{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NL4SWGCYOZ3RT3STH6E5LFFVJP","short_pith_number":"pith:NL4SWGCY","canonical_record":{"source":{"id":"2607.09222","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-10T09:13:00Z","cross_cats_sorted":[],"title_canon_sha256":"f259090a2d7d9591671e48b9aebf413876818ea9164afabbec1c880d8b26acb6","abstract_canon_sha256":"1a968f98b1776c4964a82e1dce5bae40b627d4e8e7ef529a93eece8c62c8e913"},"schema_version":"1.0"},"canonical_sha256":"6af92b1858767719ee533f89d594b54bc83a2f5758d4c227ea743252cc8e5993","source":{"kind":"arxiv","id":"2607.09222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09222","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09222v1","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09222","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"NL4SWGCYOZ3R","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"pith_short_16","alias_value":"NL4SWGCYOZ3RT3ST","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"pith_short_8","alias_value":"NL4SWGCY","created_at":"2026-07-13T01:18:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NL4SWGCYOZ3RT3STH6E5LFFVJP","target":"record","payload":{"canonical_record":{"source":{"id":"2607.09222","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-10T09:13:00Z","cross_cats_sorted":[],"title_canon_sha256":"f259090a2d7d9591671e48b9aebf413876818ea9164afabbec1c880d8b26acb6","abstract_canon_sha256":"1a968f98b1776c4964a82e1dce5bae40b627d4e8e7ef529a93eece8c62c8e913"},"schema_version":"1.0"},"canonical_sha256":"6af92b1858767719ee533f89d594b54bc83a2f5758d4c227ea743252cc8e5993","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:18:53.075194Z","signature_b64":"VAIncJz4tDLBjDLeOhe5hfxWU3zhnEGIeztbk3w0PslhwpLVt/IF6rUyAMx4EYPSftHbdfwhOGYWz/yfoRcPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6af92b1858767719ee533f89d594b54bc83a2f5758d4c227ea743252cc8e5993","last_reissued_at":"2026-07-13T01:18:53.073785Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:18:53.073785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.09222","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":"2026-07-13T01:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0uQnPJ+UBAjCk8Y3dIcIV9iAPB1IFp77RSh8kHKGorqtUEIyz3nGpYGEdGSfUW5HCKC8M67jLAJ1WazqCFgNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:14:02.203596Z"},"content_sha256":"60db898228e894a56efa1f2ffb5ed7c168688996fed9382fab7ca35a12675407","schema_version":"1.0","event_id":"sha256:60db898228e894a56efa1f2ffb5ed7c168688996fed9382fab7ca35a12675407"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NL4SWGCYOZ3RT3STH6E5LFFVJP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polyhedral extended formulations that approximate the Gomory closure for packing problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Friedrich Eisenbrand, Jiaye Wei, Lars Rohwedder, Samuel Fiorini","submitted_at":"2026-07-10T09:13:00Z","abstract_excerpt":"We consider $0/1$ packing problems $\\max\\{c^T x \\colon Ax \\leq 1, \\, x \\in \\{0,1\\}^n\\}$, with $A \\in \\mathbb{R}_{\\geq 0}^{m \\times n}$. A way to solve such problems is via tightening the linear programming relaxation $P$ with Gomory \\emph{cutting-planes}. The Gomory-closure $P'$ of $P$ is the intersection of $P$ with all its cutting planes. The optimization problem over $P'$ is NP-hard. Mastrolilli (2020) has shown that for fixed ${\\epsilon}>0$, the Lasserre hierarchy yields a polynomial-size convex but non-polyhedral extended formulation that approximates $P'$ up to a factor of $1+{\\epsilon}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09222","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09222/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-13T01:18:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RVHHa4NMfk3jCdm1+eelnrWg3cEy0FkWuywv+mXsxYoVZfUfhzviEmXSJVlAFiPOjt/PzfcTLf+4fLFxckWjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:14:02.204096Z"},"content_sha256":"b842f6d8c0d4399c8d33cf7a475cd6d010bf7c99c8512824ada859509438550d","schema_version":"1.0","event_id":"sha256:b842f6d8c0d4399c8d33cf7a475cd6d010bf7c99c8512824ada859509438550d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NL4SWGCYOZ3RT3STH6E5LFFVJP/bundle.json","state_url":"https://pith.science/pith/NL4SWGCYOZ3RT3STH6E5LFFVJP