{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BZ4UY3JJ225MQLFRVAOB3XPVR3","short_pith_number":"pith:BZ4UY3JJ","schema_version":"1.0","canonical_sha256":"0e794c6d29d6bac82cb1a81c1dddf58ed5e9a40ab9cac54a17d99eb412ff3afc","source":{"kind":"arxiv","id":"1207.0979","version":1},"attestation_state":"computed","paper":{"title":"Minimizing the number of lattice points in a translated polygon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CC","authors_text":"Friedrich Eisenbrand, Nicolai H\\\"ahnle","submitted_at":"2012-07-04T13:34:33Z","abstract_excerpt":"The parametric lattice-point counting problem is as follows: Given an integer matrix $A \\in Z^{m \\times n}$, compute an explicit formula parameterized by $b \\in R^m$ that determines the number of integer points in the polyhedron $\\{x \\in R^n : Ax \\leq b\\}$. In the last decade, this counting problem has received considerable attention in the literature. Several variants of Barvinok's algorithm have been shown to solve this problem in polynomial time if the number $n$ of columns of $A$ is fixed.\n  Central to our investigation is the following question: Can one also efficiently determine a parame"},"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":"1207.0979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-07-04T13:34:33Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"c514cfd66fc17d9c9062d9446a51d9f98aef6de5a2019207d4924e0aefa1b876","abstract_canon_sha256":"aac371014ebe60aa7a9a32dba255efc914394b6968be875723611efa8be3a19c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:47.813731Z","signature_b64":"+KTee240lu1Ib8ne5ETrV/A06e3kBpQU4qvtBCysP5HpbbaDje28gIzi07hP0KbRDkgusvYWPwKPs8aShJadAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e794c6d29d6bac82cb1a81c1dddf58ed5e9a40ab9cac54a17d99eb412ff3afc","last_reissued_at":"2026-05-18T03:51:47.813211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:47.813211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimizing the number of lattice points in a translated polygon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.CC","authors_text":"Friedrich Eisenbrand, Nicolai H\\\"ahnle","submitted_at":"2012-07-04T13:34:33Z","abstract_excerpt":"The parametric lattice-point counting problem is as follows: Given an integer matrix $A \\in Z^{m \\times n}$, compute an explicit formula parameterized by $b \\in R^m$ that determines the number of integer points in the polyhedron $\\{x \\in R^n : Ax \\leq b\\}$. In the last decade, this counting problem has received considerable attention in the literature. Several variants of Barvinok's algorithm have been shown to solve this problem in polynomial time if the number $n$ of columns of $A$ is fixed.\n  Central to our investigation is the following question: Can one also efficiently determine a parame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0979","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":"1207.0979","created_at":"2026-05-18T03:51:47.813293+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.0979v1","created_at":"2026-05-18T03:51:47.813293+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0979","created_at":"2026-05-18T03:51:47.813293+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZ4UY3JJ225M","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZ4UY3JJ225MQLFR","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZ4UY3JJ","created_at":"2026-05-18T12:27:01.376967+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/BZ4UY3JJ225MQLFRVAOB3XPVR3","json":"https://pith.science/pith/BZ4UY3JJ225MQLFRVAOB3XPVR3.json","graph_json":"https://pith.science/api/pith-number/BZ4UY3JJ225MQLFRVAOB3XPVR3/graph.json","events_json":"https://pith.science/api/pith-number/BZ4UY3JJ225MQLFRVAOB3XPVR3/events.json","paper":"https://pith.science/paper/BZ4UY3JJ"},"agent_actions":{"view_html":"https://pith.science/pith/BZ4UY3JJ225MQLFRVAOB3XPVR3","download_json":"https://pith.science/pith/BZ4UY3JJ225MQLFRVAOB3XPVR3.json","view_paper":"https://pith.science/paper/BZ4UY3JJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.0979&json=true","fetch_graph":"https://pith.science/api/pith-number/BZ4UY3JJ225MQLFRVAOB3XPVR3/graph.json","fetch_events":"https://pith.science/api/pith-number/BZ4UY3JJ225MQLFRVAOB3XPVR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZ4UY3JJ225MQLFRVAOB3XPVR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZ4UY3JJ225MQLFRVAOB3XPVR3/action/storage_attestation","attest_author":"https://pith.science/pith/BZ4UY3JJ225MQLFRVAOB3XPVR3/action/author_attestation","sign_citation":"https://pith.science/pith/BZ4UY3JJ225MQLFRVAOB3XPVR3/action/citation_signature","submit_replication":"https://pith.science/pith/BZ4UY3JJ225MQLFRVAOB3XPVR3/action/replication_record"}},"created_at":"2026-05-18T03:51:47.813293+00:00","updated_at":"2026-05-18T03:51:47.813293+00:00"}