{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MTRMMH3T6O2TXIPFCXBMKQSO7Q","short_pith_number":"pith:MTRMMH3T","canonical_record":{"source":{"id":"1501.07315","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-01-29T00:15:28Z","cross_cats_sorted":[],"title_canon_sha256":"33975a4232a0840998767c23ce435b29d5e0059dc88551e2d6dbec60a8bde8ad","abstract_canon_sha256":"e00b4e659fc10b71a7830b718d6bbbd88e57a2c29a1883c20293e578ba248080"},"schema_version":"1.0"},"canonical_sha256":"64e2c61f73f3b53ba1e515c2c5424efc2db742b0e71491ec5e68aecbc0b4a852","source":{"kind":"arxiv","id":"1501.07315","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07315","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07315v3","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07315","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"MTRMMH3T6O2T","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTRMMH3T6O2TXIPF","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTRMMH3T","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MTRMMH3T6O2TXIPFCXBMKQSO7Q","target":"record","payload":{"canonical_record":{"source":{"id":"1501.07315","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-01-29T00:15:28Z","cross_cats_sorted":[],"title_canon_sha256":"33975a4232a0840998767c23ce435b29d5e0059dc88551e2d6dbec60a8bde8ad","abstract_canon_sha256":"e00b4e659fc10b71a7830b718d6bbbd88e57a2c29a1883c20293e578ba248080"},"schema_version":"1.0"},"canonical_sha256":"64e2c61f73f3b53ba1e515c2c5424efc2db742b0e71491ec5e68aecbc0b4a852","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:04.365713Z","signature_b64":"hw0yVjXQv7uO+THztj4ZJtFHdQ5hvWF2FLSP8ChVvxPFhmyxyIXHWQ7DIJjktw44+d7DiQyN4ZTC3T48e/6rBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64e2c61f73f3b53ba1e515c2c5424efc2db742b0e71491ec5e68aecbc0b4a852","last_reissued_at":"2026-05-18T00:52:04.365243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:04.365243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.07315","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":"2026-05-18T00:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWWWqfTjGmuOjhOPlBjfwtGZufeX3+K6hcICHG9eDaptoozClcQEwL+eipDCyYxJxwVE6limLyAYpfnCaR5CDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:48:52.325759Z"},"content_sha256":"ccc822bfc0fe4145341dd948cdba194a6adc85bbd3cec7226b1981c9852f3401","schema_version":"1.0","event_id":"sha256:ccc822bfc0fe4145341dd948cdba194a6adc85bbd3cec7226b1981c9852f3401"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MTRMMH3T6O2TXIPFCXBMKQSO7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Per-Block-Convex Data Modeling by Accelerated Stochastic Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Georgios B. Giannakis, Konstantinos Slavakis","submitted_at":"2015-01-29T00:15:28Z","abstract_excerpt":"Applications involving dictionary learning, non-negative matrix factorization, subspace clustering, and parallel factor tensor decomposition tasks motivate well algorithms for per-block-convex and non-smooth optimization problems. By leveraging the stochastic approximation paradigm and first-order acceleration schemes, this paper develops an online and modular learning algorithm for a large class of non-convex data models, where convexity is manifested only per-block of variables whenever the rest of them are held fixed. The advocated algorithm incurs computational complexity that scales linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07315","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":"2026-05-18T00:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/wuEDYcrwH6ZvCQgRSZTeSUNS87Ex60tfJuFjjiUhhayOD3COgmhSM7K4VWS88wK+0OTV2I0qjm9BeqvVv5kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:48:52.326492Z"},"content_sha256":"a273346412e6ebf1e5e479675609feef3ce3885cb1fef694fb1919a4072fd37d","schema_version":"1.0","event_id":"sha256:a273346412e6ebf1e5e479675609feef3ce3885cb1fef694fb1919a4072fd37d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTRMMH3T6O2TXIPFCXBMKQSO7Q/bundle.json","state_url":"https://pith.science/pith/MTRMMH3T6O2TXIPFCXBMKQSO7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTRMMH3T6O2TXIPFCXBMKQSO7Q/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":"2026-06-09T15:48:52Z","links":{"resolver":"https://pith.science/pith/MTRMMH3T6O2TXIPFCXBMKQSO7Q","bundle":"https://pith.science/pith/MTRMMH3T6O2TXIPFCXBMKQSO7Q/bundle.json","state":"https://pith.science/pith/MTRMMH3T6O2TXIPFCXBMKQSO7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTRMMH3T6O2TXIPFCXBMKQSO7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MTRMMH3T6O2TXIPFCXBMKQSO7Q","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":"e00b4e659fc10b71a7830b718d6bbbd88e57a2c29a1883c20293e578ba248080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-01-29T00:15:28Z","title_canon_sha256":"33975a4232a0840998767c23ce435b29d5e0059dc88551e2d6dbec60a8bde8ad"},"schema_version":"1.0","source":{"id":"1501.07315","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07315","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07315v3","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07315","created_at":"2026-05-18T00:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"MTRMMH3T6O2T","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTRMMH3T6O2TXIPF","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTRMMH3T","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:a273346412e6ebf1e5e479675609feef3ce3885cb1fef694fb1919a4072fd37d","target":"graph","created_at":"2026-05-18T00:52:04Z","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":"Applications involving dictionary learning, non-negative matrix factorization, subspace clustering, and parallel factor tensor decomposition tasks motivate well algorithms for per-block-convex and non-smooth optimization problems. By leveraging the stochastic approximation paradigm and first-order acceleration schemes, this paper develops an online and modular learning algorithm for a large class of non-convex data models, where convexity is manifested only per-block of variables whenever the rest of them are held fixed. The advocated algorithm incurs computational complexity that scales linea","authors_text":"Georgios B. Giannakis, Konstantinos Slavakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-01-29T00:15:28Z","title":"Per-Block-Convex Data Modeling by Accelerated Stochastic Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07315","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:ccc822bfc0fe4145341dd948cdba194a6adc85bbd3cec7226b1981c9852f3401","target":"record","created_at":"2026-05-18T00:52:04Z","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":"e00b4e659fc10b71a7830b718d6bbbd88e57a2c29a1883c20293e578ba248080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-01-29T00:15:28Z","title_canon_sha256":"33975a4232a0840998767c23ce435b29d5e0059dc88551e2d6dbec60a8bde8ad"},"schema_version":"1.0","source":{"id":"1501.07315","kind":"arxiv","version":3}},"canonical_sha256":"64e2c61f73f3b53ba1e515c2c5424efc2db742b0e71491ec5e68aecbc0b4a852","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64e2c61f73f3b53ba1e515c2c5424efc2db742b0e71491ec5e68aecbc0b4a852","first_computed_at":"2026-05-18T00:52:04.365243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:04.365243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hw0yVjXQv7uO+THztj4ZJtFHdQ5hvWF2FLSP8ChVvxPFhmyxyIXHWQ7DIJjktw44+d7DiQyN4ZTC3T48e/6rBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:04.365713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07315","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccc822bfc0fe4145341dd948cdba194a6adc85bbd3cec7226b1981c9852f3401","sha256:a273346412e6ebf1e5e479675609feef3ce3885cb1fef694fb1919a4072fd37d"],"state_sha256":"d4d5488675313e55302378d9f9ea408d46e1047e9bec5301035eaacfea30102b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L36HNS8A2yqCWqXS4k2aHVAZZ8l0mHooPqU9o774PRd4ZdbK+6rRR8FIF1b0CPtmz5yB0VifuZGcgedn0P8KBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:48:52.331068Z","bundle_sha256":"da0c4191a4203ca453091917fa23504da8f8acd99a40957351bdc008b0e066d1"}}