{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HLIC4ZN3JWAK6VFD4DKGCR2DOL","short_pith_number":"pith:HLIC4ZN3","canonical_record":{"source":{"id":"1503.08393","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-03-29T06:49:40Z","cross_cats_sorted":["cs.IT","math.IT","stat.TH"],"title_canon_sha256":"9cf037d9e0a221d75abc80110fe29c511d6d7096f34dc57953985737dc4ebe04","abstract_canon_sha256":"76944b54d0933380c1920d8ecdd5d453e41febccc8942d0ea1c4586f79cdd7f9"},"schema_version":"1.0"},"canonical_sha256":"3ad02e65bb4d80af54a3e0d461474372e4fb7d4f6f6b094c88549d8ff9d289f3","source":{"kind":"arxiv","id":"1503.08393","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08393","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08393v3","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08393","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"pith_short_12","alias_value":"HLIC4ZN3JWAK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HLIC4ZN3JWAK6VFD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HLIC4ZN3","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HLIC4ZN3JWAK6VFD4DKGCR2DOL","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08393","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-03-29T06:49:40Z","cross_cats_sorted":["cs.IT","math.IT","stat.TH"],"title_canon_sha256":"9cf037d9e0a221d75abc80110fe29c511d6d7096f34dc57953985737dc4ebe04","abstract_canon_sha256":"76944b54d0933380c1920d8ecdd5d453e41febccc8942d0ea1c4586f79cdd7f9"},"schema_version":"1.0"},"canonical_sha256":"3ad02e65bb4d80af54a3e0d461474372e4fb7d4f6f6b094c88549d8ff9d289f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:11.387059Z","signature_b64":"W2v3nek8N8q+ocamQVmFALspa18G25aZjHnnjGq7XFvmBM0EuJuX4sEtubq1kCUhA/hs/Oz9+q75EcDbg9+OBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ad02e65bb4d80af54a3e0d461474372e4fb7d4f6f6b094c88549d8ff9d289f3","last_reissued_at":"2026-05-18T01:32:11.386344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:11.386344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08393","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H62awameAAZhthhJALZu+oMksYmSBIJ9MT4zWd8MxcenHvgOA4AmNl5k4WMBQD1RMGuogXGVh3L5OoYqe5WMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:56:52.711651Z"},"content_sha256":"ff1ab6fce88ca19752a4593ae11c26197945f80ee61c064478c8eac79e059182","schema_version":"1.0","event_id":"sha256:ff1ab6fce88ca19752a4593ae11c26197945f80ee61c064478c8eac79e059182"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HLIC4ZN3JWAK6VFD4DKGCR2DOL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Emmanuel Candes, Weijie Su","submitted_at":"2015-03-29T06:49:40Z","abstract_excerpt":"We consider high-dimensional sparse regression problems in which we observe $y = X \\beta + z$, where $X$ is an $n \\times p$ design matrix and $z$ is an $n$-dimensional vector of independent Gaussian errors, each with variance $\\sigma^2$. Our focus is on the recently introduced SLOPE estimator ((Bogdan et al., 2014)), which regularizes the least-squares estimates with the rank-dependent penalty $\\sum_{1 \\le i \\le p} \\lambda_i |\\hat \\beta|_{(i)}$, where $|\\hat \\beta|_{(i)}$ is the $i$th largest magnitude of the fitted coefficients. Under Gaussian designs, where the entries of $X$ are i.i.d.~$\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08393","kind":"arxiv","version":3},"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":"2026-05-18T01:32:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OwX062kDdde9FRagiL9Tsg9WxndRwBSUKUOrQ3Rb7imBvApP36at6w+izNQ1GmyxyMF4ZLzWPXIitCaQ2e3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:56:52.712010Z"},"content_sha256":"d8f9a4b4a2e24449a709a8b6ff8e45573e7088668058afe0b998b63560112568","schema_version":"1.0","event_id":"sha256:d8f9a4b4a2e24449a709a8b6ff8e45573e7088668058afe0b998b63560112568"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HLIC4ZN3JWAK6VFD4DKGCR2DOL/bundle.json","state_url":"https://pith.science/pith/HLIC4ZN3JWAK6VFD4DKGCR2DOL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HLIC4ZN3JWAK6VFD4DKGCR2DOL/