{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3K4OTVRA467YKGW4TFXTWMTUI4","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":"3473dfeab50bee2784adbb57b21e062c41fa45738c2495ffa33ca5d9222bf79d","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-11-03T20:26:08Z","title_canon_sha256":"b6fdfc29d17c8887a67335ebff06fa4f67697624bb0476d9b96ee74ae4a0a499"},"schema_version":"1.0","source":{"id":"1611.01179","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01179","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01179v2","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01179","created_at":"2026-05-18T00:40:07Z"},{"alias_kind":"pith_short_12","alias_value":"3K4OTVRA467Y","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3K4OTVRA467YKGW4","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3K4OTVRA","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:717665b85139e8440cd50872417374a6335cf8d775967dfa9b61bebf85c9eded","target":"graph","created_at":"2026-05-18T00:40:07Z","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 the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\\rho$ in $\\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\\mathcal{M}$ - for example supported on a $d$-dimensional Riemannian manifold. Geometric Multi-Resolution Analysis (GMRA) provides a robust and computationally efficient procedure to construct low-dimensional geometric approximations of $\\mathcal{M}$ at varying resolutions. We introduce a thresholding algorithm on the geometric wavelet coefficients, leading to what we call adaptive GMRA appro","authors_text":"Mauro Maggioni, Wenjing Liao","cross_cats":["cs.IT","math.IT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-11-03T20:26:08Z","title":"Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01179","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:c561e0a74d148a28b11dbc1e65c94cc2a2d23f3e840caefb5723cce368c22587","target":"record","created_at":"2026-05-18T00:40:07Z","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":"3473dfeab50bee2784adbb57b21e062c41fa45738c2495ffa33ca5d9222bf79d","cross_cats_sorted":["cs.IT","math.IT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-11-03T20:26:08Z","title_canon_sha256":"b6fdfc29d17c8887a67335ebff06fa4f67697624bb0476d9b96ee74ae4a0a499"},"schema_version":"1.0","source":{"id":"1611.01179","kind":"arxiv","version":2}},"canonical_sha256":"dab8e9d620e7bf851adc996f3b3274470b096e912890457c0721f82ec9c57c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dab8e9d620e7bf851adc996f3b3274470b096e912890457c0721f82ec9c57c5c","first_computed_at":"2026-05-18T00:40:07.866591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:07.866591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NMXgZEJVP25HKL7sP8g3IB/EjJsY1j6/ivFFWdv2munYKnaN74tVxEAn6CHRPnkuXBFE6BgfTvXuHECqCruxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:07.867105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01179","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c561e0a74d148a28b11dbc1e65c94cc2a2d23f3e840caefb5723cce368c22587","sha256:717665b85139e8440cd50872417374a6335cf8d775967dfa9b61bebf85c9eded"],"state_sha256":"8f7c24850f5c027baf4b201105820f25e34f922b90ae643e3ec5dc021d1d8462"}