{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YRXM5KXLRH7HPGB7OBESVRLOJH","short_pith_number":"pith:YRXM5KXL","canonical_record":{"source":{"id":"1504.07888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-29T15:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"bf512ad10b99d9b898b65c0089f893acb1cfffda90b0451b1f13a2f62b116566","abstract_canon_sha256":"686f39a70e8153b00364c69ed5556b8892acba4ea00629f92f0b6255e99ef481"},"schema_version":"1.0"},"canonical_sha256":"c46eceaaeb89fe77983f70492ac56e49f92f5f711b80a7b7da60918e59f91e32","source":{"kind":"arxiv","id":"1504.07888","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07888","created_at":"2026-05-18T01:03:23Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07888v1","created_at":"2026-05-18T01:03:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07888","created_at":"2026-05-18T01:03:23Z"},{"alias_kind":"pith_short_12","alias_value":"YRXM5KXLRH7H","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YRXM5KXLRH7HPGB7","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YRXM5KXL","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YRXM5KXLRH7HPGB7OBESVRLOJH","target":"record","payload":{"canonical_record":{"source":{"id":"1504.07888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-29T15:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"bf512ad10b99d9b898b65c0089f893acb1cfffda90b0451b1f13a2f62b116566","abstract_canon_sha256":"686f39a70e8153b00364c69ed5556b8892acba4ea00629f92f0b6255e99ef481"},"schema_version":"1.0"},"canonical_sha256":"c46eceaaeb89fe77983f70492ac56e49f92f5f711b80a7b7da60918e59f91e32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:23.821876Z","signature_b64":"0cd3p9UpMdNb1mmS+TpaCdil+yoRt0530+2TY8N62mWEV34h6fblvikpWimLYrnchcULRdYCV3AW3cKo26gEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c46eceaaeb89fe77983f70492ac56e49f92f5f711b80a7b7da60918e59f91e32","last_reissued_at":"2026-05-18T01:03:23.821411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:23.821411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.07888","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":"2026-05-18T01:03:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqbRLtnPZmvrZ6lbONJoz/Atarrvm0maSrtehP+Zt9iilX8rgrjSwHX1eBVJTiicLmJzDLyvYP//YE6g6r5PDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:36:02.863134Z"},"content_sha256":"7055e8ee2f99e7da2df7a340ab01211241381640aed587063033707888feba0d","schema_version":"1.0","event_id":"sha256:7055e8ee2f99e7da2df7a340ab01211241381640aed587063033707888feba0d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YRXM5KXLRH7HPGB7OBESVRLOJH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lift-and-project ranks of the stable set polytope of joined a-perfect graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"M. Escalante, M.S. Montelar, S. Bianchi","submitted_at":"2015-04-29T15:21:26Z","abstract_excerpt":"In this paper we study lift-and-project polyhedral operators defined by Lov?asz and Schrijver and Balas, Ceria and Cornu?ejols on the clique relaxation of the stable set polytope of web graphs. We compute the disjunctive rank of all webs and consequently of antiweb graphs. We also obtain the disjunctive rank of the antiweb constraints for which the complexity of the separation problem is still unknown. Finally, we use our results to provide bounds of the disjunctive rank of larger classes of graphs as joined a-perfect graphs, where near-bipartite graphs belong."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07888","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":"2026-05-18T01:03:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AcfK7wExQVHlbrqxN67wZotx/1GHoFmFxvudGdk/qQrNAJzjnSMntKoE2EEcaDJMHjmZKL4hSr2QZVnTFAF0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:36:02.863841Z"},"content_sha256":"ea6b33d813a8b7b1d884edd475d82a4f2c02f5ce21d351cb8a37b50336884aa8","schema_version":"1.0","event_id":"sha256:ea6b33d813a8b7b1d884edd475d82a4f2c02f5ce21d351cb8a37b50336884aa8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YRXM5KXLRH7HPGB7OBESVRLOJH/bundle.json","state_url":"https://pith.science/pith