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":"2026-05-29T18:56:52Z","links":{"resolver":"https://pith.science/pith/HLIC4ZN3JWAK6VFD4DKGCR2DOL","bundle":"https://pith.science/pith/HLIC4ZN3JWAK6VFD4DKGCR2DOL/bundle.json","state":"https://pith.science/pith/HLIC4ZN3JWAK6VFD4DKGCR2DOL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HLIC4ZN3JWAK6VFD4DKGCR2DOL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HLIC4ZN3JWAK6VFD4DKGCR2DOL","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":"76944b54d0933380c1920d8ecdd5d453e41febccc8942d0ea1c4586f79cdd7f9","cross_cats_sorted":["cs.IT","math.IT","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-03-29T06:49:40Z","title_canon_sha256":"9cf037d9e0a221d75abc80110fe29c511d6d7096f34dc57953985737dc4ebe04"},"schema_version":"1.0","source":{"id":"1503.08393","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08393","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08393v3","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08393","created_at":"2026-05-18T01:32:11Z"},{"alias_kind":"pith_short_12","alias_value":"HLIC4ZN3JWAK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HLIC4ZN3JWAK6VFD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HLIC4ZN3","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:d8f9a4b4a2e24449a709a8b6ff8e45573e7088668058afe0b998b63560112568","target":"graph","created_at":"2026-05-18T01:32:11Z","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":"We consider high-dimensional sparse regression problems in which we observe $y = X \\beta + z$, where $X$ is an $n \\times p$ design matrix and $z$ is an $n$-dimensional vector of independent Gaussian errors, each with variance $\\sigma^2$. Our focus is on the recently introduced SLOPE estimator ((Bogdan et al., 2014)), which regularizes the least-squares estimates with the rank-dependent penalty $\\sum_{1 \\le i \\le p} \\lambda_i |\\hat \\beta|_{(i)}$, where $|\\hat \\beta|_{(i)}$ is the $i$th largest magnitude of the fitted coefficients. Under Gaussian designs, where the entries of $X$ are i.i.d.~$\\ma","authors_text":"Emmanuel Candes, Weijie Su","cross_cats":["cs.IT","math.IT","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-03-29T06:49:40Z","title":"SLOPE is Adaptive to Unknown Sparsity and Asymptotically Minimax"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08393","kind":"arxiv","version":3},"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:ff1ab6fce88ca19752a4593ae11c26197945f80ee61c064478c8eac79e059182","target":"record","created_at":"2026-05-18T01:32:11Z","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":"76944b54d0933380c1920d8ecdd5d453e41febccc8942d0ea1c4586f79cdd7f9","cross_cats_sorted":["cs.IT","math.IT","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-03-29T06:49:40Z","title_canon_sha256":"9cf037d9e0a221d75abc80110fe29c511d6d7096f34dc57953985737dc4ebe04"},"schema_version":"1.0","source":{"id":"1503.08393","kind":"arxiv","version":3}},"canonical_sha256":"3ad02e65bb4d80af54a3e0d461474372e4fb7d4f6f6b094c88549d8ff9d289f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ad02e65bb4d80af54a3e0d461474372e4fb7d4f6f6b094c88549d8ff9d289f3","first_computed_at":"2026-05-18T01:32:11.386344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:11.386344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2v3nek8N8q+ocamQVmFALspa18G25aZjHnnjGq7XFvmBM0EuJuX4sEtubq1kCUhA/hs/Oz9+q75EcDbg9+OBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:11.387059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08393","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff1ab6fce88ca19752a4593ae11c26197945f80ee61c064478c8eac79e059182","sha256:d8f9a4b4a2e24449a709a8b6ff8e45573e7088668058afe0b998b63560112568"],"state_sha256":"bba1b24ac8d66813426a03006f3ab7d1967f203525b3a5184dc56210359f2a24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZ76Kqy2bMq+5Ou9OaYqANZtMwK8Ah2sMWg9aE8MUbblUglDl+qTu7lGMLtGmjQ7AuUD2o1gVtpwtiGxH8E/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:56:52.715404Z","bundle_sha256":"d995b0edc58d76fc8bf17a035fecc21ae4591a1edecbef7bd90c630e6c0cd065"}}