{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:M3KPMNQE7PXAIQLWOAAR3EHSK6","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":"1f125543a633004a81eb89990d7ad4e503946f0d7c5240b21ea4e24520e5db1a","cross_cats_sorted":["cs.GT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-19T11:22:49Z","title_canon_sha256":"cb3f613cf89a3caeb7809c1324ca2637ff54ca1b8dc32bc3bd3b64ec2fd3b6a7"},"schema_version":"1.0","source":{"id":"1110.4241","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4241","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4241v3","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4241","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"M3KPMNQE7PXA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M3KPMNQE7PXAIQLW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M3KPMNQE","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:9b5897506bc1862cb7fd7095406e617b3fb0f96263d3dcc635fc1e8eb8047283","target":"graph","created_at":"2026-05-18T00:48:06Z","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 upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of precision.","authors_text":"Camilla Di Luca, Marco Dall'Aglio","cross_cats":["cs.GT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-19T11:22:49Z","title":"Finding maxmin allocations in cooperative and competitive fair division"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4241","kind":"arxiv","version":3},"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:a35aa03e7c90fcf882d3b43854e42f2afb1f12148be40b0e84675e886fbea764","target":"record","created_at":"2026-05-18T00:48:06Z","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":"1f125543a633004a81eb89990d7ad4e503946f0d7c5240b21ea4e24520e5db1a","cross_cats_sorted":["cs.GT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-10-19T11:22:49Z","title_canon_sha256":"cb3f613cf89a3caeb7809c1324ca2637ff54ca1b8dc32bc3bd3b64ec2fd3b6a7"},"schema_version":"1.0","source":{"id":"1110.4241","kind":"arxiv","version":3}},"canonical_sha256":"66d4f63604fbee04417670011d90f257bb8d8764f6e074f5e3c684c93f8941e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66d4f63604fbee04417670011d90f257bb8d8764f6e074f5e3c684c93f8941e6","first_computed_at":"2026-05-18T00:48:06.112127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:06.112127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5XktkNH+1MSF+VwjiCj7cnIGkoUXmJo1ylBlK7CVdh968YKMX7YDhcShvaUicl/d43Q5EKZrAlxOv9LOHz0QCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:06.112738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4241","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a35aa03e7c90fcf882d3b43854e42f2afb1f12148be40b0e84675e886fbea764","sha256:9b5897506bc1862cb7fd7095406e617b3fb0f96263d3dcc635fc1e8eb8047283"],"state_sha256":"dbf84863c63ef75c5069702531685df7a515ef9e073c00d538bd9f4315410c9b"}