{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XEBMIXE57NXEAF3TU5KDHTZ3WM","short_pith_number":"pith:XEBMIXE5","schema_version":"1.0","canonical_sha256":"b902c45c9dfb6e401773a75433cf3bb3128be9e509cdb8c8be376391d3da2fee","source":{"kind":"arxiv","id":"1709.00876","version":2},"attestation_state":"computed","paper":{"title":"On the length of perverse sheaves and D-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Botong Wang, Nero Budur, Pietro Gatti, Yongqiang Liu","submitted_at":"2017-09-04T09:40:23Z","abstract_excerpt":"We prove that the length function for perverse sheaves and algebraic regular holonomic D-modules on a smooth complex algebraic variety Y is an absolute Q-constructible function. One consequence is: for \"any\" fixed natural (derived) functor F between constructible complexes or perverse sheaves on two smooth varieties X and Y, the loci of rank one local systems L on X whose image F(L) has prescribed length are Zariski constructible subsets defined over Q, obtained from finitely many torsion-translated complex affine algebraic subtori of the moduli of rank one local systems via a finite sequence "},"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":"1709.00876","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-04T09:40:23Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"eff809fb6d3344c5a05cac4f0caa97413e2aa2da440daba03f6495ce2d9bc124","abstract_canon_sha256":"b935bfe4c2af05221c2ebff6ece17767d2d8a8bdff7fbb61e6e762d20bc24c28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:26.227088Z","signature_b64":"CiqUt3vdkxOMxb5k4gfyG3gqIUGzp+xOkuStBYoFhKWYRm0K1gCCIVb52fnTujriI9UT/vHWPkk6o9LBG5o1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b902c45c9dfb6e401773a75433cf3bb3128be9e509cdb8c8be376391d3da2fee","last_reissued_at":"2026-05-17T23:51:26.226586Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:26.226586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the length of perverse sheaves and D-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Botong Wang, Nero Budur, Pietro Gatti, Yongqiang Liu","submitted_at":"2017-09-04T09:40:23Z","abstract_excerpt":"We prove that the length function for perverse sheaves and algebraic regular holonomic D-modules on a smooth complex algebraic variety Y is an absolute Q-constructible function. One consequence is: for \"any\" fixed natural (derived) functor F between constructible complexes or perverse sheaves on two smooth varieties X and Y, the loci of rank one local systems L on X whose image F(L) has prescribed length are Zariski constructible subsets defined over Q, obtained from finitely many torsion-translated complex affine algebraic subtori of the moduli of rank one local systems via a finite sequence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00876","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":""},"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":"1709.00876","created_at":"2026-05-17T23:51:26.226667+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.00876v2","created_at":"2026-05-17T23:51:26.226667+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00876","created_at":"2026-05-17T23:51:26.226667+00:00"},{"alias_kind":"pith_short_12","alias_value":"XEBMIXE57NXE","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"XEBMIXE57NXEAF3T","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"XEBMIXE5","created_at":"2026-05-18T12:31:53.515858+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/XEBMIXE57NXEAF3TU5KDHTZ3WM","json":"https://pith.science/pith/XEBMIXE57NXEAF3TU5KDHTZ3WM.json","graph_json":"https://pith.science/api/pith-number/XEBMIXE57NXEAF3TU5KDHTZ3WM/graph.json","events_json":"https://pith.science/api/pith-number/XEBMIXE57NXEAF3TU5KDHTZ3WM/events.json","paper":"https://pith.science/paper/XEBMIXE5"},"agent_actions":{"view_html":"https://pith.science/pith/XEBMIXE57NXEAF3TU5KDHTZ3WM","download_json":"https://pith.science/pith/XEBMIXE57NXEAF3TU5KDHTZ3WM.json","view_paper":"https://pith.science/paper/XEBMIXE5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.00876&json=true","fetch_graph":"https://pith.science/api/pith-number/XEBMIXE57NXEAF3TU5KDHTZ3WM/graph.json","fetch_events":"https://pith.science/api/pith-number/XEBMIXE57NXEAF3TU5KDHTZ3WM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XEBMIXE57NXEAF3TU5KDHTZ3WM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XEBMIXE57NXEAF3TU5KDHTZ3WM/action/storage_attestation","attest_author":"https://pith.science/pith/XEBMIXE57NXEAF3TU5KDHTZ3WM/action/author_attestation","sign_citation":"https://pith.science/pith/XEBMIXE57NXEAF3TU5KDHTZ3WM/action/citation_signature","submit_replication":"https://pith.science/pith/XEBMIXE57NXEAF3TU5KDHTZ3WM/action/replication_record"}},"created_at":"2026-05-17T23:51:26.226667+00:00","updated_at":"2026-05-17T23:51:26.226667+00:00"}