{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:B3B7Q5CVCBJK4SWPJYD4VHY5NV","short_pith_number":"pith:B3B7Q5CV","canonical_record":{"source":{"id":"1905.12091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T21:11:27Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3621e1aef4b49d24321735faf41f1bfec48029cafb084bda4328266300533b49","abstract_canon_sha256":"933a1b5052bbe6f9256704cd424d2a9a0a4f10d00817ecf37a732614f7d71069"},"schema_version":"1.0"},"canonical_sha256":"0ec3f874551052ae4acf4e07ca9f1d6d769c298f008a291ed871b8c29b990a72","source":{"kind":"arxiv","id":"1905.12091","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.12091","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1905.12091v1","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12091","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"B3B7Q5CVCBJK","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"B3B7Q5CVCBJK4SWP","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"B3B7Q5CV","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:B3B7Q5CVCBJK4SWPJYD4VHY5NV","target":"record","payload":{"canonical_record":{"source":{"id":"1905.12091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T21:11:27Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3621e1aef4b49d24321735faf41f1bfec48029cafb084bda4328266300533b49","abstract_canon_sha256":"933a1b5052bbe6f9256704cd424d2a9a0a4f10d00817ecf37a732614f7d71069"},"schema_version":"1.0"},"canonical_sha256":"0ec3f874551052ae4acf4e07ca9f1d6d769c298f008a291ed871b8c29b990a72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:48.988496Z","signature_b64":"GKBNiN/t+kxN15FFQEXyhJRufR5UouXffUu7Nf3XrPL9nD7mpNCNl4fX/tZ13o4gzk2UNwuQQ03VoueVFjpaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ec3f874551052ae4acf4e07ca9f1d6d769c298f008a291ed871b8c29b990a72","last_reissued_at":"2026-05-17T23:44:48.987839Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:48.987839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.12091","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":"2026-05-17T23:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gprDuOWbeRcLpaKQkUHFwy919b6rn2oVyKK11Jm8FVo2tm0tif2Pg4KI0uoEkKYRx+yuA57K4ad53UEoejz1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:57:43.468775Z"},"content_sha256":"5e0951b01ad1aa35e6948e3fead72ba4675e711f4e4e048d09c8b0470bf88d59","schema_version":"1.0","event_id":"sha256:5e0951b01ad1aa35e6948e3fead72ba4675e711f4e4e048d09c8b0470bf88d59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:B3B7Q5CVCBJK4SWPJYD4VHY5NV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Guarantees for Dictionary Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Aditya Bhaskara, Wai Ming Tai","submitted_at":"2019-05-28T21:11:27Z","abstract_excerpt":"In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\\mathbb{R}^d$), and the goal is to find a \"basis\" in which the signals have a sparse (approximate) representation. The problem has received a lot of attention in signal processing, learning, and theoretical computer science. The problem is formalized as factorizing a matrix $X (d \\times n)$ (whose columns are the signals) as $X = AY$, where $A$ has a prescribed number $m$ of columns (typically $m \\ll n$), and $Y$ has columns that are $k$-sparse (typically $k \\ll d$). Most of the known theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12091","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":""},"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":"2026-05-17T23:44:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLY9+nIcxiL9T+CUftX7eZn5idP2EvetGGdRtgzSsBF3K0U1mUSeGZSvQSCFjMukreaQjrDSTIYeveOukB62Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:57:43.469125Z"},"content_sha256":"8dffb52ae900bc6eae5a04ef88216aa99fa3afb88b00ec2c1f86d408276a264d","schema_version":"1.0","event_id":"sha256:8dffb52ae900bc6eae5a04ef88216aa99fa3afb88b00ec2c1f86d408276a264d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/bundle.json","state_url":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/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":"2026-06-02T21:57:43Z","links":{"resolver":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV","bundle":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/bundle.json","state":"https://pith.science/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3B7Q5CVCBJK4SWPJYD4VHY5NV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:B3B7Q5CVCBJK4SWPJYD4VHY5NV","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":"933a1b5052bbe6f9256704cd424d2a9a0a4f10d00817ecf37a732614f7d71069","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T21:11:27Z","title_canon_sha256":"3621e1aef4b49d24321735faf41f1bfec48029cafb084bda4328266300533b49"},"schema_version":"1.0","source":{"id":"1905.12091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.12091","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"1905.12091v1","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12091","created_at":"2026-05-17T23:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"B3B7Q5CVCBJK","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"B3B7Q5CVCBJK4SWP","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"B3B7Q5CV","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:8dffb52ae900bc6eae5a04ef88216aa99fa3afb88b00ec2c1f86d408276a264d","target":"graph","created_at":"2026-05-17T23:44:48Z","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":"In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\\mathbb{R}^d$), and the goal is to find a \"basis\" in which the signals have a sparse (approximate) representation. The problem has received a lot of attention in signal processing, learning, and theoretical computer science. The problem is formalized as factorizing a matrix $X (d \\times n)$ (whose columns are the signals) as $X = AY$, where $A$ has a prescribed number $m$ of columns (typically $m \\ll n$), and $Y$ has columns that are $k$-sparse (typically $k \\ll d$). Most of the known theor","authors_text":"Aditya Bhaskara, Wai Ming Tai","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T21:11:27Z","title":"Approximate Guarantees for Dictionary Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12091","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":"sha256:5e0951b01ad1aa35e6948e3fead72ba4675e711f4e4e048d09c8b0470bf88d59","target":"record","created_at":"2026-05-17T23:44:48Z","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":"933a1b5052bbe6f9256704cd424d2a9a0a4f10d00817ecf37a732614f7d71069","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-05-28T21:11:27Z","title_canon_sha256":"3621e1aef4b49d24321735faf41f1bfec48029cafb084bda4328266300533b49"},"schema_version":"1.0","source":{"id":"1905.12091","kind":"arxiv","version":1}},"canonical_sha256":"0ec3f874551052ae4acf4e07ca9f1d6d769c298f008a291ed871b8c29b990a72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ec3f874551052ae4acf4e07ca9f1d6d769c298f008a291ed871b8c29b990a72","first_computed_at":"2026-05-17T23:44:48.987839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:48.987839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GKBNiN/t+kxN15FFQEXyhJRufR5UouXffUu7Nf3XrPL9nD7mpNCNl4fX/tZ13o4gzk2UNwuQQ03VoueVFjpaDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:48.988496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.12091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e0951b01ad1aa35e6948e3fead72ba4675e711f4e4e048d09c8b0470bf88d59","sha256:8dffb52ae900bc6eae5a04ef88216aa99fa3afb88b00ec2c1f86d408276a264d"],"state_sha256":"542016f4032ba385406cab7a67e3c1ca3d701dbea5dd6c361fb4f1f48d6f3554"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gsUQbXqQO5ghGfPjLufCi5JEdgwpNfD/mr0B10JMJ+vb3S4vfo2HfM68kB9/zWbWR7s2YsHSqKO6wuoicscBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:57:43.471064Z","bundle_sha256":"4c30c1ff5482de5fce103a8fac9e28d87d701ac46aa698f5903a34008ae0ef70"}}