{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2ICM3JCGHDBFTTQY7PELLMBXFY","short_pith_number":"pith:2ICM3JCG","canonical_record":{"source":{"id":"1812.06820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-17T14:59:25Z","cross_cats_sorted":[],"title_canon_sha256":"82d3ab19a28aebf12c73e08cfc371cbae190de36d9acfe00f2db608fc8124ea7","abstract_canon_sha256":"990efc8fd20dc5a06a8c06196440dfaf4e60ae8f9eeccfcb37c50b163bb12008"},"schema_version":"1.0"},"canonical_sha256":"d204cda44638c259ce18fbc8b5b0372e0e55d8a8240be482d38daa5e16fdc0a9","source":{"kind":"arxiv","id":"1812.06820","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.06820","created_at":"2026-05-17T23:58:09Z"},{"alias_kind":"arxiv_version","alias_value":"1812.06820v1","created_at":"2026-05-17T23:58:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.06820","created_at":"2026-05-17T23:58:09Z"},{"alias_kind":"pith_short_12","alias_value":"2ICM3JCGHDBF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ICM3JCGHDBFTTQY","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ICM3JCG","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2ICM3JCGHDBFTTQY7PELLMBXFY","target":"record","payload":{"canonical_record":{"source":{"id":"1812.06820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-17T14:59:25Z","cross_cats_sorted":[],"title_canon_sha256":"82d3ab19a28aebf12c73e08cfc371cbae190de36d9acfe00f2db608fc8124ea7","abstract_canon_sha256":"990efc8fd20dc5a06a8c06196440dfaf4e60ae8f9eeccfcb37c50b163bb12008"},"schema_version":"1.0"},"canonical_sha256":"d204cda44638c259ce18fbc8b5b0372e0e55d8a8240be482d38daa5e16fdc0a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:09.296431Z","signature_b64":"qmM7iKDwdzWfxPxxyDA2SQrXYq6E1NPMzaiqXDNqwegr4n34AiHBu0fhV26q2vf7AxwylOmIJoC3Nm7Zz7wiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d204cda44638c259ce18fbc8b5b0372e0e55d8a8240be482d38daa5e16fdc0a9","last_reissued_at":"2026-05-17T23:58:09.295718Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:09.295718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.06820","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":"2026-05-17T23:58:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNEK3MQT4Vu6mzFCOj+K6B7/G5VmMD9sXYOpfHc/q5A6FiHfzh0nTK3TEUKl76JfSZwxYcG2+3zVqRGpxCNPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:33:58.559220Z"},"content_sha256":"4175f429dd9e7e156a180b0871d14574e93c74f192389117310f2d65a4f1e415","schema_version":"1.0","event_id":"sha256:4175f429dd9e7e156a180b0871d14574e93c74f192389117310f2d65a4f1e415"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2ICM3JCGHDBFTTQY7PELLMBXFY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence Result for Generalized Variational Equality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Allahkaram Shafie, Farid Bozorgnia","submitted_at":"2018-12-17T14:59:25Z","abstract_excerpt":"In this paper, we prove the existence of a solution to the Stampachia variational inequality under weakened assumptions on the given operator. As a consequence, we provide some sufficient conditions that under them the generalized equation $0\\in T(x)$ has a solution. Furthermore, by using generalized results of continuity and monotonicity, we extend the related existence results and we answer an open problem proposed by Kassay and Miholka (J Optim Theory Appl 159 (2013) 721-740)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06820","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":"2026-05-17T23:58:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C/TL1IoV+fO+d700VfwF55/AoWMO/zAnWEh8cev9hj07qdiRAge3/NzaMuO6k6UVKbPhEdhunNdkAmzFSb1HCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:33:58.559583Z"},"content_sha256":"28629c9314aa99026b71e46d3d4b72d278a4bf25ee7aa3d748545dadfd2a22a0","schema_version":"1.0","event_id":"sha256:28629c9314aa99026b71e46d3d4b72d278a4bf25ee7aa3d748545dadfd2a22a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ICM3JCGHDBFTTQY7PELLMBXFY/bundle.json","state_url":"https://pith.science/pith/2ICM