/YRXM5KXLRH7HPGB7OBESVRLOJH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YRXM5KXLRH7HPGB7OBESVRLOJH/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":"2026-06-11T16:36:02Z","links":{"resolver":"https://pith.science/pith/YRXM5KXLRH7HPGB7OBESVRLOJH","bundle":"https://pith.science/pith/YRXM5KXLRH7HPGB7OBESVRLOJH/bundle.json","state":"https://pith.science/pith/YRXM5KXLRH7HPGB7OBESVRLOJH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YRXM5KXLRH7HPGB7OBESVRLOJH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YRXM5KXLRH7HPGB7OBESVRLOJH","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":"686f39a70e8153b00364c69ed5556b8892acba4ea00629f92f0b6255e99ef481","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-29T15:21:26Z","title_canon_sha256":"bf512ad10b99d9b898b65c0089f893acb1cfffda90b0451b1f13a2f62b116566"},"schema_version":"1.0","source":{"id":"1504.07888","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07888","created_at":"2026-05-18T01:03:23Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07888v1","created_at":"2026-05-18T01:03:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07888","created_at":"2026-05-18T01:03:23Z"},{"alias_kind":"pith_short_12","alias_value":"YRXM5KXLRH7H","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YRXM5KXLRH7HPGB7","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YRXM5KXL","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:ea6b33d813a8b7b1d884edd475d82a4f2c02f5ce21d351cb8a37b50336884aa8","target":"graph","created_at":"2026-05-18T01:03:23Z","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":"In this paper we study lift-and-project polyhedral operators defined by Lov?asz and Schrijver and Balas, Ceria and Cornu?ejols on the clique relaxation of the stable set polytope of web graphs. We compute the disjunctive rank of all webs and consequently of antiweb graphs. We also obtain the disjunctive rank of the antiweb constraints for which the complexity of the separation problem is still unknown. Finally, we use our results to provide bounds of the disjunctive rank of larger classes of graphs as joined a-perfect graphs, where near-bipartite graphs belong.","authors_text":"M. Escalante, M.S. Montelar, S. Bianchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-29T15:21:26Z","title":"Lift-and-project ranks of the stable set polytope of joined a-perfect graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07888","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":"sha256:7055e8ee2f99e7da2df7a340ab01211241381640aed587063033707888feba0d","target":"record","created_at":"2026-05-18T01:03:23Z","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":"686f39a70e8153b00364c69ed5556b8892acba4ea00629f92f0b6255e99ef481","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-29T15:21:26Z","title_canon_sha256":"bf512ad10b99d9b898b65c0089f893acb1cfffda90b0451b1f13a2f62b116566"},"schema_version":"1.0","source":{"id":"1504.07888","kind":"arxiv","version":1}},"canonical_sha256":"c46eceaaeb89fe77983f70492ac56e49f92f5f711b80a7b7da60918e59f91e32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c46eceaaeb89fe77983f70492ac56e49f92f5f711b80a7b7da60918e59f91e32","first_computed_at":"2026-05-18T01:03:23.821411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:23.821411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0cd3p9UpMdNb1mmS+TpaCdil+yoRt0530+2TY8N62mWEV34h6fblvikpWimLYrnchcULRdYCV3AW3cKo26gEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:23.821876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07888","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7055e8ee2f99e7da2df7a340ab01211241381640aed587063033707888feba0d","sha256:ea6b33d813a8b7b1d884edd475d82a4f2c02f5ce21d351cb8a37b50336884aa8"],"state_sha256":"24c0723e6bdea06133dc9908881b2a9c1f1055e05f3f0c4f417b2263f52c1b9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rADDTjoNTCqTA/2Y8N8uAGFPz+0hEYdJPO7T3lTSG8Qt6I6DG5xxsr8tf3Mq8VeorGQR/ue4djSoTtz7qb6OAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:36:02.867547Z","bundle_sha256":"656fc41e4e1a71b1590373badec83320ea0dcc789d6147476bbfd3b8742bf544"}}