{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AZ5LWOKLQ56L7HUNUUSSFFNGAB","short_pith_number":"pith:AZ5LWOKL","canonical_record":{"source":{"id":"1910.07600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-16T20:25:45Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"ff9a8dc857fdd827654b160680b5e5eb69fbff6c6dce932bc9fcfeafc76f6e1a","abstract_canon_sha256":"9b816b333ff551ab6a7d97ad4a18135f7d86f16a58ef1911e1ce0502a045f474"},"schema_version":"1.0"},"canonical_sha256":"067abb394b877cbf9e8da5252295a60049e47d48b977419bccba3efb51fe3907","source":{"kind":"arxiv","id":"1910.07600","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.07600","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1910.07600v1","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.07600","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"AZ5LWOKLQ56L","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"pith_short_16","alias_value":"AZ5LWOKLQ56L7HUN","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"pith_short_8","alias_value":"AZ5LWOKL","created_at":"2026-07-05T00:12:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AZ5LWOKLQ56L7HUNUUSSFFNGAB","target":"record","payload":{"canonical_record":{"source":{"id":"1910.07600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-16T20:25:45Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"ff9a8dc857fdd827654b160680b5e5eb69fbff6c6dce932bc9fcfeafc76f6e1a","abstract_canon_sha256":"9b816b333ff551ab6a7d97ad4a18135f7d86f16a58ef1911e1ce0502a045f474"},"schema_version":"1.0"},"canonical_sha256":"067abb394b877cbf9e8da5252295a60049e47d48b977419bccba3efb51fe3907","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:12:38.647374Z","signature_b64":"JjOj3aExt9wlEamaHCwCs/gYumidVOYhL8oO3C9cQoXKebvm0orMbs85ZFSRdf+32jN3SbkKUAAOYSivHSTQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"067abb394b877cbf9e8da5252295a60049e47d48b977419bccba3efb51fe3907","last_reissued_at":"2026-07-05T00:12:38.646865Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:12:38.646865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.07600","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":"2026-07-05T00:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9lHKWylvac+E2DDCdwPCXNmUKBd7ELmPLb2/zR3oWyPZH0cJzc6uGFy6Q8ZJss1voWDI0Hj8OiPCefDunSQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:04:39.572774Z"},"content_sha256":"ae5a10095693c39cd0ae6f8c294b60a6e64b45cd95ef9b77869e04354684dd53","schema_version":"1.0","event_id":"sha256:ae5a10095693c39cd0ae6f8c294b60a6e64b45cd95ef9b77869e04354684dd53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AZ5LWOKLQ56L7HUNUUSSFFNGAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning chordal extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andrea Lodi, Defeng Liu, Mathieu Tanneau","submitted_at":"2019-10-16T20:25:45Z","abstract_excerpt":"A highly influential ingredient of many techniques designed to exploit sparsity in numerical optimization is the so-called chordal extension of a graph representation of the optimization problem. The definitive relation between chordal extension and the performance of the optimization algorithm that uses the extension is not a mathematically understood task. For this reason, we follow the current research trend of looking at Combinatorial Optimization tasks by using a Machine Learning lens, and we devise a framework for learning elimination rules yielding high-quality chordal extensions. As a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.07600","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/1910.07600/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":"2026-07-05T00:12:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XkyZgYUXTEH50QhUPBnY4RZfYYtH0m9EyFWwei9baezpzMsebE14MGFgREft60k7UxnkRqshhFM/XvB8SnMmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:04:39.573325Z"},"content_sha256":"8a1cf440557f0de666f6c562a37b2278f37f2319465b989d77f6e072fc3b7477","schema_version":"1.0","event_id":"sha256:8a1cf440557f0de666f6c562a37b2278f37f2319465b989d77f6e072fc3b7477"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AZ5LWOKLQ56L7HUNUUSSFFNGAB/bundle.json","state_url":"https://pith.science