{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IXZ46ZA2E4HLPXPU47EGCDDPY2","short_pith_number":"pith:IXZ46ZA2","canonical_record":{"source":{"id":"1301.4506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-18T21:11:23Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"4f97c567edb13f110c6f29e482b0d58937cf7d2a90f2a65a61eb55ace2616c74","abstract_canon_sha256":"d25edd751384e37c2c68bd850f8cdf8d0e99feecab5e03f1e2578f96383f2e6c"},"schema_version":"1.0"},"canonical_sha256":"45f3cf641a270eb7ddf4e7c8610c6fc6957ccdc7b6a33d8037ba50d437c93754","source":{"kind":"arxiv","id":"1301.4506","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4506","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4506v1","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4506","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"IXZ46ZA2E4HL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IXZ46ZA2E4HLPXPU","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IXZ46ZA2","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IXZ46ZA2E4HLPXPU47EGCDDPY2","target":"record","payload":{"canonical_record":{"source":{"id":"1301.4506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-18T21:11:23Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"4f97c567edb13f110c6f29e482b0d58937cf7d2a90f2a65a61eb55ace2616c74","abstract_canon_sha256":"d25edd751384e37c2c68bd850f8cdf8d0e99feecab5e03f1e2578f96383f2e6c"},"schema_version":"1.0"},"canonical_sha256":"45f3cf641a270eb7ddf4e7c8610c6fc6957ccdc7b6a33d8037ba50d437c93754","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:03.714507Z","signature_b64":"8u6wY7RBHfRmp55aqsj+BDrt3TJyyrreoFAnb3P0BO3K6Aww2PDnTn3dB7qJBdMtpnieQnRNYW4boTUM9l6JDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45f3cf641a270eb7ddf4e7c8610c6fc6957ccdc7b6a33d8037ba50d437c93754","last_reissued_at":"2026-05-18T03:36:03.714068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:03.714068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.4506","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":"2026-05-18T03:36:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4p4qc8hz/RK+oBzuiw0QI/vohIBvLBySLTlmo3m2ajYxPDKT1R1qGPqM2dmApg72cCrKAr6nVWbSq+wUsAUmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:36:32.074132Z"},"content_sha256":"1b3454e801df13f670f72d83805282be88d36249c2c4de9f60dc709c56166671","schema_version":"1.0","event_id":"sha256:1b3454e801df13f670f72d83805282be88d36249c2c4de9f60dc709c56166671"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IXZ46ZA2E4HLPXPU47EGCDDPY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"Heinz H. Bauschke, Valentin R. Koch","submitted_at":"2013-01-18T21:11:23Z","abstract_excerpt":"We model a problem motivated by road design as a feasibility problem. Projections onto the constraint sets are obtained, and projection methods for solving the feasibility problem are studied. We present results of numerical experiments which demonstrate the efficacy of projection methods even for challenging nonconvex problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4506","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":"2026-05-18T03:36:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7mPku+4V50s/BkEs/MULUIEA2nu35vrteTnRSvg/AtajB8uidTj5tt/xruemmWiaOYsUQ+l0YUrEL8FJAhAMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:36:32.074505Z"},"content_sha256":"7cd609feee39e141328b8a842f5b7501fa3189d3fd837441fdf99f83b5c7fbc8","schema_version":"1.0","event_id":"sha256:7cd609feee39e141328b8a842f5b7501fa3189d3fd837441fdf99f83b5c7fbc8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IXZ46ZA2E4HLPXPU47EGCDDPY2/bundle.json","state_url":"https://pith.science/pith/IXZ46ZA2E4HLPXPU47EGCDDPY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IXZ46ZA2E4HLPXPU47EGCDDPY2/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":"2026-06-12T00:36:32Z","links":{"resolver":"https://pith.science/pith/IXZ46ZA2E4HLPXPU47EGCDDPY2","bundle":"https://pith.science/pith/IXZ46ZA2E4HLPXPU47EGCDDPY2/bundle.json","state":"https://pith.science/pith/IXZ46ZA2E4HLPXPU47EGCDDPY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IXZ46ZA2E4HLPXPU47EGCDDPY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IXZ46ZA2E4HLPXPU47EGCDDPY2","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":"d25edd751384e37c2c68bd850f8cdf8d0e99feecab5e03f1e2578f96383f2e6c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-18T21:11:23Z","title_canon_sha256":"4f97c567edb13f110c6f29e482b0d58937cf7d2a90f2a65a61eb55ace2616c74"},"schema_version":"1.0","source":{"id":"1301.4506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4506","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4506v1","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4506","created_at":"2026-05-18T03:36:03Z"},{"alias_kind":"pith_short_12","alias_value":"IXZ46ZA2E4HL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IXZ46ZA2E4HLPXPU","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IXZ46ZA2","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:7cd609feee39e141328b8a842f5b7501fa3189d3fd837441fdf99f83b5c7fbc8","target":"graph","created_at":"2026-05-18T03:36:03Z","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 model a problem motivated by road design as a feasibility problem. Projections onto the constraint sets are obtained, and projection methods for solving the feasibility problem are studied. We present results of numerical experiments which demonstrate the efficacy of projection methods even for challenging nonconvex problems.","authors_text":"Heinz H. Bauschke, Valentin R. Koch","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-18T21:11:23Z","title":"Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4506","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":"sha256:1b3454e801df13f670f72d83805282be88d36249c2c4de9f60dc709c56166671","target":"record","created_at":"2026-05-18T03:36:03Z","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":"d25edd751384e37c2c68bd850f8cdf8d0e99feecab5e03f1e2578f96383f2e6c","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-18T21:11:23Z","title_canon_sha256":"4f97c567edb13f110c6f29e482b0d58937cf7d2a90f2a65a61eb55ace2616c74"},"schema_version":"1.0","source":{"id":"1301.4506","kind":"arxiv","version":1}},"canonical_sha256":"45f3cf641a270eb7ddf4e7c8610c6fc6957ccdc7b6a33d8037ba50d437c93754","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45f3cf641a270eb7ddf4e7c8610c6fc6957ccdc7b6a33d8037ba50d437c93754","first_computed_at":"2026-05-18T03:36:03.714068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:03.714068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8u6wY7RBHfRmp55aqsj+BDrt3TJyyrreoFAnb3P0BO3K6Aww2PDnTn3dB7qJBdMtpnieQnRNYW4boTUM9l6JDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:03.714507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b3454e801df13f670f72d83805282be88d36249c2c4de9f60dc709c56166671","sha256:7cd609feee39e141328b8a842f5b7501fa3189d3fd837441fdf99f83b5c7fbc8"],"state_sha256":"82b68f6bed6283dccb5171a2884684f9299e8a7030f88a1ecf4f86a8c9ad35c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZxOh4K7N+wDPBVAOGgMwhvp+bGGqy6YFMPO4IkJ3MZRMcUiZYmhYpcya5+7dTcMaT80JIbXCHHrny9TTjrTrAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:36:32.076687Z","bundle_sha256":"4a62ec61ee8eb7aff38325ab7a08af37c7d9e65b80276441b6ed96de21eb834c"}}