{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7RKCKGSHUHFPRVC4RGTBURYTZO","short_pith_number":"pith:7RKCKGSH","canonical_record":{"source":{"id":"2110.14779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-10-27T21:21:19Z","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"title_canon_sha256":"fb89c8c18eab2a4157c16b3e53182601ef8e0d7e67d4b00c3d68abc8b84f7204","abstract_canon_sha256":"22b77025e684ee28483cfb63e750a8e6720bd8ed2c4a8f481591834444b79fda"},"schema_version":"1.0"},"canonical_sha256":"fc54251a47a1caf8d45c89a61a4713cb9cde2db9a60a2d6e77318ebc89157355","source":{"kind":"arxiv","id":"2110.14779","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14779","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14779v1","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14779","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"7RKCKGSHUHFP","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"7RKCKGSHUHFPRVC4","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"7RKCKGSH","created_at":"2026-07-05T03:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7RKCKGSHUHFPRVC4RGTBURYTZO","target":"record","payload":{"canonical_record":{"source":{"id":"2110.14779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-10-27T21:21:19Z","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"title_canon_sha256":"fb89c8c18eab2a4157c16b3e53182601ef8e0d7e67d4b00c3d68abc8b84f7204","abstract_canon_sha256":"22b77025e684ee28483cfb63e750a8e6720bd8ed2c4a8f481591834444b79fda"},"schema_version":"1.0"},"canonical_sha256":"fc54251a47a1caf8d45c89a61a4713cb9cde2db9a60a2d6e77318ebc89157355","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:27:06.284728Z","signature_b64":"WyhtQUzgkbpkeYJ484VjUpaRrV5q7FKn8gipeT/6Fhyxj90R8IAouGRuzYpz3zczByy9sFRkGbRf4y0cWus1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc54251a47a1caf8d45c89a61a4713cb9cde2db9a60a2d6e77318ebc89157355","last_reissued_at":"2026-07-05T03:27:06.284276Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:27:06.284276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.14779","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":"2026-07-05T03:27:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LD71HxuqMYJITyzVaYSSuCYca+Y3832uzxhlKdOndGVktAGYFy+XGSH0FymHa+2KWMO4f7gNx2E25L0LpMnYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T16:47:06.030265Z"},"content_sha256":"6c969326d1b952b6981aa8d82169b91844db466ab1d9196714c08595d6da817a","schema_version":"1.0","event_id":"sha256:6c969326d1b952b6981aa8d82169b91844db466ab1d9196714c08595d6da817a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7RKCKGSHUHFPRVC4RGTBURYTZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectrahedral Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.ML","stat.TH"],"primary_cat":"math.OC","authors_text":"Eliza O'Reilly, Venkat Chandrasekaran","submitted_at":"2021-10-27T21:21:19Z","abstract_excerpt":"Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data, i.e. a function that is the maximum eigenvalue of an affine matrix expression of the input. This method represents a significant generalization of polyhedral (also called max-affine) regression, in which a polyhedral function (a maximum of a fixed number of affine functions) is fit to the data. We prove bounds on how well spectrahedral functions can approxima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14779","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/2110.14779/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":"2026-07-05T03:27:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6IJOknMybDmR/e0uaa3USzSEN8W5F/uiX3hoYIDzriw7thI7mesbcPolnEFWXwqUdLjh1f2Pvu3c9hbknPU1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T16:47:06.030798Z"},"content_sha256":"ac8007f3e19dccfbda33bcf6470e5e676a90dae7e34477c329ead83c5a5d37ce","schema_version":"1.0","event_id":"sha256:ac8007f3e19dccfbda33bcf6470e5e676a90dae7e34477c329ead83c5a5d37ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/bundle.json","state_url":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/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":"2026-08-01T16:47:06Z","links":{"resolver":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO","bundle":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/bundle.json","state":"https://pith.science/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RKCKGSHUHFPRVC4RGTBURYTZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7RKCKGSHUHFPRVC4RGTBURYTZO","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":"22b77025e684ee28483cfb63e750a8e6720bd8ed2c4a8f481591834444b79fda","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-10-27T21:21:19Z","title_canon_sha256":"fb89c8c18eab2a4157c16b3e53182601ef8e0d7e67d4b00c3d68abc8b84f7204"},"schema_version":"1.0","source":{"id":"2110.14779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14779","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14779v1","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14779","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"7RKCKGSHUHFP","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"7RKCKGSHUHFPRVC4","created_at":"2026-07-05T03:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"7RKCKGSH","created_at":"2026-07-05T03:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:ac8007f3e19dccfbda33bcf6470e5e676a90dae7e34477c329ead83c5a5d37ce","target":"graph","created_at":"2026-07-05T03:27:06Z","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/2110.14779/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data, i.e. a function that is the maximum eigenvalue of an affine matrix expression of the input. This method represents a significant generalization of polyhedral (also called max-affine) regression, in which a polyhedral function (a maximum of a fixed number of affine functions) is fit to the data. We prove bounds on how well spectrahedral functions can approxima","authors_text":"Eliza O'Reilly, Venkat Chandrasekaran","cross_cats":["math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-10-27T21:21:19Z","title":"Spectrahedral Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14779","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":"sha256:6c969326d1b952b6981aa8d82169b91844db466ab1d9196714c08595d6da817a","target":"record","created_at":"2026-07-05T03:27:06Z","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":"22b77025e684ee28483cfb63e750a8e6720bd8ed2c4a8f481591834444b79fda","cross_cats_sorted":["math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-10-27T21:21:19Z","title_canon_sha256":"fb89c8c18eab2a4157c16b3e53182601ef8e0d7e67d4b00c3d68abc8b84f7204"},"schema_version":"1.0","source":{"id":"2110.14779","kind":"arxiv","version":1}},"canonical_sha256":"fc54251a47a1caf8d45c89a61a4713cb9cde2db9a60a2d6e77318ebc89157355","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc54251a47a1caf8d45c89a61a4713cb9cde2db9a60a2d6e77318ebc89157355","first_computed_at":"2026-07-05T03:27:06.284276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:27:06.284276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WyhtQUzgkbpkeYJ484VjUpaRrV5q7FKn8gipeT/6Fhyxj90R8IAouGRuzYpz3zczByy9sFRkGbRf4y0cWus1Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:27:06.284728Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.14779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c969326d1b952b6981aa8d82169b91844db466ab1d9196714c08595d6da817a","sha256:ac8007f3e19dccfbda33bcf6470e5e676a90dae7e34477c329ead83c5a5d37ce"],"state_sha256":"4a36abfd759983336b83220c93eeb3f9c4b2ccef8a3a3eff59b953ca93dd5422"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tIL1p+tUGJ9GMc9tpXr4FKH+O37wQ5duB4zHyJng+OmAhKJls4Z+fcuNpk8r/u1eBhvqQKkgISd/PhW0uXOdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T16:47:06.036623Z","bundle_sha256":"64acad5d48f29e2696d7aff0e3fca6cf969e606a5181353e6a7d0aeb945622b3"}}