{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PJDAPL5ND3QMKEGAYLXHQKJUNZ","short_pith_number":"pith:PJDAPL5N","canonical_record":{"source":{"id":"1304.1198","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-03T21:59:17Z","cross_cats_sorted":[],"title_canon_sha256":"ac3b7cc22312de17bc236094f5546f4fe233074e2fc550cc4a9d6f38397bfbf7","abstract_canon_sha256":"f2a1e68a9f0e778918bb569e1111fba5f37ae7c812f695ea4f5af62e9d10338f"},"schema_version":"1.0"},"canonical_sha256":"7a4607afad1ee0c510c0c2ee7829346e49b56a1a69518867cf05febb4898f63b","source":{"kind":"arxiv","id":"1304.1198","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1198","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1198v2","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1198","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"PJDAPL5ND3QM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PJDAPL5ND3QMKEGA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PJDAPL5N","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PJDAPL5ND3QMKEGAYLXHQKJUNZ","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1198","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-03T21:59:17Z","cross_cats_sorted":[],"title_canon_sha256":"ac3b7cc22312de17bc236094f5546f4fe233074e2fc550cc4a9d6f38397bfbf7","abstract_canon_sha256":"f2a1e68a9f0e778918bb569e1111fba5f37ae7c812f695ea4f5af62e9d10338f"},"schema_version":"1.0"},"canonical_sha256":"7a4607afad1ee0c510c0c2ee7829346e49b56a1a69518867cf05febb4898f63b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:16.902022Z","signature_b64":"IAy/wRTDSfHsoOPpkZY6Tt3FSz1fdCJeL4B8WayQY2rX7ORmZFNTy7QWYPEo8SaUoEslvvWQAvuD3BSue/k1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a4607afad1ee0c510c0c2ee7829346e49b56a1a69518867cf05febb4898f63b","last_reissued_at":"2026-05-18T03:28:16.901339Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:16.901339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1198","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ENbyBJvurLyX6z2k98BsB83Zn0lvXRVQpUivtWpb/2MNnf+zPNPKgIBSWlsdek34jFPbT11zoUWXAbHEn4QVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:27:41.650889Z"},"content_sha256":"c4aeb39cad296bde709cac19c14c96b0eead430a82740b1601210e7cd62ae826","schema_version":"1.0","event_id":"sha256:c4aeb39cad296bde709cac19c14c96b0eead430a82740b1601210e7cd62ae826"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PJDAPL5ND3QMKEGAYLXHQKJUNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal Invariance and Identifiability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Adrian S. Lewis, Aris Daniilidis, Dmitriy Drusvyatskiy","submitted_at":"2013-04-03T21:59:17Z","abstract_excerpt":"Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann's theorem on matrix norms is an early example. We discuss the example of \"identifiability\", a common property of nonsmooth functions associated with the existence of a smooth manifold of approximate critical points. Identifiability (or its synonym, \"partial smoothness\") is the key idea underlying active set methods in optimization. Polyhedral functions, in particular, are always partly smooth, and hence so are many standard examples from eigenvalue optimization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1198","kind":"arxiv","version":2},"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":"2026-05-18T03:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEKxBOeUjXxmhX6o2YQnIAUoQ1eHGfVv93itV2pvi+srhBqS0YFKPjgWeLsBybfALfMG3yaZvwbSa7nj/04xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:27:41.651546Z"},"content_sha256":"695a910a4cd0ecdcca90535ed8b0b4276eca5e5e95195f15299b06452b142e08","schema_version":"1.0","event_id":"sha256:695a910a4cd0ecdcca90535ed8b0b4276eca5e5e95195f15299b06452b142e08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJDAPL5ND3QMKEGAYLXHQKJUNZ/bundle.json","state_url":"https://pith.science/pith/PJDAPL5ND3QMKEGAYLXHQKJUNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJDAPL5ND3QMKEGAYLXHQKJUNZ/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":"2026-05-30T02:27:41Z","links":{"resolver":"https://pith.science/pith/PJDAPL5ND3QMKEGAYLXHQKJUNZ","bundle":"https://pith.science/pith/PJDAPL5ND3QMKEGAYLXHQKJUNZ/bundle.json","state":"https://pith.science/pith/PJDAPL5ND3QMKEGAYLXHQKJUNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJDAPL5ND3QMKEGAYLXHQKJUNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PJDAPL5ND3QMKEGAYLXHQKJUNZ","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":"f2a1e68a9f0e778918bb569e1111fba5f37ae7c812f695ea4f5af62e9d10338f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-03T21:59:17Z","title_canon_sha256":"ac3b7cc22312de17bc236094f5546f4fe233074e2fc550cc4a9d6f38397bfbf7"},"schema_version":"1.0","source":{"id":"1304.1198","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1198","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1198v2","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1198","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"PJDAPL5ND3QM","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PJDAPL5ND3QMKEGA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PJDAPL5N","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:695a910a4cd0ecdcca90535ed8b0b4276eca5e5e95195f15299b06452b142e08","target":"graph","created_at":"2026-05-18T03:28:16Z","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":"Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann's theorem on matrix norms is an early example. We discuss the example of \"identifiability\", a common property of nonsmooth functions associated with the existence of a smooth manifold of approximate critical points. Identifiability (or its synonym, \"partial smoothness\") is the key idea underlying active set methods in optimization. Polyhedral functions, in particular, are always partly smooth, and hence so are many standard examples from eigenvalue optimization.","authors_text":"Adrian S. Lewis, Aris Daniilidis, Dmitriy Drusvyatskiy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-03T21:59:17Z","title":"Orthogonal Invariance and Identifiability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1198","kind":"arxiv","version":2},"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:c4aeb39cad296bde709cac19c14c96b0eead430a82740b1601210e7cd62ae826","target":"record","created_at":"2026-05-18T03:28:16Z","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":"f2a1e68a9f0e778918bb569e1111fba5f37ae7c812f695ea4f5af62e9d10338f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-03T21:59:17Z","title_canon_sha256":"ac3b7cc22312de17bc236094f5546f4fe233074e2fc550cc4a9d6f38397bfbf7"},"schema_version":"1.0","source":{"id":"1304.1198","kind":"arxiv","version":2}},"canonical_sha256":"7a4607afad1ee0c510c0c2ee7829346e49b56a1a69518867cf05febb4898f63b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a4607afad1ee0c510c0c2ee7829346e49b56a1a69518867cf05febb4898f63b","first_computed_at":"2026-05-18T03:28:16.901339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:16.901339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IAy/wRTDSfHsoOPpkZY6Tt3FSz1fdCJeL4B8WayQY2rX7ORmZFNTy7QWYPEo8SaUoEslvvWQAvuD3BSue/k1DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:16.902022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1198","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4aeb39cad296bde709cac19c14c96b0eead430a82740b1601210e7cd62ae826","sha256:695a910a4cd0ecdcca90535ed8b0b4276eca5e5e95195f15299b06452b142e08"],"state_sha256":"ce594d79a5ce4be826f816f4187ce08f03a3554dc667cdd2bd17cebbe3894add"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qwoxmyDW+pRXjS3etlgqDLlyiRpx/0wqTcUvHVNKoKn+iNgKG7OQQH4w+0YIzGKJrhhGGiW6E9IA6VGu0ATJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:27:41.655351Z","bundle_sha256":"740297f9501a1e265df2371e488da5662213e87f1d21b0789b017d6f1e3dd796"}}