{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:4F7E47Y3QFW3CEJTSMKZ6ZT5FO","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":"922da142c97f7f0432bf16c672c565eeb50a8ffdd425769b1af5009695ecd486","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.OC","submitted_at":"2007-10-16T10:21:54Z","title_canon_sha256":"82aa6ed04c03b9db8efed6a4268939e5c6906555c0adeaef31fd56581e01bbed"},"schema_version":"1.0","source":{"id":"0710.3003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.3003","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"0710.3003v1","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.3003","created_at":"2026-05-18T04:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"4F7E47Y3QFW3","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"4F7E47Y3QFW3CEJT","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"4F7E47Y3","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:ea8805866e0b29c2a2a80e1ed40e4818cf0f651bf4893f649aab109fb5f426df","target":"graph","created_at":"2026-05-18T04:31:30Z","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 consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.","authors_text":"Raymond Hemmecke, Robert Weismantel, Shmuel Onn","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.OC","submitted_at":"2007-10-16T10:21:54Z","title":"A polynomial oracle-time algorithm for convex integer minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.3003","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:d6afaae752443bdf60c1b60ee4978481beb48e167831a629fbd3121db9e02928","target":"record","created_at":"2026-05-18T04:31:30Z","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":"922da142c97f7f0432bf16c672c565eeb50a8ffdd425769b1af5009695ecd486","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.OC","submitted_at":"2007-10-16T10:21:54Z","title_canon_sha256":"82aa6ed04c03b9db8efed6a4268939e5c6906555c0adeaef31fd56581e01bbed"},"schema_version":"1.0","source":{"id":"0710.3003","kind":"arxiv","version":1}},"canonical_sha256":"e17e4e7f1b816db1113393159f667d2b85b84415a2d86013923944e32ddbc03f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e17e4e7f1b816db1113393159f667d2b85b84415a2d86013923944e32ddbc03f","first_computed_at":"2026-05-18T04:31:30.073288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:30.073288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"02eHvfClsm8xk091BrUomodT66OgPeuwAcCcxvXYrFodMRmoCc0eZvdBXbbiH2C9eWW+uq8UWiE8FJX2MWyNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:30.073958Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.3003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6afaae752443bdf60c1b60ee4978481beb48e167831a629fbd3121db9e02928","sha256:ea8805866e0b29c2a2a80e1ed40e4818cf0f651bf4893f649aab109fb5f426df"],"state_sha256":"d89f541583c4c61db4139843555449a6be240cf4f1d7aa9a574e1091b531c457"}