{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IISYGDQKFI6UDV2CTIUVD34ZKJ","short_pith_number":"pith:IISYGDQK","schema_version":"1.0","canonical_sha256":"4225830e0a2a3d41d7429a2951ef995267a40077bc1aa40dd1daaae33667b9ab","source":{"kind":"arxiv","id":"1011.6002","version":1},"attestation_state":"computed","paper":{"title":"Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Matthias K\\\"oppe, Mich\\`ele Vergne, Nicole Berline, Velleda Baldoni","submitted_at":"2010-11-27T21:47:29Z","abstract_excerpt":"We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449--1466]. For a given semi-rational polytope P and a rational subspace L, we integrate a given polynomial function h over all lattice slices of the polytope P parallel to the subspace L and sum up the integrals. We first develop an algorithmic theory of parametric intermediate generating functions. Then we study the Ehrhart theory of these intermediate sums, that is, the dependence of the res"},"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":"1011.6002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-27T21:47:29Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"8eec0c6e2cc273fdf1421a6930c5efb282037894aa113ec1fa1a93a18720dbda","abstract_canon_sha256":"afb9ac84b48b25775af5c10be253d298b09df1de77ed6b130ebf54ec190e190b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:44.322992Z","signature_b64":"xgKEGymPYL1Ba/eHGQ3ulgOcR45SCsydgBNW2/SovNYuyxaYJv6x/eJ6/MXvAC8CLT1Qmj+JyQAGSARxCwn1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4225830e0a2a3d41d7429a2951ef995267a40077bc1aa40dd1daaae33667b9ab","last_reissued_at":"2026-05-18T03:02:44.322352Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:44.322352Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.CO","authors_text":"Matthias K\\\"oppe, Mich\\`ele Vergne, Nicole Berline, Velleda Baldoni","submitted_at":"2010-11-27T21:47:29Z","abstract_excerpt":"We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449--1466]. For a given semi-rational polytope P and a rational subspace L, we integrate a given polynomial function h over all lattice slices of the polytope P parallel to the subspace L and sum up the integrals. We first develop an algorithmic theory of parametric intermediate generating functions. Then we study the Ehrhart theory of these intermediate sums, that is, the dependence of the res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6002","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.6002","created_at":"2026-05-18T03:02:44.322453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.6002v1","created_at":"2026-05-18T03:02:44.322453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6002","created_at":"2026-05-18T03:02:44.322453+00:00"},{"alias_kind":"pith_short_12","alias_value":"IISYGDQKFI6U","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IISYGDQKFI6UDV2C","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IISYGDQK","created_at":"2026-05-18T12:26:09.077623+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/IISYGDQKFI6UDV2CTIUVD34ZKJ","json":"https://pith.science/pith/IISYGDQKFI6UDV2CTIUVD34ZKJ.json","graph_json":"https://pith.science/api/pith-number/IISYGDQKFI6UDV2CTIUVD34ZKJ/graph.json","events_json":"https://pith.science/api/pith-number/IISYGDQKFI6UDV2CTIUVD34ZKJ/events.json","paper":"https://pith.science/paper/IISYGDQK"},"agent_actions":{"view_html":"https://pith.science/pith/IISYGDQKFI6UDV2CTIUVD34ZKJ","download_json":"https://pith.science/pith/IISYGDQKFI6UDV2CTIUVD34ZKJ.json","view_paper":"https://pith.science/paper/IISYGDQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.6002&json=true","fetch_graph":"https://pith.science/api/pith-number/IISYGDQKFI6UDV2CTIUVD34ZKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/IISYGDQKFI6UDV2CTIUVD34ZKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IISYGDQKFI6UDV2CTIUVD34ZKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IISYGDQKFI6UDV2CTIUVD34ZKJ/action/storage_attestation","attest_author":"https://pith.science/pith/IISYGDQKFI6UDV2CTIUVD34ZKJ/action/author_attestation","sign_citation":"https://pith.science/pith/IISYGDQKFI6UDV2CTIUVD34ZKJ/action/citation_signature","submit_replication":"https://pith.science/pith/IISYGDQKFI6UDV2CTIUVD34ZKJ/action/replication_record"}},"created_at":"2026-05-18T03:02:44.322453+00:00","updated_at":"2026-05-18T03:02:44.322453+00:00"}