{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3L7DNGEWLLUL725FFZ2ZA2XMVI","short_pith_number":"pith:3L7DNGEW","canonical_record":{"source":{"id":"1203.2742","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-13T08:59:26Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a11e373f4d90f0246837bdb3389f4de9e3a4f912567f3f5585ef563a876f5064","abstract_canon_sha256":"295ca2be88718c89b189c2a3527f945c88ab3409359ba4030385e87be03d8ff4"},"schema_version":"1.0"},"canonical_sha256":"dafe3698965ae8bfeba52e75906aecaa3374fd5c1662e8758fac8dc8362c073a","source":{"kind":"arxiv","id":"1203.2742","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2742","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2742v1","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2742","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"3L7DNGEWLLUL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3L7DNGEWLLUL725F","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3L7DNGEW","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3L7DNGEWLLUL725FFZ2ZA2XMVI","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2742","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-13T08:59:26Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a11e373f4d90f0246837bdb3389f4de9e3a4f912567f3f5585ef563a876f5064","abstract_canon_sha256":"295ca2be88718c89b189c2a3527f945c88ab3409359ba4030385e87be03d8ff4"},"schema_version":"1.0"},"canonical_sha256":"dafe3698965ae8bfeba52e75906aecaa3374fd5c1662e8758fac8dc8362c073a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:42.163987Z","signature_b64":"Md2MFogY0lMsPhXD5Z9oUWe1vOjQ4xqgq/ds4aIgeYhp+x41u4EhgkO+JcIy1vE4MySbpa0UsXIYJD+DaRgyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dafe3698965ae8bfeba52e75906aecaa3374fd5c1662e8758fac8dc8362c073a","last_reissued_at":"2026-05-18T03:53:42.163533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:42.163533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2742","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":"2026-05-18T03:53:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tUrPql4KQ6UmVQUnHRh0QfXuEVopiEATNEleM7/qNvxl30g45mY4fXeqdbtkukT/BLsJY09TGCGcXZawfIvUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:34:50.266184Z"},"content_sha256":"04f72f8ee46f66aebc7b28d047b0685ddae58b4d7aa426f4b2fe5ebd214d9844","schema_version":"1.0","event_id":"sha256:04f72f8ee46f66aebc7b28d047b0685ddae58b4d7aa426f4b2fe5ebd214d9844"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3L7DNGEWLLUL725FFZ2ZA2XMVI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logarithmic barriers for sparse matrix cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.OC","authors_text":"Joachim Dahl, Lieven Vandenberghe, Martin S. Andersen","submitted_at":"2012-03-13T08:59:26Z","abstract_excerpt":"Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with the same pattern that have a positive semidefinite completion. Efficient large-scale algorithms for evaluating these barriers and their derivatives are important in interior-point methods for nonsymmetric conic formulations of sparse semidefinite programs. The algorithms are based on the multifrontal method for sparse Cholesky factorization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2742","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":"2026-05-18T03:53:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZFkgvQUBijH7evTEEHFGi8w5q63OpkWHkEw0TK0gZywy/7BGuKrEwbpRxdMSuRtukUjGOgaMZxy0d4SX9ieWBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:34:50.266937Z"},"content_sha256":"9af8b28a3a8fc4928a5419e151355016f36b545f7497a47bf3c6757672623886","schema_version":"1.0","event_id":"sha256:9af8b28a3a8fc4928a5419e151355016f36b545f7497a47bf3c6757672623886"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3L7DNGEWLLUL725FFZ2ZA2XMVI/bundle.json","state_url":"https://pith.science/pith/3L7DNGEWLLUL725FFZ2ZA2XMVI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3L7DNGEWLLUL725FFZ2ZA2XMVI/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":"2026-06-09T08:34:50Z","links":{"resolver":"https://pith.science/pith/3L7DNGEWLLUL725FFZ2ZA2XMVI","bundle":"https://pith.science/pith/3L7DNGEWLLUL725FFZ2ZA2XMVI/bundle.json","state":"https://pith.science/pith/3L7DNGEWLLUL725FFZ2ZA2XMVI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3L7DNGEWLLUL725FFZ2ZA2XMVI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3L7DNGEWLLUL725FFZ2ZA2XMVI","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":"295ca2be88718c89b189c2a3527f945c88ab3409359ba4030385e87be03d8ff4","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-13T08:59:26Z","title_canon_sha256":"a11e373f4d90f0246837bdb3389f4de9e3a4f912567f3f5585ef563a876f5064"},"schema_version":"1.0","source":{"id":"1203.2742","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2742","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2742v1","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2742","created_at":"2026-05-18T03:53:42Z"},{"alias_kind":"pith_short_12","alias_value":"3L7DNGEWLLUL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3L7DNGEWLLUL725F","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3L7DNGEW","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:9af8b28a3a8fc4928a5419e151355016f36b545f7497a47bf3c6757672623886","target":"graph","created_at":"2026-05-18T03:53:42Z","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":"Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with the same pattern that have a positive semidefinite completion. Efficient large-scale algorithms for evaluating these barriers and their derivatives are important in interior-point methods for nonsymmetric conic formulations of sparse semidefinite programs. The algorithms are based on the multifrontal method for sparse Cholesky factorization.","authors_text":"Joachim Dahl, Lieven Vandenberghe, Martin S. Andersen","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-13T08:59:26Z","title":"Logarithmic barriers for sparse matrix cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2742","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":"sha256:04f72f8ee46f66aebc7b28d047b0685ddae58b4d7aa426f4b2fe5ebd214d9844","target":"record","created_at":"2026-05-18T03:53:42Z","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":"295ca2be88718c89b189c2a3527f945c88ab3409359ba4030385e87be03d8ff4","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-03-13T08:59:26Z","title_canon_sha256":"a11e373f4d90f0246837bdb3389f4de9e3a4f912567f3f5585ef563a876f5064"},"schema_version":"1.0","source":{"id":"1203.2742","kind":"arxiv","version":1}},"canonical_sha256":"dafe3698965ae8bfeba52e75906aecaa3374fd5c1662e8758fac8dc8362c073a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dafe3698965ae8bfeba52e75906aecaa3374fd5c1662e8758fac8dc8362c073a","first_computed_at":"2026-05-18T03:53:42.163533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:42.163533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Md2MFogY0lMsPhXD5Z9oUWe1vOjQ4xqgq/ds4aIgeYhp+x41u4EhgkO+JcIy1vE4MySbpa0UsXIYJD+DaRgyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:42.163987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2742","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04f72f8ee46f66aebc7b28d047b0685ddae58b4d7aa426f4b2fe5ebd214d9844","sha256:9af8b28a3a8fc4928a5419e151355016f36b545f7497a47bf3c6757672623886"],"state_sha256":"4f49d6b6e103c378dc402b1cee42de551163d6674efd5656ccd9adaee6cc43d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jVjNibnS5m0phiZ3IxGAJFV9YTsidJozer1PyLL0vhRUSkZ1vv+ttoMaDaSYEypFpbtDr+Ndk7e0NAwnI0lWCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:34:50.270853Z","bundle_sha256":"789ba6d4bf77b1b8618967c655f52aab7f0dd8b3ee0983a314dcc08c40ba1553"}}