{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4MF22OKD5QE6HTDLWZCJXUI7OO","short_pith_number":"pith:4MF22OKD","canonical_record":{"source":{"id":"1205.6142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-28T15:35:05Z","cross_cats_sorted":[],"title_canon_sha256":"618a094cea477a57ecc99b020a00a052dbb5f021b1072adf259cb7bdced6df00","abstract_canon_sha256":"e621e15c066a003f78c4b057210da062d2b5738aa7c2375fb8c5ec7c95e3ff1e"},"schema_version":"1.0"},"canonical_sha256":"e30bad3943ec09e3cc6bb6449bd11f73b7253ab3bd2575ae9d977adbd18d4ce6","source":{"kind":"arxiv","id":"1205.6142","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6142","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6142v1","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6142","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"4MF22OKD5QE6","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4MF22OKD5QE6HTDL","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4MF22OKD","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4MF22OKD5QE6HTDLWZCJXUI7OO","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-28T15:35:05Z","cross_cats_sorted":[],"title_canon_sha256":"618a094cea477a57ecc99b020a00a052dbb5f021b1072adf259cb7bdced6df00","abstract_canon_sha256":"e621e15c066a003f78c4b057210da062d2b5738aa7c2375fb8c5ec7c95e3ff1e"},"schema_version":"1.0"},"canonical_sha256":"e30bad3943ec09e3cc6bb6449bd11f73b7253ab3bd2575ae9d977adbd18d4ce6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:48.213517Z","signature_b64":"ARWiACgTdh1ko5O5AEYrkkF7jPwv2LHhTdBTJ9zVGgpQKL8ftXjHO9HxDVNqBAZ0IBRH47aRvL2epZnNnP/BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e30bad3943ec09e3cc6bb6449bd11f73b7253ab3bd2575ae9d977adbd18d4ce6","last_reissued_at":"2026-05-18T03:54:48.213019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:48.213019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6142","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":"2026-05-18T03:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oqfbE+u/yLNBriucjLQLDetA229647bA7Ydw3Aqz1SpCHCAoJjviA4IXlgfQ+FiziyRpTF6wDmMlXAFVss/+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:17:42.799005Z"},"content_sha256":"581e58762d570a768b55e472f8657a307b5f777b3426e161595f4e85bbf3b2e7","schema_version":"1.0","event_id":"sha256:581e58762d570a768b55e472f8657a307b5f777b3426e161595f4e85bbf3b2e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4MF22OKD5QE6HTDLWZCJXUI7OO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some advances on the set covering polyhedron of circulant matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Graciela Nasini, Paola Tolomei, Silvia Bianchi","submitted_at":"2012-05-28T15:35:05Z","abstract_excerpt":"Working on the set covering polyhedron of consecutive ones circulant matrices, Argiroffo and Bianchi found a class of facet defining inequalities, induced by a particular family of circulant minors. In this work we extend these results to inequalities associated with every circulant minor. We also obtain polynomial separation algorithms for particular classes of such inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6142","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":"2026-05-18T03:54:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U9nCj31JFtTOgpdBSwgka16MZUTzTnNzYB2s8qdYcsbFomQx+VlXe4cR3mY9KfFIsILvQjygfqIJVT1DIxu7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:17:42.799655Z"},"content_sha256":"627aa455d7bac9552dfe0cc3dc62cdb7ec951d851ab283ba6f4a26c9d2302731","schema_version":"1.0","event_id":"sha256:627aa455d7bac9552dfe0cc3dc62cdb7ec951d851ab283ba6f4a26c9d2302731"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4MF22OKD5QE6HTDLWZCJXUI7OO/bundle.json","state_url":"https://pith.science/pith/4MF22OKD5QE6HTDLWZCJXUI7OO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4MF22OKD5QE6HTDLWZCJXUI7OO/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":"2026-05-31T10:17:42Z","links":{"resolver":"https://pith.science/pith/4MF22OKD5QE6HTDLWZCJXUI7OO","bundle":"https://pith.science/pith/4MF22OKD5QE6HTDLWZCJXUI7OO/bundle.json","state":"https://pith.science/pith/4MF22OKD5QE6HTDLWZCJXUI7OO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4MF22OKD5QE6HTDLWZCJXUI7OO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4MF22OKD5QE6HTDLWZCJXUI7OO","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":"e621e15c066a003f78c4b057210da062d2b5738aa7c2375fb8c5ec7c95e3ff1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-28T15:35:05Z","title_canon_sha256":"618a094cea477a57ecc99b020a00a052dbb5f021b1072adf259cb7bdced6df00"},"schema_version":"1.0","source":{"id":"1205.6142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6142","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6142v1","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6142","created_at":"2026-05-18T03:54:48Z"},{"alias_kind":"pith_short_12","alias_value":"4MF22OKD5QE6","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4MF22OKD5QE6HTDL","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4MF22OKD","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:627aa455d7bac9552dfe0cc3dc62cdb7ec951d851ab283ba6f4a26c9d2302731","target":"graph","created_at":"2026-05-18T03:54:48Z","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":"Working on the set covering polyhedron of consecutive ones circulant matrices, Argiroffo and Bianchi found a class of facet defining inequalities, induced by a particular family of circulant minors. In this work we extend these results to inequalities associated with every circulant minor. We also obtain polynomial separation algorithms for particular classes of such inequalities.","authors_text":"Graciela Nasini, Paola Tolomei, Silvia Bianchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-28T15:35:05Z","title":"Some advances on the set covering polyhedron of circulant matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6142","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":"sha256:581e58762d570a768b55e472f8657a307b5f777b3426e161595f4e85bbf3b2e7","target":"record","created_at":"2026-05-18T03:54:48Z","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":"e621e15c066a003f78c4b057210da062d2b5738aa7c2375fb8c5ec7c95e3ff1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-28T15:35:05Z","title_canon_sha256":"618a094cea477a57ecc99b020a00a052dbb5f021b1072adf259cb7bdced6df00"},"schema_version":"1.0","source":{"id":"1205.6142","kind":"arxiv","version":1}},"canonical_sha256":"e30bad3943ec09e3cc6bb6449bd11f73b7253ab3bd2575ae9d977adbd18d4ce6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e30bad3943ec09e3cc6bb6449bd11f73b7253ab3bd2575ae9d977adbd18d4ce6","first_computed_at":"2026-05-18T03:54:48.213019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:48.213019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ARWiACgTdh1ko5O5AEYrkkF7jPwv2LHhTdBTJ9zVGgpQKL8ftXjHO9HxDVNqBAZ0IBRH47aRvL2epZnNnP/BDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:48.213517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:581e58762d570a768b55e472f8657a307b5f777b3426e161595f4e85bbf3b2e7","sha256:627aa455d7bac9552dfe0cc3dc62cdb7ec951d851ab283ba6f4a26c9d2302731"],"state_sha256":"7d23575bed4d5b9096a5825078cc8efc7233adcaae735e37489c2cbcbd0bca67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WVUEA5fSUtvfoBgF3saV3e9xn1Y/mfC0v8fFcSb4o/R7I5PMUy7BUHE5a10+slDwEn2E8trUrKhoJhTem8KLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:17:42.802511Z","bundle_sha256":"a68592e591970733d4ac83d26b218b639846f0d408eedc70268f6198b4a31f28"}}