{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BXS5MSQO472AYIUYW3EN2OBWKB","short_pith_number":"pith:BXS5MSQO","canonical_record":{"source":{"id":"1005.2247","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-13T02:21:50Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"366aa2789f5d58e4b9048e7dbecec30ca34d32b8e6e6f1ab3af9a104c6773030","abstract_canon_sha256":"faa859ed629ae71f7758a7b1b6f6390a222bbf03c2fcd78dc674375ef4b6490e"},"schema_version":"1.0"},"canonical_sha256":"0de5d64a0ee7f40c2298b6c8dd3836506b19e3dff04afe0227d54249873a2e54","source":{"kind":"arxiv","id":"1005.2247","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2247","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2247v2","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2247","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"BXS5MSQO472A","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BXS5MSQO472AYIUY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BXS5MSQO","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BXS5MSQO472AYIUYW3EN2OBWKB","target":"record","payload":{"canonical_record":{"source":{"id":"1005.2247","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-13T02:21:50Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"366aa2789f5d58e4b9048e7dbecec30ca34d32b8e6e6f1ab3af9a104c6773030","abstract_canon_sha256":"faa859ed629ae71f7758a7b1b6f6390a222bbf03c2fcd78dc674375ef4b6490e"},"schema_version":"1.0"},"canonical_sha256":"0de5d64a0ee7f40c2298b6c8dd3836506b19e3dff04afe0227d54249873a2e54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:13.561632Z","signature_b64":"nWpjeWyMs9EWxWgXdCEZFU4xAYcgUa3b8p7N1N6Pb3JitXB7mXkMHtypq51EDIirYZ57tDdvTJEq84oXYHo5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0de5d64a0ee7f40c2298b6c8dd3836506b19e3dff04afe0227d54249873a2e54","last_reissued_at":"2026-05-18T04:42:13.561178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:13.561178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.2247","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JQNMRggIdAU4liW1XUMd9kp6vJCF+snmeqa0J32TdJpuYAt7h/FDNUyDvZf5STYvt5WojIdhpZ2oPGy0vbJ+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:56:36.505071Z"},"content_sha256":"58c6369e7178b8f77e22fb4ac6be6ee08043f7efb70cb2def1fb34ece3d77d88","schema_version":"1.0","event_id":"sha256:58c6369e7178b8f77e22fb4ac6be6ee08043f7efb70cb2def1fb34ece3d77d88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BXS5MSQO472AYIUYW3EN2OBWKB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.FA","authors_text":"Liangjin Yao","submitted_at":"2010-05-13T02:21:50Z","abstract_excerpt":"The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qualification holds.\n  In this paper, we prove the maximal monotonicity of $A+B$ provided that $A$ and $B$ are maximal monotone operators such that $\\dom A\\cap\\inte\\dom B\\neq\\varnothing$, $A+N_{\\overline{\\dom B}}$ is of type (FPV), and $\\dom A\\cap\\overline{\\dom B}\\subseteq\\dom B$. The proof utilizes the Fitzpatrick function in an essential way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2247","kind":"arxiv","version":2},"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":"2026-05-18T04:42:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rwsYw59jQUSz/JtJzZnxvt8gwHh0DcQfJMorOP57KSJ5eQkd3C80CU9SSzYP+fiHpMRIpNWI3X6euqX/zlAwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:56:36.505443Z"},"content_sha256":"779d94e85d22af8c8138c010ac319bdb49a5ee419a929c648c5f66a84bd9b15d","schema_version":"1.0","event_id":"sha256:779d94e85d22af8c8138c010ac319bdb49a5ee419a929c648c5f66a84bd9b15d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXS5MSQO472AYIUYW3EN2OBWKB/bundle.json","state_url":"https://pith.science/pith/BXS5MSQO472AYIUYW3EN2OBWKB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXS5MSQO472AYIUYW3EN2OBWKB/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":"2026-06-08T09:56:36Z","links":{"resolver":"https://pith.science/pith/BXS5MSQO472AYIUYW3EN2OBWKB","bundle":"https://pith.science/pith/BXS5MSQO472AYIUYW3EN2OBWKB/bundle.json","state":"https://pith.science/pith/BXS5MSQO472AYIUYW3EN2OBWKB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXS5MSQO472AYIUYW3EN2OBWKB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BXS5MSQO472AYIUYW3EN2OBWKB","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":"faa859ed629ae71f7758a7b1b6f6390a222bbf03c2fcd78dc674375ef4b6490e","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-13T02:21:50Z","title_canon_sha256":"366aa2789f5d58e4b9048e7dbecec30ca34d32b8e6e6f1ab3af9a104c6773030"},"schema_version":"1.0","source":{"id":"1005.2247","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.2247","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1005.2247v2","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2247","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"BXS5MSQO472A","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BXS5MSQO472AYIUY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BXS5MSQO","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:779d94e85d22af8c8138c010ac319bdb49a5ee419a929c648c5f66a84bd9b15d","target":"graph","created_at":"2026-05-18T04:42:13Z","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":"The most important open problem in Monotone Operator Theory concerns the maximal monotonicity of the sum of two maximal monotone operators provided that Rockafellar's constraint qualification holds.\n  In this paper, we prove the maximal monotonicity of $A+B$ provided that $A$ and $B$ are maximal monotone operators such that $\\dom A\\cap\\inte\\dom B\\neq\\varnothing$, $A+N_{\\overline{\\dom B}}$ is of type (FPV), and $\\dom A\\cap\\overline{\\dom B}\\subseteq\\dom B$. The proof utilizes the Fitzpatrick function in an essential way.","authors_text":"Liangjin Yao","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-13T02:21:50Z","title":"The sum of a maximal monotone operator of type (FPV) and a maximal monotone operator with full domain is maximal monotone"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2247","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":"sha256:58c6369e7178b8f77e22fb4ac6be6ee08043f7efb70cb2def1fb34ece3d77d88","target":"record","created_at":"2026-05-18T04:42:13Z","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":"faa859ed629ae71f7758a7b1b6f6390a222bbf03c2fcd78dc674375ef4b6490e","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-13T02:21:50Z","title_canon_sha256":"366aa2789f5d58e4b9048e7dbecec30ca34d32b8e6e6f1ab3af9a104c6773030"},"schema_version":"1.0","source":{"id":"1005.2247","kind":"arxiv","version":2}},"canonical_sha256":"0de5d64a0ee7f40c2298b6c8dd3836506b19e3dff04afe0227d54249873a2e54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0de5d64a0ee7f40c2298b6c8dd3836506b19e3dff04afe0227d54249873a2e54","first_computed_at":"2026-05-18T04:42:13.561178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:13.561178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nWpjeWyMs9EWxWgXdCEZFU4xAYcgUa3b8p7N1N6Pb3JitXB7mXkMHtypq51EDIirYZ57tDdvTJEq84oXYHo5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:13.561632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.2247","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58c6369e7178b8f77e22fb4ac6be6ee08043f7efb70cb2def1fb34ece3d77d88","sha256:779d94e85d22af8c8138c010ac319bdb49a5ee419a929c648c5f66a84bd9b15d"],"state_sha256":"e6f5a5589915be4a366c83102e26341ae78360f6da34b2ae9b31883967ae20de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gUKxFEkFpusNeP46Mzm/ioLnnqkOMtIFQ7SFGDhP2oWRqtJr2dRkvnEMaWoN2wna4wF+xXgCNTF3ohtFRP1cBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:56:36.507705Z","bundle_sha256":"4d15151d566ea1dc85457c45e588d435ce91c3a3cacd7a36390bda82cd1d5e89"}}