{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:Y4EQ7FPPP7XCOQ2SA3XPWYC4QN","short_pith_number":"pith:Y4EQ7FPP","schema_version":"1.0","canonical_sha256":"c7090f95ef7fee27435206eefb605c834124ad7ada75c8d44f69acdcdd75edf9","source":{"kind":"arxiv","id":"math/0603678","version":2},"attestation_state":"computed","paper":{"title":"Packing and Partitioning Orbitopes","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Marc E. Pfetsch, Volker Kaibel","submitted_at":"2006-03-29T10:23:16Z","abstract_excerpt":"We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a well-known formulation of the graph coloring problem.\n  We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the"},"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":"math/0603678","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OC","submitted_at":"2006-03-29T10:23:16Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"28195931697017551f569425d644551f631ef0426ca12cbdbfc257bb21c4b10d","abstract_canon_sha256":"d4b3d3e495a8090171d19c4b19c1dce5d5f92af0fe644a3db3b0292115428c53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:54:01.367362Z","signature_b64":"uTvcRC2R/JtFg/tuwQ4IqvtIjg/SwMpCJwP9KimWyVGXRsV1u3HzZt/gXSjfRNwsQQZd6cFG196CtsaxkmBpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7090f95ef7fee27435206eefb605c834124ad7ada75c8d44f69acdcdd75edf9","last_reissued_at":"2026-07-04T14:54:01.366375Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:54:01.366375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Packing and Partitioning Orbitopes","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Marc E. Pfetsch, Volker Kaibel","submitted_at":"2006-03-29T10:23:16Z","abstract_excerpt":"We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a well-known formulation of the graph coloring problem.\n  We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603678","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0603678/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0603678","created_at":"2026-07-04T14:54:01.366437+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0603678v2","created_at":"2026-07-04T14:54:01.366437+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0603678","created_at":"2026-07-04T14:54:01.366437+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y4EQ7FPPP7XC","created_at":"2026-07-04T14:54:01.366437+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y4EQ7FPPP7XCOQ2S","created_at":"2026-07-04T14:54:01.366437+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y4EQ7FPP","created_at":"2026-07-04T14:54:01.366437+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/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN","json":"https://pith.science/pith/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN.json","graph_json":"https://pith.science/api/pith-number/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/graph.json","events_json":"https://pith.science/api/pith-number/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/events.json","paper":"https://pith.science/paper/Y4EQ7FPP"},"agent_actions":{"view_html":"https://pith.science/pith/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN","download_json":"https://pith.science/pith/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN.json","view_paper":"https://pith.science/paper/Y4EQ7FPP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0603678&json=true","fetch_graph":"https://pith.science/api/pith-number/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/graph.json","fetch_events":"https://pith.science/api/pith-number/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/action/storage_attestation","attest_author":"https://pith.science/pith/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/action/author_attestation","sign_citation":"https://pith.science/pith/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/action/citation_signature","submit_replication":"https://pith.science/pith/Y4EQ7FPPP7XCOQ2SA3XPWYC4QN/action/replication_record"}},"created_at":"2026-07-04T14:54:01.366437+00:00","updated_at":"2026-07-04T14:54:01.366437+00:00"}