{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RHHWZZV6GYSX6XCYVU2HSUZKJ2","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":"978fbaf859baac0b088173e5bf7c3cbe3dc5910402445931a3521dd21e6f969e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-04-24T12:10:57Z","title_canon_sha256":"0f960029488b24216e49a97a064afad89d482582d33fc9198988e5dfb6dcecfe"},"schema_version":"1.0","source":{"id":"1804.08977","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.08977","created_at":"2026-05-18T00:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"1804.08977v1","created_at":"2026-05-18T00:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.08977","created_at":"2026-05-18T00:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"RHHWZZV6GYSX","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RHHWZZV6GYSX6XCY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RHHWZZV6","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:f58fb0542e3e32e45c5b25c8646b1dd3cf7af03409931d80920c9212de1086c9","target":"graph","created_at":"2026-05-18T00:17:36Z","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":"A polyhedron is box-integer if its intersection with any integer box $\\{\\ell\\leq x \\leq u\\}$ is integer. We define principally box-integer polyhedra to be the polyhedra $P$ such that $kP$ is box-integer whenever $kP$ is integer. We characterize them in several ways, involving equimodular matrices and box-total dual integral (box-TDI) systems. A rational $r\\times n$ matrix is equimodular if it has full row rank and its nonzero $r\\times r$ determinants all have the same absolute value. A face-defining matrix is a full row rank matrix describing the affine hull of a face of the polyhedron. Box-TD","authors_text":"Louis-Hadrien Robert, Patrick Chervet, Roland Grappe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-04-24T12:10:57Z","title":"Principally Box-integer Polyhedra and Equimodular Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08977","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":"sha256:45e8cccf1aae8c3574285bd4fc466ee3053259669e004e78b64174efed83f7ed","target":"record","created_at":"2026-05-18T00:17:36Z","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":"978fbaf859baac0b088173e5bf7c3cbe3dc5910402445931a3521dd21e6f969e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-04-24T12:10:57Z","title_canon_sha256":"0f960029488b24216e49a97a064afad89d482582d33fc9198988e5dfb6dcecfe"},"schema_version":"1.0","source":{"id":"1804.08977","kind":"arxiv","version":1}},"canonical_sha256":"89cf6ce6be36257f5c58ad3479532a4ea5370279d1b61669c0eca6f334aa0a5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89cf6ce6be36257f5c58ad3479532a4ea5370279d1b61669c0eca6f334aa0a5e","first_computed_at":"2026-05-18T00:17:36.728735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:36.728735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vH3mXVl9SECnFUqKq+PUhTHsA8dRohyIN1y65di1OecmYjkCBv+pcaVVpDuTi/aNQ5wCzKkdV+kZ02Itj2gVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:36.729405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.08977","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45e8cccf1aae8c3574285bd4fc466ee3053259669e004e78b64174efed83f7ed","sha256:f58fb0542e3e32e45c5b25c8646b1dd3cf7af03409931d80920c9212de1086c9"],"state_sha256":"fc59241d94ba69185bfb63172448e926faaa3a10ad3fbf0882a218b607e93b20"}