{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CSBASJG3QEVBG5WKY4BFJXEN3X","short_pith_number":"pith:CSBASJG3","canonical_record":{"source":{"id":"1807.05348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-14T07:30:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"31274e16ea8e08373541e95bd3a09fd96baddcf5ffc8ed1bbd0821632b88eb66","abstract_canon_sha256":"d021c0d45fc7c8324b7a0ff1ab76fb95546f4e49c8d8ebaba2edcc77d06f1b19"},"schema_version":"1.0"},"canonical_sha256":"14820924db812a1376cac70254dc8dddd55b5826b91c92393abe1129a48a8f8c","source":{"kind":"arxiv","id":"1807.05348","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05348","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05348v1","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05348","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"pith_short_12","alias_value":"CSBASJG3QEVB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CSBASJG3QEVBG5WK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CSBASJG3","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CSBASJG3QEVBG5WKY4BFJXEN3X","target":"record","payload":{"canonical_record":{"source":{"id":"1807.05348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-14T07:30:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"31274e16ea8e08373541e95bd3a09fd96baddcf5ffc8ed1bbd0821632b88eb66","abstract_canon_sha256":"d021c0d45fc7c8324b7a0ff1ab76fb95546f4e49c8d8ebaba2edcc77d06f1b19"},"schema_version":"1.0"},"canonical_sha256":"14820924db812a1376cac70254dc8dddd55b5826b91c92393abe1129a48a8f8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:43.755142Z","signature_b64":"skN+oq0zaIYVI9Vij9P7Pzyau930mIIhy7G8w95SG1+Eozb3glJNLFNZb5LYiG1Q0aagOkKryNQTPxf6zdP4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14820924db812a1376cac70254dc8dddd55b5826b91c92393abe1129a48a8f8c","last_reissued_at":"2026-05-18T00:10:43.754697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:43.754697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.05348","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdu4r+6JgEjXZswlNxa9sSN/0NhfSrpYNVoxWHkT64HygWuX9eQSEVFBqiHYaNt1E7FQpeqTPEthL3orx7gKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:36:05.914076Z"},"content_sha256":"6ed22f08d7416a97ca59a4ac368c4d8d76196c729a80f60851b3733610cb09ec","schema_version":"1.0","event_id":"sha256:6ed22f08d7416a97ca59a4ac368c4d8d76196c729a80f60851b3733610cb09ec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CSBASJG3QEVBG5WKY4BFJXEN3X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting Integral Points in Polytopes via Numerical Analysis of Contour Integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Hiroshi Hirai, Ken'ichiro Tanaka, Ryunosuke Oshiro","submitted_at":"2018-07-14T07:30:35Z","abstract_excerpt":"In this paper, we address the problem of counting integer points in a rational polytope described by $P(y) = \\{ x \\in \\mathbb{R}^m \\colon Ax = y, x \\geq 0\\}$, where $A$ is an $n \\times m$ integer matrix and $y$ is an $n$-dimensional integer vector. We study the Z-transformation approach initiated by Brion-Vergne, Beck, and Lasserre-Zeron from the numerical analysis point of view, and obtain a new algorithm on this problem: If $A$ is nonnegative, then the number of integer points in $P(y)$ can be computed in $O(\\mathrm{poly} (n,m, \\|y\\|_\\infty) (\\|y\\|_\\infty + 1)^n)$ time and $O(\\mathrm{poly} ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05348","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q3ZvuayAyR/VKlLzU1UZmHWso0dOqohp8QK6aIqAjcSaRVkIpczFkt9Sb05uq+QLvA0ONtBRT9+XIfq32qaIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:36:05.914761Z"},"content_sha256":"17c010e47ad42ebb657c93ce8b44e77d75ca4adbe45fb87b5fa714898e9a7c07","schema_version":"1.0","event_id":"sha256:17c010e47ad42ebb657c93ce8b44e77d75ca4adbe45fb87b5fa714898e9a7c07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CSBASJG3QEVBG5WKY4BFJXEN3X/bundle.json","state_url":"https://pith.science/pith/CSBASJG3QEVBG5WKY4BFJXEN3X