{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:76VZOE27HYFGRG2YJG37YK5J2Z","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":"77565ea1a8bd5472bff9b6d61571877ba5e4625cd9c738d1cf10e6731fb71fa4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-10T15:34:06Z","title_canon_sha256":"7d7f2c9e8281ecc7b9875e9fbcade150d591be525ab25207e72600aaa3115cf8"},"schema_version":"1.0","source":{"id":"2006.05898","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.05898","created_at":"2026-07-05T02:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"2006.05898v2","created_at":"2026-07-05T02:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.05898","created_at":"2026-07-05T02:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"76VZOE27HYFG","created_at":"2026-07-05T02:23:08Z"},{"alias_kind":"pith_short_16","alias_value":"76VZOE27HYFGRG2Y","created_at":"2026-07-05T02:23:08Z"},{"alias_kind":"pith_short_8","alias_value":"76VZOE27","created_at":"2026-07-05T02:23:08Z"}],"graph_snapshots":[{"event_id":"sha256:e4bc15e7660d6a5af8c2a9ecee4114d665b30e9d79faa50d8ccfb5abec354088","target":"graph","created_at":"2026-07-05T02:23:08Z","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/2006.05898/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a reformulation technique that converts a many-set feasibility problem into an equivalent two-set problem. This technique involves reformulating the original feasibility problem by replacing a pair of its constraint sets with their intersection, before applying Pierra's classical product space reformulation. The step of combining the two constraint sets reduces the dimension of the product spaces. We refer to this as the constraint reduction reformulation and use it to obtain constraint-reduced variants of well-known projection algorithms such as the Douglas--Rachford algorithm an","authors_text":"Jeffrey Hogan, Matthew Tam, Minh Dao, Neil Dizon","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-10T15:34:06Z","title":"Constraint reduction reformulations for projection algorithms with applications to wavelet construction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.05898","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":"sha256:6668cf0a54486487bf5f68c4cd0a57f9ff7eedcc9e15e0232ee9ddcb80db3d96","target":"record","created_at":"2026-07-05T02:23:08Z","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":"77565ea1a8bd5472bff9b6d61571877ba5e4625cd9c738d1cf10e6731fb71fa4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-10T15:34:06Z","title_canon_sha256":"7d7f2c9e8281ecc7b9875e9fbcade150d591be525ab25207e72600aaa3115cf8"},"schema_version":"1.0","source":{"id":"2006.05898","kind":"arxiv","version":2}},"canonical_sha256":"ffab97135f3e0a689b5849b7fc2ba9d64d98a2e6fc17f0a129ade443615805e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffab97135f3e0a689b5849b7fc2ba9d64d98a2e6fc17f0a129ade443615805e9","first_computed_at":"2026-07-05T02:23:08.294415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:23:08.294415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B83LVlQgN4vLUTDabMUwTU0U1EuaKXJ01oQQpJ6DbZND6yqgTJ7FAFKi/6XxEfgaP7jE9r710QbFRhJ+ogOHDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:23:08.294882Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.05898","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6668cf0a54486487bf5f68c4cd0a57f9ff7eedcc9e15e0232ee9ddcb80db3d96","sha256:e4bc15e7660d6a5af8c2a9ecee4114d665b30e9d79faa50d8ccfb5abec354088"],"state_sha256":"b0a1070bb3d0c2ae834bd12987f98bf9a929d0b84396ef65ce58606768e51a62"}