{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:HBTOBDBSDFSZ6ELOVRUHALBQ7K","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":"1cffabd93c63c8d04f21d7b4d8856e7c6edd3825a2db1e8c2c0e2102606abca4","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"1997-04-29T00:00:00Z","title_canon_sha256":"4e6ca23ed6c2a1caa6a4ee9846db3880213d62536b503fed3ea0a7d23fc13f94"},"schema_version":"1.0","source":{"id":"math/9704226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9704226","created_at":"2026-05-18T01:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/9704226v1","created_at":"2026-05-18T01:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9704226","created_at":"2026-05-18T01:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"HBTOBDBSDFSZ","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"HBTOBDBSDFSZ6ELO","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"HBTOBDBS","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:a0f41b59e1bf7ac03add7ef5f636a012de937fc3038d1093c50c2ed51000b555","target":"graph","created_at":"2026-05-18T01:05:36Z","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":"We consider the {\\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary constraints on the number of elements in each part. In addressing this problem, we study the {\\em Shaped Partition Polytope} defined as the convex hull of solutions. The Shaped Partition Problem captures ${\\cal N}{\\cal P}$-hard problems such as the Max-Cut problem and the Traveling Salesperson problem, and the Shaped Partition Polytope may have exponentially ma","authors_text":"Frank K. Hwang, Shmuel Onn, Uriel G. Rothblum","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"1997-04-29T00:00:00Z","title":"A Polynomial Time Algorithm for Vertex Enumeration and Optimization over Shaped Partition Polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9704226","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":"sha256:0f854aad2e76874e1cb63c8691e935ab8d03f1c2700c0aae2ab36533cb372c90","target":"record","created_at":"2026-05-18T01:05:36Z","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":"1cffabd93c63c8d04f21d7b4d8856e7c6edd3825a2db1e8c2c0e2102606abca4","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"1997-04-29T00:00:00Z","title_canon_sha256":"4e6ca23ed6c2a1caa6a4ee9846db3880213d62536b503fed3ea0a7d23fc13f94"},"schema_version":"1.0","source":{"id":"math/9704226","kind":"arxiv","version":1}},"canonical_sha256":"3866e08c3219659f116eac68702c30faaf68b957af72dca6842fbe0fbfc30067","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3866e08c3219659f116eac68702c30faaf68b957af72dca6842fbe0fbfc30067","first_computed_at":"2026-05-18T01:05:36.939874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:36.939874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ijmq9WdYfbW7NJjJgAIc+F2KCZuGrwjbeFqlxmwdz3YVcP2x6NPmcVl+3mGK7k036TGb9Ww6kt1EL2A480lNBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:36.940331Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9704226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f854aad2e76874e1cb63c8691e935ab8d03f1c2700c0aae2ab36533cb372c90","sha256:a0f41b59e1bf7ac03add7ef5f636a012de937fc3038d1093c50c2ed51000b555"],"state_sha256":"33bd94ee476ec12b23938a5ebb2e6e361c1f9d437a6b0dfaf90de084360e3ea5"}