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CSBASJG3QEVBG5WKY4BFJXEN3X/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T03:36:05Z","links":{"resolver":"https://pith.science/pith/CSBASJG3QEVBG5WKY4BFJXEN3X","bundle":"https://pith.science/pith/CSBASJG3QEVBG5WKY4BFJXEN3X/bundle.json","state":"https://pith.science/pith/CSBASJG3QEVBG5WKY4BFJXEN3X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CSBASJG3QEVBG5WKY4BFJXEN3X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CSBASJG3QEVBG5WKY4BFJXEN3X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d021c0d45fc7c8324b7a0ff1ab76fb95546f4e49c8d8ebaba2edcc77d06f1b19","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-14T07:30:35Z","title_canon_sha256":"31274e16ea8e08373541e95bd3a09fd96baddcf5ffc8ed1bbd0821632b88eb66"},"schema_version":"1.0","source":{"id":"1807.05348","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05348","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05348v1","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05348","created_at":"2026-05-18T00:10:43Z"},{"alias_kind":"pith_short_12","alias_value":"CSBASJG3QEVB","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CSBASJG3QEVBG5WK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CSBASJG3","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:17c010e47ad42ebb657c93ce8b44e77d75ca4adbe45fb87b5fa714898e9a7c07","target":"graph","created_at":"2026-05-18T00:10:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we address the problem of counting integer points in a rational polytope described by $P(y) = \\{ x \\in \\mathbb{R}^m \\colon Ax = y, x \\geq 0\\}$, where $A$ is an $n \\times m$ integer matrix and $y$ is an $n$-dimensional integer vector. We study the Z-transformation approach initiated by Brion-Vergne, Beck, and Lasserre-Zeron from the numerical analysis point of view, and obtain a new algorithm on this problem: If $A$ is nonnegative, then the number of integer points in $P(y)$ can be computed in $O(\\mathrm{poly} (n,m, \\|y\\|_\\infty) (\\|y\\|_\\infty + 1)^n)$ time and $O(\\mathrm{poly} (","authors_text":"Hiroshi Hirai, Ken'ichiro Tanaka, Ryunosuke Oshiro","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-14T07:30:35Z","title":"Counting Integral Points in Polytopes via Numerical Analysis of Contour Integration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05348","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6ed22f08d7416a97ca59a4ac368c4d8d76196c729a80f60851b3733610cb09ec","target":"record","created_at":"2026-05-18T00:10:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d021c0d45fc7c8324b7a0ff1ab76fb95546f4e49c8d8ebaba2edcc77d06f1b19","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-07-14T07:30:35Z","title_canon_sha256":"31274e16ea8e08373541e95bd3a09fd96baddcf5ffc8ed1bbd0821632b88eb66"},"schema_version":"1.0","source":{"id":"1807.05348","kind":"arxiv","version":1}},"canonical_sha256":"14820924db812a1376cac70254dc8dddd55b5826b91c92393abe1129a48a8f8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14820924db812a1376cac70254dc8dddd55b5826b91c92393abe1129a48a8f8c","first_computed_at":"2026-05-18T00:10:43.754697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:43.754697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"skN+oq0zaIYVI9Vij9P7Pzyau930mIIhy7G8w95SG1+Eozb3glJNLFNZb5LYiG1Q0aagOkKryNQTPxf6zdP4AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:43.755142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.05348","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ed22f08d7416a97ca59a4ac368c4d8d76196c729a80f60851b3733610cb09ec","sha256:17c010e47ad42ebb657c93ce8b44e77d75ca4adbe45fb87b5fa714898e9a7c07"],"state_sha256":"91cb231c3ef8b2d92227a19225a8505802286f4aeab825bd0a3b28217f06c9eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kL3mZzpp59Ml+9VsgJ4FIhkt8bM6gcsM7F/H3CEzLTcaiIs+xU+mBF6qAuaLCRzYqy4L/Sh1Kwb+ydfinMo1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:36:05.918008Z","bundle_sha256":"57cfc57e8132ed7880e64640e83a06842d16ae38ae47f269802b1eba5493444d"}}