{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:G6PTGVI3DYFZWXDHDKAFN5ZBCL","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":"980889251f227eff4eeea94fe8ef6a6e3ae229bfdacf26cb5af42ad2451d387b","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-16T10:45:51Z","title_canon_sha256":"e049825491960fa0fe750f14d6ee41f93eb96652c70792264164c191752a0451"},"schema_version":"1.0","source":{"id":"2506.13353","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.13353","created_at":"2026-07-05T11:23:30Z"},{"alias_kind":"arxiv_version","alias_value":"2506.13353v2","created_at":"2026-07-05T11:23:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13353","created_at":"2026-07-05T11:23:30Z"},{"alias_kind":"pith_short_12","alias_value":"G6PTGVI3DYFZ","created_at":"2026-07-05T11:23:30Z"},{"alias_kind":"pith_short_16","alias_value":"G6PTGVI3DYFZWXDH","created_at":"2026-07-05T11:23:30Z"},{"alias_kind":"pith_short_8","alias_value":"G6PTGVI3","created_at":"2026-07-05T11:23:30Z"}],"graph_snapshots":[{"event_id":"sha256:78afa225ab94f2996e0873f9ee669fd687b22bf4db182b1c16e394a9db55cb90","target":"graph","created_at":"2026-07-05T11:23:30Z","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/2506.13353/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Estimating high-dimensional precision matrices is a fundamental problem in modern statistics, with the graphical lasso and its $\\ell_1$-penalty being a standard approach for recovering sparsity patterns. However, many statistical models, e.g. colored graphical models, exhibit richer structures like symmetry or equality constraints, which the $\\ell_1$-norm cannot adequately capture. This paper addresses the gap by extending the high-dimensional analysis of pattern recovery to a general class of atomic norm penalties, particularly those whose unit balls are polytopes, where patterns correspond t","authors_text":"Bartosz Ko{\\l}odziejek, Hideto Nakashima, Maciej Wilczy\\'nski, Piotr Graczyk","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-16T10:45:51Z","title":"From Graphical Lasso to Atomic Norms: High-Dimensional Pattern Recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13353","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:be5c4cded8bc851cf63d708f2796c5ece534ca335199a1372ba28072dce902a3","target":"record","created_at":"2026-07-05T11:23:30Z","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":"980889251f227eff4eeea94fe8ef6a6e3ae229bfdacf26cb5af42ad2451d387b","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-16T10:45:51Z","title_canon_sha256":"e049825491960fa0fe750f14d6ee41f93eb96652c70792264164c191752a0451"},"schema_version":"1.0","source":{"id":"2506.13353","kind":"arxiv","version":2}},"canonical_sha256":"379f33551b1e0b9b5c671a8056f72112dd11ef0b4c69e1439ad8937b72cfd928","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"379f33551b1e0b9b5c671a8056f72112dd11ef0b4c69e1439ad8937b72cfd928","first_computed_at":"2026-07-05T11:23:30.521008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:23:30.521008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aieNuUzwCKz/5DZ5X26V5S9SH8y5QKFZlSgmzVbso7WsDYJykqc45dzO9Chj9qwIqD89O0zENPKtUVo2RBGNAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:23:30.521512Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.13353","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be5c4cded8bc851cf63d708f2796c5ece534ca335199a1372ba28072dce902a3","sha256:78afa225ab94f2996e0873f9ee669fd687b22bf4db182b1c16e394a9db55cb90"],"state_sha256":"dadefd2ec027a656cdd651812d8734908f23c49f128ed0eaf9fe9c6d95e15f5a"}