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NL4SWGCYOZ3RT3STH6E5LFFVJP/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":"2026-08-18T14:14:02Z","links":{"resolver":"https://pith.science/pith/NL4SWGCYOZ3RT3STH6E5LFFVJP","bundle":"https://pith.science/pith/NL4SWGCYOZ3RT3STH6E5LFFVJP/bundle.json","state":"https://pith.science/pith/NL4SWGCYOZ3RT3STH6E5LFFVJP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NL4SWGCYOZ3RT3STH6E5LFFVJP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NL4SWGCYOZ3RT3STH6E5LFFVJP","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":"1a968f98b1776c4964a82e1dce5bae40b627d4e8e7ef529a93eece8c62c8e913","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-10T09:13:00Z","title_canon_sha256":"f259090a2d7d9591671e48b9aebf413876818ea9164afabbec1c880d8b26acb6"},"schema_version":"1.0","source":{"id":"2607.09222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.09222","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"arxiv_version","alias_value":"2607.09222v1","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09222","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"pith_short_12","alias_value":"NL4SWGCYOZ3R","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"pith_short_16","alias_value":"NL4SWGCYOZ3RT3ST","created_at":"2026-07-13T01:18:53Z"},{"alias_kind":"pith_short_8","alias_value":"NL4SWGCY","created_at":"2026-07-13T01:18:53Z"}],"graph_snapshots":[{"event_id":"sha256:b842f6d8c0d4399c8d33cf7a475cd6d010bf7c99c8512824ada859509438550d","target":"graph","created_at":"2026-07-13T01:18:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.09222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider $0/1$ packing problems $\\max\\{c^T x \\colon Ax \\leq 1, \\, x \\in \\{0,1\\}^n\\}$, with $A \\in \\mathbb{R}_{\\geq 0}^{m \\times n}$. A way to solve such problems is via tightening the linear programming relaxation $P$ with Gomory \\emph{cutting-planes}. The Gomory-closure $P'$ of $P$ is the intersection of $P$ with all its cutting planes. The optimization problem over $P'$ is NP-hard. Mastrolilli (2020) has shown that for fixed ${\\epsilon}>0$, the Lasserre hierarchy yields a polynomial-size convex but non-polyhedral extended formulation that approximates $P'$ up to a factor of $1+{\\epsilon}$","authors_text":"Friedrich Eisenbrand, Jiaye Wei, Lars Rohwedder, Samuel Fiorini","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-10T09:13:00Z","title":"Polyhedral extended formulations that approximate the Gomory closure for packing problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09222","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":"sha256:60db898228e894a56efa1f2ffb5ed7c168688996fed9382fab7ca35a12675407","target":"record","created_at":"2026-07-13T01:18:53Z","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":"1a968f98b1776c4964a82e1dce5bae40b627d4e8e7ef529a93eece8c62c8e913","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-10T09:13:00Z","title_canon_sha256":"f259090a2d7d9591671e48b9aebf413876818ea9164afabbec1c880d8b26acb6"},"schema_version":"1.0","source":{"id":"2607.09222","kind":"arxiv","version":1}},"canonical_sha256":"6af92b1858767719ee533f89d594b54bc83a2f5758d4c227ea743252cc8e5993","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6af92b1858767719ee533f89d594b54bc83a2f5758d4c227ea743252cc8e5993","first_computed_at":"2026-07-13T01:18:53.073785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-13T01:18:53.073785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VAIncJz4tDLBjDLeOhe5hfxWU3zhnEGIeztbk3w0PslhwpLVt/IF6rUyAMx4EYPSftHbdfwhOGYWz/yfoRcPAg==","signature_status":"signed_v1","signed_at":"2026-07-13T01:18:53.075194Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.09222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60db898228e894a56efa1f2ffb5ed7c168688996fed9382fab7ca35a12675407","sha256:b842f6d8c0d4399c8d33cf7a475cd6d010bf7c99c8512824ada859509438550d"],"state_sha256":"caa969f2536e13eda05884f8d0709ff3c330ede04e3f6c59130870472ae2a64f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KMDRRGemCFalRuBJYcEB4muMM/NNRvZzSRmkylm4jTjhBUpoltfgHSSmbZo4SFm32SWN1nxoaVAMSxBrzoiKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T14:14:02.209552Z","bundle_sha256":"99c31637e83b31782fba24fbc7514e039fb89b986eff6555753af486eb4b2727"}}