3JCGHDBFTTQY7PELLMBXFY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ICM3JCGHDBFTTQY7PELLMBXFY/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":"2026-06-25T22:33:58Z","links":{"resolver":"https://pith.science/pith/2ICM3JCGHDBFTTQY7PELLMBXFY","bundle":"https://pith.science/pith/2ICM3JCGHDBFTTQY7PELLMBXFY/bundle.json","state":"https://pith.science/pith/2ICM3JCGHDBFTTQY7PELLMBXFY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ICM3JCGHDBFTTQY7PELLMBXFY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2ICM3JCGHDBFTTQY7PELLMBXFY","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":"990efc8fd20dc5a06a8c06196440dfaf4e60ae8f9eeccfcb37c50b163bb12008","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-17T14:59:25Z","title_canon_sha256":"82d3ab19a28aebf12c73e08cfc371cbae190de36d9acfe00f2db608fc8124ea7"},"schema_version":"1.0","source":{"id":"1812.06820","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.06820","created_at":"2026-05-17T23:58:09Z"},{"alias_kind":"arxiv_version","alias_value":"1812.06820v1","created_at":"2026-05-17T23:58:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.06820","created_at":"2026-05-17T23:58:09Z"},{"alias_kind":"pith_short_12","alias_value":"2ICM3JCGHDBF","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ICM3JCGHDBFTTQY","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ICM3JCG","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:28629c9314aa99026b71e46d3d4b72d278a4bf25ee7aa3d748545dadfd2a22a0","target":"graph","created_at":"2026-05-17T23:58:09Z","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":"In this paper, we prove the existence of a solution to the Stampachia variational inequality under weakened assumptions on the given operator. As a consequence, we provide some sufficient conditions that under them the generalized equation $0\\in T(x)$ has a solution. Furthermore, by using generalized results of continuity and monotonicity, we extend the related existence results and we answer an open problem proposed by Kassay and Miholka (J Optim Theory Appl 159 (2013) 721-740).","authors_text":"Allahkaram Shafie, Farid Bozorgnia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-17T14:59:25Z","title":"Existence Result for Generalized Variational Equality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06820","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":"sha256:4175f429dd9e7e156a180b0871d14574e93c74f192389117310f2d65a4f1e415","target":"record","created_at":"2026-05-17T23:58:09Z","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":"990efc8fd20dc5a06a8c06196440dfaf4e60ae8f9eeccfcb37c50b163bb12008","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-17T14:59:25Z","title_canon_sha256":"82d3ab19a28aebf12c73e08cfc371cbae190de36d9acfe00f2db608fc8124ea7"},"schema_version":"1.0","source":{"id":"1812.06820","kind":"arxiv","version":1}},"canonical_sha256":"d204cda44638c259ce18fbc8b5b0372e0e55d8a8240be482d38daa5e16fdc0a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d204cda44638c259ce18fbc8b5b0372e0e55d8a8240be482d38daa5e16fdc0a9","first_computed_at":"2026-05-17T23:58:09.295718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:09.295718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qmM7iKDwdzWfxPxxyDA2SQrXYq6E1NPMzaiqXDNqwegr4n34AiHBu0fhV26q2vf7AxwylOmIJoC3Nm7Zz7wiDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:09.296431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.06820","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4175f429dd9e7e156a180b0871d14574e93c74f192389117310f2d65a4f1e415","sha256:28629c9314aa99026b71e46d3d4b72d278a4bf25ee7aa3d748545dadfd2a22a0"],"state_sha256":"a8e3e09dafb4f9d11574c6ec1956b7061b68a92b7712f1852c02e5ee2cd31232"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DetqlIL4KXF2tLXG+w9GUDBAp9q/BU30dE1aThEBNmYWiu5Fz6SFV6NyrxtnepW8l30Xc+hF1abkfdkhjptBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:33:58.561742Z","bundle_sha256":"41df1efe4dfee41454916260086bdf159465d33993128382a43e99c52b91e495"}}