{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VWKYHQVDZ5WBIBFOFBKCCWEJOO","short_pith_number":"pith:VWKYHQVD","canonical_record":{"source":{"id":"1505.00571","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.CV","submitted_at":"2015-05-04T09:50:25Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"893c80210b06d9c5d017ccebf33a8812c552ef55c06858316ff43c3551d77939","abstract_canon_sha256":"5c69bea7b99003b2c9a2ebf335df68f4ca59c14499dcfb880235cadeb34e009e"},"schema_version":"1.0"},"canonical_sha256":"ad9583c2a3cf6c1404ae2854215889738e48f90a146e9fdddbbfade70b93dcf5","source":{"kind":"arxiv","id":"1505.00571","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00571","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00571v1","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00571","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"VWKYHQVDZ5WB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VWKYHQVDZ5WBIBFO","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VWKYHQVD","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VWKYHQVDZ5WBIBFOFBKCCWEJOO","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00571","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.CV","submitted_at":"2015-05-04T09:50:25Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"893c80210b06d9c5d017ccebf33a8812c552ef55c06858316ff43c3551d77939","abstract_canon_sha256":"5c69bea7b99003b2c9a2ebf335df68f4ca59c14499dcfb880235cadeb34e009e"},"schema_version":"1.0"},"canonical_sha256":"ad9583c2a3cf6c1404ae2854215889738e48f90a146e9fdddbbfade70b93dcf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:02.555939Z","signature_b64":"tBnbvifj+boteQ4EOEvluckUXMy/dwVXF1vlacKq23wXekba7PlTV5nPQMqELqyPtFRXnZ8ZW1vKBrZwC0e1CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad9583c2a3cf6c1404ae2854215889738e48f90a146e9fdddbbfade70b93dcf5","last_reissued_at":"2026-05-18T02:17:02.555342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:02.555342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00571","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HjldVXjRU7ypJq6jN9rx6rI/J3CZ/qw7lRhR8c662kO9Cs2jIuK31U0WRSDJHkYLbqxAZAlku0Up583FGTm5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:43:40.047691Z"},"content_sha256":"cd82d70697d0ba259325d6f91439d37b9c590325f2b08fd6457eae3f0451c665","schema_version":"1.0","event_id":"sha256:cd82d70697d0ba259325d6f91439d37b9c590325f2b08fd6457eae3f0451c665"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VWKYHQVDZ5WBIBFOFBKCCWEJOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher Order Maximum Persistency and Comparison Theorems","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"cs.CV","authors_text":"Alexander Shekhovtsov","submitted_at":"2015-05-04T09:50:25Z","abstract_excerpt":"We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1 polynomial programming). For polyhedral relaxations of such problems it is generally not true that variables integer in the relaxed solution will retain the same values in the optimal discrete solution. Those which do are called persistent. Such persistent variables define a part of a globally optimal solution. Once identified, they can be excluded from the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00571","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pq0spddwswE7qVYDPZyzQtEuB39Bpwbyc3FbGDb1abXoyQIQfI1TngkuXvARd25pBYy0CLxLxXEkJ55BQhp8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:43:40.048436Z"},"content_sha256":"594c53559d82201fbc6577e1a330d8d7653e18474d380274c84e83e02adeeed4","schema_version":"1.0","event_id":"sha256:594c53559d82201fbc6577e1a330d8d7653e18474d380274c84e83e02adeeed4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWKYHQVDZ5WBIBFOFBKCCWEJOO/bundle.json","state_url":"https://pith.science/pith/VWKYHQVDZ5WBIBFOFBKCCWEJOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWKYHQVDZ5WBIBFOFBKCCWEJOO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T02:43:40Z","links":{"resolver":"https://pith.science/pith/VWKYHQVDZ5WBIBFOFBKCCWEJOO","bundle":"https://pith.science/pith/VWKYHQVDZ5WBIBFOFBKCCWEJOO/bundle.json","state":"https://pith.science/pith/VWKYHQVDZ5WBIBFOFBKCCWEJOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWKYHQVDZ5WBIBFOFBKCCWEJOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VWKYHQVDZ5WBIBFOFBKCCWEJOO","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":"5c69bea7b99003b2c9a2ebf335df68f4ca59c14499dcfb880235cadeb34e009e","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.CV","submitted_at":"2015-05-04T09:50:25Z","title_canon_sha256":"893c80210b06d9c5d017ccebf33a8812c552ef55c06858316ff43c3551d77939"},"schema_version":"1.0","source":{"id":"1505.00571","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00571","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00571v1","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00571","created_at":"2026-05-18T02:17:02Z"},{"alias_kind":"pith_short_12","alias_value":"VWKYHQVDZ5WB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VWKYHQVDZ5WBIBFO","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VWKYHQVD","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:594c53559d82201fbc6577e1a330d8d7653e18474d380274c84e83e02adeeed4","target":"graph","created_at":"2026-05-18T02:17:02Z","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 address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1 polynomial programming). For polyhedral relaxations of such problems it is generally not true that variables integer in the relaxed solution will retain the same values in the optimal discrete solution. Those which do are called persistent. Such persistent variables define a part of a globally optimal solution. Once identified, they can be excluded from the pr","authors_text":"Alexander Shekhovtsov","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.CV","submitted_at":"2015-05-04T09:50:25Z","title":"Higher Order Maximum Persistency and Comparison Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00571","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:cd82d70697d0ba259325d6f91439d37b9c590325f2b08fd6457eae3f0451c665","target":"record","created_at":"2026-05-18T02:17:02Z","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":"5c69bea7b99003b2c9a2ebf335df68f4ca59c14499dcfb880235cadeb34e009e","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.CV","submitted_at":"2015-05-04T09:50:25Z","title_canon_sha256":"893c80210b06d9c5d017ccebf33a8812c552ef55c06858316ff43c3551d77939"},"schema_version":"1.0","source":{"id":"1505.00571","kind":"arxiv","version":1}},"canonical_sha256":"ad9583c2a3cf6c1404ae2854215889738e48f90a146e9fdddbbfade70b93dcf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad9583c2a3cf6c1404ae2854215889738e48f90a146e9fdddbbfade70b93dcf5","first_computed_at":"2026-05-18T02:17:02.555342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:02.555342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tBnbvifj+boteQ4EOEvluckUXMy/dwVXF1vlacKq23wXekba7PlTV5nPQMqELqyPtFRXnZ8ZW1vKBrZwC0e1CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:02.555939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00571","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd82d70697d0ba259325d6f91439d37b9c590325f2b08fd6457eae3f0451c665","sha256:594c53559d82201fbc6577e1a330d8d7653e18474d380274c84e83e02adeeed4"],"state_sha256":"6b3819c40faee0441db0aa9d110d08e24e5d8bb3be85c87b97cd717c00ea3bee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"08yzpItEbZwvmRBW1GDOY0F0c5XDLFgE1RcLaCztPbveys5Na7O3mGQ4XOjRbBGoQEVDdLAE533P8aE8RcbRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:43:40.052383Z","bundle_sha256":"9e66e7b578bceb6df9be418ba6e83348cca6beb0f2e8d3e146bff256ecc28d24"}}