adb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UK7EUNFNTC6WDVLJD4XI4MDRCZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Syzygies and singularities of tensor product surfaces of bidegree (2,1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alexandra Seceleanu, Hal Schenck, Javid Validashti","submitted_at":"2012-11-07T19:48:01Z","abstract_excerpt":"Let U be a basepoint free four-dimensional subspace of the space of sections of O(2,1) on P^1 x P^1. The sections corresponding to U determine a regular map p_U: P^1 x P^1 --> P^3. We study the associated bigraded ideal I_U in k[s,t;u,v] from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free resolution. These resolutions play a key role in determining the implicit equation of the image p_U(P^1 x P^1), via work of Buse-Jouanolou, Buse-Chardin, Botbol and Botbol-Dickenstein-Dohm on the approximation complex. In four of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1648","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLGm6zxv4YLNFW4nZWXRqzoLYmg2qYSLiPnuJv4NTgZl7HGQ4eporhZzrMg5Qm87pgesL/UzxeQmW1rzqVyzDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:10:21.189040Z"},"content_sha256":"6a02d3f692bbe77f17c68d727777ad2d099fade98151876607f911e29eeee3c0","schema_version":"1.0","event_id":"sha256:6a02d3f692bbe77f17c68d727777ad2d099fade98151876607f911e29eeee3c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UK7EUNFNTC6WDVLJD4XI4MDRCZ/bundle.json","state_url":"https://pith.science/pith/UK7EUNFNTC6WDVLJD4XI4MDRCZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UK7EUNFNTC6WDVLJD4XI4MDRCZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T16:10:21Z","links":{"resolver":"https://pith.science/pith/UK7EUNFNTC6WDVLJD4XI4MDRCZ","bundle":"https://pith.science/pith/UK7EUNFNTC6WDVLJD4XI4MDRCZ/bundle.json","state":"https://pith.science/pith/UK7EUNFNTC6WDVLJD4XI4MDRCZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UK7EUNFNTC6WDVLJD4XI4MDRCZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UK7EUNFNTC6WDVLJD4XI4MDRCZ","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":"6d97f99a3cd383089cfc3a90bccfe250b9bb80d93b587f2e2812e2645a2d1d10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-07T19:48:01Z","title_canon_sha256":"7c12cad614df43baf641a070d0bda524e535cb98fbc0a9be4f67b2279ba4bb5d"},"schema_version":"1.0","source":{"id":"1211.1648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1648","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1648v1","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1648","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"UK7EUNFNTC6W","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UK7EUNFNTC6WDVLJ","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UK7EUNFN","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:6a02d3f692bbe77f17c68d727777ad2d099fade98151876607f911e29eeee3c0","target":"graph","created_at":"2026-05-18T02:47:53Z","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":"Let U be a basepoint free four-dimensional subspace of the space of sections of O(2,1) on P^1 x P^1. The sections corresponding to U determine a regular map p_U: P^1 x P^1 --> P^3. We study the associated bigraded ideal I_U in k[s,t;u,v] from the standpoint of commutative algebra, proving that there are exactly six numerical types of possible bigraded minimal free resolution. These resolutions play a key role in determining the implicit equation of the image p_U(P^1 x P^1), via work of Buse-Jouanolou, Buse-Chardin, Botbol and Botbol-Dickenstein-Dohm on the approximation complex. In four of the","authors_text":"Alexandra Seceleanu, Hal Schenck, Javid Validashti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-07T19:48:01Z","title":"Syzygies and singularities of tensor product surfaces of bidegree (2,1)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1648","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":"sha256:5afb6a197229700b3d55929c5fb740383505e8988fe314f6ef56785047d2adb6","target":"record","created_at":"2026-05-18T02:47:53Z","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":"6d97f99a3cd383089cfc3a90bccfe250b9bb80d93b587f2e2812e2645a2d1d10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-07T19:48:01Z","title_canon_sha256":"7c12cad614df43baf641a070d0bda524e535cb98fbc0a9be4f67b2279ba4bb5d"},"schema_version":"1.0","source":{"id":"1211.1648","kind":"arxiv","version":1}},"canonical_sha256":"a2be4a34ad98bd61d5691f2e8e30711643bdfee61834476be540a54cc00f614b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2be4a34ad98bd61d5691f2e8e30711643bdfee61834476be540a54cc00f614b","first_computed_at":"2026-05-18T02:47:53.196437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:53.196437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Brw7p6wiIX0VGwBTuowtyPU81J/DYLRMSDqzxi+TDefzr3eGF8PqG1ie3kC4OTsnelcEbYcd/+F33Gkb2RLRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:53.196908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5afb6a197229700b3d55929c5fb740383505e8988fe314f6ef56785047d2adb6","sha256:6a02d3f692bbe77f17c68d727777ad2d099fade98151876607f911e29eeee3c0"],"state_sha256":"0121b84274a868d09155ea4426b5c51db7decd29d29cee2846a3a55785a20c6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvP185DKhhNLT2tTqpFkEI4ua+MJ1jLl9xDkS8L286QnFfYoJ+pqg6Sz0LPoZjdJGWZekhV7Bm5kQT3FdSVgBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:10:21.191081Z","bundle_sha256":"d9a90a170423fa325689c08ced2b35dba601c8b009da650791750da72e024fa8"}}