{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:R7GB2TTOGYFJ3XRXE4RP2S7YAL","short_pith_number":"pith:R7GB2TTO","canonical_record":{"source":{"id":"1304.0690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-02T16:54:19Z","cross_cats_sorted":[],"title_canon_sha256":"600d86a6a003e1bacb8652a2220356eeae065f3ff42eecbbd720b1309db8eec9","abstract_canon_sha256":"9e0d19dfcfe82822589d12a2104319a45059f2ecad9d2972e9425109251a1a01"},"schema_version":"1.0"},"canonical_sha256":"8fcc1d4e6e360a9dde372722fd4bf802e4d5a6e7dc6e8b05bf486ef9437765cb","source":{"kind":"arxiv","id":"1304.0690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0690","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0690v1","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0690","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"R7GB2TTOGYFJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R7GB2TTOGYFJ3XRX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R7GB2TTO","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:R7GB2TTOGYFJ3XRXE4RP2S7YAL","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-02T16:54:19Z","cross_cats_sorted":[],"title_canon_sha256":"600d86a6a003e1bacb8652a2220356eeae065f3ff42eecbbd720b1309db8eec9","abstract_canon_sha256":"9e0d19dfcfe82822589d12a2104319a45059f2ecad9d2972e9425109251a1a01"},"schema_version":"1.0"},"canonical_sha256":"8fcc1d4e6e360a9dde372722fd4bf802e4d5a6e7dc6e8b05bf486ef9437765cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:14.613839Z","signature_b64":"4ku8OfqxY1NBs4tCdW2ZpcVYPphF4UfqUe9Cgc8sHY0duCkXw0VLiXM2V+hBAM32pwsVjtp2ACjEbXfM2gwtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fcc1d4e6e360a9dde372722fd4bf802e4d5a6e7dc6e8b05bf486ef9437765cb","last_reissued_at":"2026-05-18T03:29:14.613218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:14.613218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0690","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":"2026-05-18T03:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rOCK4tAIIY2nzlc9toxNM/bn4kw7H+hBN5tZ9+Kg3gXRsnxEzOPIbXjf89e2kmsLQ30DNvo2doDN7X/yRrVvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:11:14.552841Z"},"content_sha256":"93cd3e568890921899d4702aaba1a9cc72d3ed5c820980698d060bf98df674dc","schema_version":"1.0","event_id":"sha256:93cd3e568890921899d4702aaba1a9cc72d3ed5c820980698d060bf98df674dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:R7GB2TTOGYFJ3XRXE4RP2S7YAL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andrzej Cegielski, Aviv Gibali, Rafa{\\l} Zalas, Simeon Reich","submitted_at":"2013-04-02T16:54:19Z","abstract_excerpt":"This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0690","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":"2026-05-18T03:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a2+DZ5Br3vXZaszVEnWjCm9Hv3UjgvJFP9b6BJqmQR/PCNdZu5JM3+gg/i8p5ceVA0Snx2Qzti83BaZyFm33Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:11:14.553476Z"},"content_sha256":"a3d2858fe3569ce4e79802821708da7acc670c5c50f681387df8b6d0ec211c09","schema_version":"1.0","event_id":"sha256:a3d2858fe3569ce4e79802821708da7acc670c5c50f681387df8b6d0ec211c09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R7GB2TTOGYFJ3XRXE4RP2S7YAL/bundle.json","state_url":"https://pith.science/pith/R7GB2TTOGYFJ3XRXE4RP2S7YAL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R7GB2TTOGYFJ3XRXE4RP2S7YAL/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":"2026-05-31T20:11:14Z","links":{"resolver":"https://pith.science/pith/R7GB2TTOGYFJ3XRXE4RP2S7YAL","bundle":"https://pith.science/pith/R7GB2TTOGYFJ3XRXE4RP2S7YAL/bundle.json","state":"https://pith.science/pith/R7GB2TTOGYFJ3XRXE4RP2S7YAL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R7GB2TTOGYFJ3XRXE4RP2S7YAL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:R7GB2TTOGYFJ3XRXE4RP2S7YAL","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":"9e0d19dfcfe82822589d12a2104319a45059f2ecad9d2972e9425109251a1a01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-02T16:54:19Z","title_canon_sha256":"600d86a6a003e1bacb8652a2220356eeae065f3ff42eecbbd720b1309db8eec9"},"schema_version":"1.0","source":{"id":"1304.0690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0690","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0690v1","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0690","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"R7GB2TTOGYFJ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R7GB2TTOGYFJ3XRX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R7GB2TTO","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:a3d2858fe3569ce4e79802821708da7acc670c5c50f681387df8b6d0ec211c09","target":"graph","created_at":"2026-05-18T03:29:14Z","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":"This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization problem.","authors_text":"Andrzej Cegielski, Aviv Gibali, Rafa{\\l} Zalas, Simeon Reich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-02T16:54:19Z","title":"An algorithm for solving the variational inequality problem over the fixed point set of a quasi-nonexpansive operator in Euclidean space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0690","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":"sha256:93cd3e568890921899d4702aaba1a9cc72d3ed5c820980698d060bf98df674dc","target":"record","created_at":"2026-05-18T03:29:14Z","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":"9e0d19dfcfe82822589d12a2104319a45059f2ecad9d2972e9425109251a1a01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-02T16:54:19Z","title_canon_sha256":"600d86a6a003e1bacb8652a2220356eeae065f3ff42eecbbd720b1309db8eec9"},"schema_version":"1.0","source":{"id":"1304.0690","kind":"arxiv","version":1}},"canonical_sha256":"8fcc1d4e6e360a9dde372722fd4bf802e4d5a6e7dc6e8b05bf486ef9437765cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fcc1d4e6e360a9dde372722fd4bf802e4d5a6e7dc6e8b05bf486ef9437765cb","first_computed_at":"2026-05-18T03:29:14.613218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:14.613218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ku8OfqxY1NBs4tCdW2ZpcVYPphF4UfqUe9Cgc8sHY0duCkXw0VLiXM2V+hBAM32pwsVjtp2ACjEbXfM2gwtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:14.613839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93cd3e568890921899d4702aaba1a9cc72d3ed5c820980698d060bf98df674dc","sha256:a3d2858fe3569ce4e79802821708da7acc670c5c50f681387df8b6d0ec211c09"],"state_sha256":"3e0ad4903273b52ea04877490059919b0eaa159b90df1e64e3fd864fd9bd1031"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opK5Wz5nNfbimzoE+7Blog7jH/Xj+iXMBjWLCd3rbfy4jOIOl734nfmsCxkaxQdT1XLSW6LfHiAbHSymy23GDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:11:14.557874Z","bundle_sha256":"668fe4ee2c00509ab385f8b28b8a89feeb3e5d7e40e046ba4f8fdd297e040a23"}}