{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XJANX2NRWP4WNFWFOTY4HZ2QOX","short_pith_number":"pith:XJANX2NR","canonical_record":{"source":{"id":"1204.4813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-21T14:07:00Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e7d62c32e40df4e969e69ba63bd403432bb1f2eb4dd01b96104019b4656fd772","abstract_canon_sha256":"8ba333edbc00b2e10d74f3781cf9ae98771a847b1c63bf223fa476a0c694f0dc"},"schema_version":"1.0"},"canonical_sha256":"ba40dbe9b1b3f96696c574f1c3e75075e7b2f3898a21ee6c847ae8cf396a49ab","source":{"kind":"arxiv","id":"1204.4813","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4813","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4813v2","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4813","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"pith_short_12","alias_value":"XJANX2NRWP4W","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XJANX2NRWP4WNFWF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XJANX2NR","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XJANX2NRWP4WNFWFOTY4HZ2QOX","target":"record","payload":{"canonical_record":{"source":{"id":"1204.4813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-21T14:07:00Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"e7d62c32e40df4e969e69ba63bd403432bb1f2eb4dd01b96104019b4656fd772","abstract_canon_sha256":"8ba333edbc00b2e10d74f3781cf9ae98771a847b1c63bf223fa476a0c694f0dc"},"schema_version":"1.0"},"canonical_sha256":"ba40dbe9b1b3f96696c574f1c3e75075e7b2f3898a21ee6c847ae8cf396a49ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:56.005618Z","signature_b64":"hjf6SCiH8hPAi3ad5SKwKqDcQ51zp98oqsel6fvRTmwrvUhbEskcdH+YujnOEvF8AXeb5SqfinsFoO0uD+boCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba40dbe9b1b3f96696c574f1c3e75075e7b2f3898a21ee6c847ae8cf396a49ab","last_reissued_at":"2026-05-18T03:38:56.004934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:56.004934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.4813","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":"2026-05-18T03:38:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gcKKErvp1puSpffejYKk4sP//puvqvrHm8dTovCsNWhyx/rl6StS5L0WyD4tOltn/sRcx4mwGZq6lCcqk1llDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:57:26.348865Z"},"content_sha256":"61acda5cbd0fe38c856a265aa27da48afffc97b32877938b23a09f1d9b3ed687","schema_version":"1.0","event_id":"sha256:61acda5cbd0fe38c856a265aa27da48afffc97b32877938b23a09f1d9b3ed687"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XJANX2NRWP4WNFWFOTY4HZ2QOX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weakly decomposable regularization penalties and structured sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Sara van de Geer","submitted_at":"2012-04-21T14:07:00Z","abstract_excerpt":"It has been shown in literature that the Lasso estimator, or l1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the l1-penalty allow for sharp oracle results, and then extends the situation to general norm-based penalties that satisfy a weak decomposability condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4813","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":"2026-05-18T03:38:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6huTPlO6LQ4+o7Fh6lKysEybf1vjjaXbXfJjY01mp94X0ouHmmnVmx/idNUpWgcQ356bzhfy8eyJX8unRmY4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T10:57:26.349209Z"},"content_sha256":"5585a443d4bdf390e9f50ad1339bc92cc1d215d3be9366660cfc5370849ea3fb","schema_version":"1.0","event_id":"sha256:5585a443d4bdf390e9f50ad1339bc92cc1d215d3be9366660cfc5370849ea3fb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/bundle.json","state_url":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/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":"2026-06-02T10:57:26Z","links":{"resolver":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX","bundle":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/bundle.json","state":"https://pith.science/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJANX2NRWP4WNFWFOTY4HZ2QOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XJANX2NRWP4WNFWFOTY4HZ2QOX","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":"8ba333edbc00b2e10d74f3781cf9ae98771a847b1c63bf223fa476a0c694f0dc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-21T14:07:00Z","title_canon_sha256":"e7d62c32e40df4e969e69ba63bd403432bb1f2eb4dd01b96104019b4656fd772"},"schema_version":"1.0","source":{"id":"1204.4813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4813","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4813v2","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4813","created_at":"2026-05-18T03:38:56Z"},{"alias_kind":"pith_short_12","alias_value":"XJANX2NRWP4W","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XJANX2NRWP4WNFWF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XJANX2NR","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:5585a443d4bdf390e9f50ad1339bc92cc1d215d3be9366660cfc5370849ea3fb","target":"graph","created_at":"2026-05-18T03:38:56Z","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":"It has been shown in literature that the Lasso estimator, or l1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the l1-penalty allow for sharp oracle results, and then extends the situation to general norm-based penalties that satisfy a weak decomposability condition.","authors_text":"Sara van de Geer","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-21T14:07:00Z","title":"Weakly decomposable regularization penalties and structured sparsity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4813","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":"sha256:61acda5cbd0fe38c856a265aa27da48afffc97b32877938b23a09f1d9b3ed687","target":"record","created_at":"2026-05-18T03:38:56Z","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":"8ba333edbc00b2e10d74f3781cf9ae98771a847b1c63bf223fa476a0c694f0dc","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-21T14:07:00Z","title_canon_sha256":"e7d62c32e40df4e969e69ba63bd403432bb1f2eb4dd01b96104019b4656fd772"},"schema_version":"1.0","source":{"id":"1204.4813","kind":"arxiv","version":2}},"canonical_sha256":"ba40dbe9b1b3f96696c574f1c3e75075e7b2f3898a21ee6c847ae8cf396a49ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba40dbe9b1b3f96696c574f1c3e75075e7b2f3898a21ee6c847ae8cf396a49ab","first_computed_at":"2026-05-18T03:38:56.004934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:56.004934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hjf6SCiH8hPAi3ad5SKwKqDcQ51zp98oqsel6fvRTmwrvUhbEskcdH+YujnOEvF8AXeb5SqfinsFoO0uD+boCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:56.005618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61acda5cbd0fe38c856a265aa27da48afffc97b32877938b23a09f1d9b3ed687","sha256:5585a443d4bdf390e9f50ad1339bc92cc1d215d3be9366660cfc5370849ea3fb"],"state_sha256":"1f81108980fab6f7f8591a608362bdfc4d5713fae47e0bbb18079ce82a0078bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2VjkuFZduTLm2OjXA4LFMafWSkS4Ap+o9UWlzNfov3eFsXhU/dExvr/H0x8q3dGea93YHvGXw5Xwek5isIMhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T10:57:26.351119Z","bundle_sha256":"6e8a79633ebab2e99cd4cb0a89058642e1ff07e56c69dc784d9d03e27904395a"}}