{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DFXILRCIABSVGRSP23Q5BJNN2Q","short_pith_number":"pith:DFXILRCI","schema_version":"1.0","canonical_sha256":"196e85c448006553464fd6e1d0a5add42594dc77b846c236644dee98ed67ba28","source":{"kind":"arxiv","id":"2506.02636","version":1},"attestation_state":"computed","paper":{"title":"Some computational aspects of spectral sequences in \\v{C}ech cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Matthias Zach","submitted_at":"2025-06-03T08:53:29Z","abstract_excerpt":"Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily challenges the capacities of modern computers. We describe an algorithm and its implementation to compute a spectral sequence converging to the higher direct images of a bounded complex of sheaves on a product of projective spaces $\\mathbb P = \\mathbb P^{r_1}\\times \\dots \\times \\mathbb P^{r_m}$ over an arbitrary affine base $\\mathrm{Spec} R$. We assume the ring $R"},"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":"2506.02636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-06-03T08:53:29Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"22376148a176e6577582c2478442f8d1d781e50ea0bc8584e4b3cc7f646e93cf","abstract_canon_sha256":"56b0bdbbaa69c2ed7ec6ce1298fcf5970bd77206e4f7906d554b898203333df5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:15:05.766870Z","signature_b64":"8z2JhCwJb+6iEKzhj9dbQJ+scwAqycAODgNYs95Jn/wnhhunWRamnF8yMIIjBfHKsdLGFLGpIcDLTTpdlBJ8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"196e85c448006553464fd6e1d0a5add42594dc77b846c236644dee98ed67ba28","last_reissued_at":"2026-07-05T11:15:05.766439Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:15:05.766439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some computational aspects of spectral sequences in \\v{C}ech cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Matthias Zach","submitted_at":"2025-06-03T08:53:29Z","abstract_excerpt":"Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily challenges the capacities of modern computers. We describe an algorithm and its implementation to compute a spectral sequence converging to the higher direct images of a bounded complex of sheaves on a product of projective spaces $\\mathbb P = \\mathbb P^{r_1}\\times \\dots \\times \\mathbb P^{r_m}$ over an arbitrary affine base $\\mathrm{Spec} R$. We assume the ring $R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02636","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02636/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":"2506.02636","created_at":"2026-07-05T11:15:05.766495+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.02636v1","created_at":"2026-07-05T11:15:05.766495+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02636","created_at":"2026-07-05T11:15:05.766495+00:00"},{"alias_kind":"pith_short_12","alias_value":"DFXILRCIABSV","created_at":"2026-07-05T11:15:05.766495+00:00"},{"alias_kind":"pith_short_16","alias_value":"DFXILRCIABSVGRSP","created_at":"2026-07-05T11:15:05.766495+00:00"},{"alias_kind":"pith_short_8","alias_value":"DFXILRCI","created_at":"2026-07-05T11:15:05.766495+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q","json":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q.json","graph_json":"https://pith.science/api/pith-number/DFXILRCIABSVGRSP23Q5BJNN2Q/graph.json","events_json":"https://pith.science/api/pith-number/DFXILRCIABSVGRSP23Q5BJNN2Q/events.json","paper":"https://pith.science/paper/DFXILRCI"},"agent_actions":{"view_html":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q","download_json":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q.json","view_paper":"https://pith.science/paper/DFXILRCI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.02636&json=true","fetch_graph":"https://pith.science/api/pith-number/DFXILRCIABSVGRSP23Q5BJNN2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/DFXILRCIABSVGRSP23Q5BJNN2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q/action/storage_attestation","attest_author":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q/action/author_attestation","sign_citation":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q/action/citation_signature","submit_replication":"https://pith.science/pith/DFXILRCIABSVGRSP23Q5BJNN2Q/action/replication_record"}},"created_at":"2026-07-05T11:15:05.766495+00:00","updated_at":"2026-07-05T11:15:05.766495+00:00"}