{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:LUQO3FAVEICJJRDCBFTJE2BQ65","short_pith_number":"pith:LUQO3FAV","schema_version":"1.0","canonical_sha256":"5d20ed9415220494c4620966926830f74c29858d7b4d3389d26bcbc656f56119","source":{"kind":"arxiv","id":"2312.12247","version":2},"attestation_state":"computed","paper":{"title":"Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Fulvio Gesmundo, Hal Schenck, Hang (Amy) Huang, Jerzy Weyman","submitted_at":"2023-12-19T15:31:45Z","abstract_excerpt":"We describe the minimal free resolution of the ideal of $2 \\times 2$ subpermanents of a $2 \\times n$ generic matrix $M$. In contrast to the case of $2 \\times 2$ determinants, the $2 \\times 2$ permanents define an ideal which is neither prime nor Cohen-Macaulay. We combine work of Laubenbacher-Swanson on the Gr\\\"obner basis of an ideal of $2 \\times 2$ permanents of a generic matrix with our previous work connecting the initial ideal of $2 \\times 2$ permanents to a simplicial complex. The main technical tool is a spectral sequence arising from the Bernstein-Gelfand-Gelfand correspondence."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2312.12247","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2023-12-19T15:31:45Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"f578a27c78fb91586525abd4b36ee63a3db24b261e167360d03c06072af1042d","abstract_canon_sha256":"4983e0a6636addbe51a83f3bba796f3c5231b2d11ee60cec6489040ede0ec258"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:37:51.179694Z","signature_b64":"ekFR3yxRtP6vqbY8TzUZo06QOXQeu17f3QigOU2+FT37LDkJxfyI6hipEWJ0QiEqg/Bl9d1JSBX606pI7DDMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d20ed9415220494c4620966926830f74c29858d7b4d3389d26bcbc656f56119","last_reissued_at":"2026-07-05T09:37:51.178193Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:37:51.178193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Fulvio Gesmundo, Hal Schenck, Hang (Amy) Huang, Jerzy Weyman","submitted_at":"2023-12-19T15:31:45Z","abstract_excerpt":"We describe the minimal free resolution of the ideal of $2 \\times 2$ subpermanents of a $2 \\times n$ generic matrix $M$. In contrast to the case of $2 \\times 2$ determinants, the $2 \\times 2$ permanents define an ideal which is neither prime nor Cohen-Macaulay. We combine work of Laubenbacher-Swanson on the Gr\\\"obner basis of an ideal of $2 \\times 2$ permanents of a generic matrix with our previous work connecting the initial ideal of $2 \\times 2$ permanents to a simplicial complex. The main technical tool is a spectral sequence arising from the Bernstein-Gelfand-Gelfand correspondence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.12247","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.12247/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2312.12247","created_at":"2026-07-05T09:37:51.179151+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.12247v2","created_at":"2026-07-05T09:37:51.179151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.12247","created_at":"2026-07-05T09:37:51.179151+00:00"},{"alias_kind":"pith_short_12","alias_value":"LUQO3FAVEICJ","created_at":"2026-07-05T09:37:51.179151+00:00"},{"alias_kind":"pith_short_16","alias_value":"LUQO3FAVEICJJRDC","created_at":"2026-07-05T09:37:51.179151+00:00"},{"alias_kind":"pith_short_8","alias_value":"LUQO3FAV","created_at":"2026-07-05T09:37:51.179151+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.05358","citing_title":"Equivariant Syzygies of the Ideal of 2 x 2 Permanents of a 2 x n Matrix","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65","json":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65.json","graph_json":"https://pith.science/api/pith-number/LUQO3FAVEICJJRDCBFTJE2BQ65/graph.json","events_json":"https://pith.science/api/pith-number/LUQO3FAVEICJJRDCBFTJE2BQ65/events.json","paper":"https://pith.science/paper/LUQO3FAV"},"agent_actions":{"view_html":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65","download_json":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65.json","view_paper":"https://pith.science/paper/LUQO3FAV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.12247&json=true","fetch_graph":"https://pith.science/api/pith-number/LUQO3FAVEICJJRDCBFTJE2BQ65/graph.json","fetch_events":"https://pith.science/api/pith-number/LUQO3FAVEICJJRDCBFTJE2BQ65/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65/action/storage_attestation","attest_author":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65/action/author_attestation","sign_citation":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65/action/citation_signature","submit_replication":"https://pith.science/pith/LUQO3FAVEICJJRDCBFTJE2BQ65/action/replication_record"}},"created_at":"2026-07-05T09:37:51.179151+00:00","updated_at":"2026-07-05T09:37:51.179151+00:00"}