/pith/AZ5LWOKLQ56L7HUNUUSSFFNGAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AZ5LWOKLQ56L7HUNUUSSFFNGAB/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":"2026-08-04T15:04:39Z","links":{"resolver":"https://pith.science/pith/AZ5LWOKLQ56L7HUNUUSSFFNGAB","bundle":"https://pith.science/pith/AZ5LWOKLQ56L7HUNUUSSFFNGAB/bundle.json","state":"https://pith.science/pith/AZ5LWOKLQ56L7HUNUUSSFFNGAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AZ5LWOKLQ56L7HUNUUSSFFNGAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AZ5LWOKLQ56L7HUNUUSSFFNGAB","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":"9b816b333ff551ab6a7d97ad4a18135f7d86f16a58ef1911e1ce0502a045f474","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-16T20:25:45Z","title_canon_sha256":"ff9a8dc857fdd827654b160680b5e5eb69fbff6c6dce932bc9fcfeafc76f6e1a"},"schema_version":"1.0","source":{"id":"1910.07600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.07600","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1910.07600v1","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.07600","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"AZ5LWOKLQ56L","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"pith_short_16","alias_value":"AZ5LWOKLQ56L7HUN","created_at":"2026-07-05T00:12:38Z"},{"alias_kind":"pith_short_8","alias_value":"AZ5LWOKL","created_at":"2026-07-05T00:12:38Z"}],"graph_snapshots":[{"event_id":"sha256:8a1cf440557f0de666f6c562a37b2278f37f2319465b989d77f6e072fc3b7477","target":"graph","created_at":"2026-07-05T00:12:38Z","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/1910.07600/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A highly influential ingredient of many techniques designed to exploit sparsity in numerical optimization is the so-called chordal extension of a graph representation of the optimization problem. The definitive relation between chordal extension and the performance of the optimization algorithm that uses the extension is not a mathematically understood task. For this reason, we follow the current research trend of looking at Combinatorial Optimization tasks by using a Machine Learning lens, and we devise a framework for learning elimination rules yielding high-quality chordal extensions. As a ","authors_text":"Andrea Lodi, Defeng Liu, Mathieu Tanneau","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-16T20:25:45Z","title":"Learning chordal extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.07600","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:ae5a10095693c39cd0ae6f8c294b60a6e64b45cd95ef9b77869e04354684dd53","target":"record","created_at":"2026-07-05T00:12:38Z","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":"9b816b333ff551ab6a7d97ad4a18135f7d86f16a58ef1911e1ce0502a045f474","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-10-16T20:25:45Z","title_canon_sha256":"ff9a8dc857fdd827654b160680b5e5eb69fbff6c6dce932bc9fcfeafc76f6e1a"},"schema_version":"1.0","source":{"id":"1910.07600","kind":"arxiv","version":1}},"canonical_sha256":"067abb394b877cbf9e8da5252295a60049e47d48b977419bccba3efb51fe3907","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"067abb394b877cbf9e8da5252295a60049e47d48b977419bccba3efb51fe3907","first_computed_at":"2026-07-05T00:12:38.646865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:12:38.646865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JjOj3aExt9wlEamaHCwCs/gYumidVOYhL8oO3C9cQoXKebvm0orMbs85ZFSRdf+32jN3SbkKUAAOYSivHSTQBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:12:38.647374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.07600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae5a10095693c39cd0ae6f8c294b60a6e64b45cd95ef9b77869e04354684dd53","sha256:8a1cf440557f0de666f6c562a37b2278f37f2319465b989d77f6e072fc3b7477"],"state_sha256":"471b677143c49e37ba5990cd3e41d60ca3fbd803b3b3e3b1610a45db349cc351"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dz+KBB5yAnKnxNaehWXyBVHlMAkZlzammWNWzrVwDugiNBjsM+GhmhNd5h41GqUiRQ3Qc2iMc86mWNZm3TIHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T15:04:39.585453Z","bundle_sha256":"a8ccdad799259e496de9d5fb8e2d692a90503cb8896f5ecb9a201699a5a46017"}}