{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3HRNNH3Q7HAQT5BJWNS5YMCB2U","short_pith_number":"pith:3HRNNH3Q","canonical_record":{"source":{"id":"1801.04873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-15T16:49:47Z","cross_cats_sorted":[],"title_canon_sha256":"cfa7227e851916832dc90af6c9d74f85fe20aba86c0f90dd64c9beacd425b4da","abstract_canon_sha256":"549b2f9d19cf33a3ceef8407db3df737159f19fd6f3269518e5ed244adc35dd9"},"schema_version":"1.0"},"canonical_sha256":"d9e2d69f70f9c109f429b365dc3041d5358fec761b292991a52191aa8bc782cb","source":{"kind":"arxiv","id":"1801.04873","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04873","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04873v1","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04873","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"3HRNNH3Q7HAQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3HRNNH3Q7HAQT5BJ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3HRNNH3Q","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3HRNNH3Q7HAQT5BJWNS5YMCB2U","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-15T16:49:47Z","cross_cats_sorted":[],"title_canon_sha256":"cfa7227e851916832dc90af6c9d74f85fe20aba86c0f90dd64c9beacd425b4da","abstract_canon_sha256":"549b2f9d19cf33a3ceef8407db3df737159f19fd6f3269518e5ed244adc35dd9"},"schema_version":"1.0"},"canonical_sha256":"d9e2d69f70f9c109f429b365dc3041d5358fec761b292991a52191aa8bc782cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:02.967248Z","signature_b64":"VCDi/UCtFWnOw2ZwS7Us+GqnrSbyzOSATUJuWPKKe7xHEU7/ckH2LEyBxj9PTykzfOPjm9i6A7aovODnV4UxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9e2d69f70f9c109f429b365dc3041d5358fec761b292991a52191aa8bc782cb","last_reissued_at":"2026-05-18T00:26:02.966551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:02.966551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04873","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":"2026-05-18T00:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fHQMliM0dtgdDCTyO3rUpR0RpGGteyCqJhUJxoAcdW9QsGWzf+Qb/1WrmowmSdHE4l9xuX1Ak5YoHQlh0t9RDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:16:36.342114Z"},"content_sha256":"903347b1b243687359de3e710ffd14d038c6bd2877a96cdf433b47e0c706b590","schema_version":"1.0","event_id":"sha256:903347b1b243687359de3e710ffd14d038c6bd2877a96cdf433b47e0c706b590"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3HRNNH3Q7HAQT5BJWNS5YMCB2U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized projection methods for convex feasibility problems: conditioning and convergence rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrei Patrascu, Ion Necoara, Peter Richtarik","submitted_at":"2018-01-15T16:49:47Z","abstract_excerpt":"Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations of the convex feasibility problem in order to facilitate the development of new algorithmic schemes. We also analyze the conditioning problem parameters using certain (linear) regularity assumptions on the individual convex sets. Then, we introduce a general random projection algorithmic framework, which extends to the random settings many existing projecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04873","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":"2026-05-18T00:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j9je4j63V0lDfDNkKIZOucyM2EI23ZePvwAL2aMHQmTLt1MUXg+gIHaxkV90+tw0Zk0UgF3XwRu/+rGRYQouBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:16:36.342829Z"},"content_sha256":"32653e3b45ea936ea93c621546986da3acff0351c937fb75219a1e2bc0aa6b69","schema_version":"1.0","event_id":"sha256:32653e3b45ea936ea93c621546986da3acff0351c937fb75219a1e2bc0aa6b69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HRNNH3Q7HAQT5BJWNS5YMCB2U/bundle.json","state_url":"https://pith.science/pith/3HRNNH3Q7HAQT5BJWNS5YMCB2U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HRNNH3Q7HAQT5BJWNS5YMCB2U/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":"2026-05-29T20:16:36Z","links":{"resolver":"https://pith.science/pith/3HRNNH3Q7HAQT5BJWNS5YMCB2U","bundle":"https://pith.science/pith/3HRNNH3Q7HAQT5BJWNS5YMCB2U/bundle.json","state":"https://pith.science/pith/3HRNNH3Q7HAQT5BJWNS5YMCB2U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HRNNH3Q7HAQT5BJWNS5YMCB2U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3HRNNH3Q7HAQT5BJWNS5YMCB2U","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":"549b2f9d19cf33a3ceef8407db3df737159f19fd6f3269518e5ed244adc35dd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-15T16:49:47Z","title_canon_sha256":"cfa7227e851916832dc90af6c9d74f85fe20aba86c0f90dd64c9beacd425b4da"},"schema_version":"1.0","source":{"id":"1801.04873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04873","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04873v1","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04873","created_at":"2026-05-18T00:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"3HRNNH3Q7HAQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3HRNNH3Q7HAQT5BJ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3HRNNH3Q","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:32653e3b45ea936ea93c621546986da3acff0351c937fb75219a1e2bc0aa6b69","target":"graph","created_at":"2026-05-18T00:26:02Z","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":"Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations of the convex feasibility problem in order to facilitate the development of new algorithmic schemes. We also analyze the conditioning problem parameters using certain (linear) regularity assumptions on the individual convex sets. Then, we introduce a general random projection algorithmic framework, which extends to the random settings many existing projecti","authors_text":"Andrei Patrascu, Ion Necoara, Peter Richtarik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-15T16:49:47Z","title":"Randomized projection methods for convex feasibility problems: conditioning and convergence rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04873","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":"sha256:903347b1b243687359de3e710ffd14d038c6bd2877a96cdf433b47e0c706b590","target":"record","created_at":"2026-05-18T00:26:02Z","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":"549b2f9d19cf33a3ceef8407db3df737159f19fd6f3269518e5ed244adc35dd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-01-15T16:49:47Z","title_canon_sha256":"cfa7227e851916832dc90af6c9d74f85fe20aba86c0f90dd64c9beacd425b4da"},"schema_version":"1.0","source":{"id":"1801.04873","kind":"arxiv","version":1}},"canonical_sha256":"d9e2d69f70f9c109f429b365dc3041d5358fec761b292991a52191aa8bc782cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9e2d69f70f9c109f429b365dc3041d5358fec761b292991a52191aa8bc782cb","first_computed_at":"2026-05-18T00:26:02.966551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:02.966551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VCDi/UCtFWnOw2ZwS7Us+GqnrSbyzOSATUJuWPKKe7xHEU7/ckH2LEyBxj9PTykzfOPjm9i6A7aovODnV4UxDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:02.967248Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:903347b1b243687359de3e710ffd14d038c6bd2877a96cdf433b47e0c706b590","sha256:32653e3b45ea936ea93c621546986da3acff0351c937fb75219a1e2bc0aa6b69"],"state_sha256":"3642d3b409e7f5281fef1c1022e23e18342726146d92f26af5634414d2967113"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V6SYfankMyS0xMfyu0vJ+y09F31JIeH1vVE90UFAvihfnWJ8GxyQ67ee+qR7K8MUnozSJ8qfM5E6OtR9qMFfCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:16:36.346527Z","bundle_sha256":"c14d356b57a2edff3a0e36ffb0a90f90f7149d664f521fb78a35f17912d52fe9"}}