{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CSTOV5GM6I5MBLWYDYNU2RWXM5","short_pith_number":"pith:CSTOV5GM","canonical_record":{"source":{"id":"1103.1409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-08T01:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"04c7a25fd972df308ec4d4887744522ee451ecf815813d181c477c1116f864aa","abstract_canon_sha256":"07a5f77ce20c83b18eee7f189f59fa38f8c58821ece0928c7c5a8cd02797a3b1"},"schema_version":"1.0"},"canonical_sha256":"14a6eaf4ccf23ac0aed81e1b4d46d7675c7395e6411e776051c79f259aa66243","source":{"kind":"arxiv","id":"1103.1409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1409","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1409v1","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1409","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"CSTOV5GM6I5M","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CSTOV5GM6I5MBLWY","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CSTOV5GM","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CSTOV5GM6I5MBLWYDYNU2RWXM5","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-08T01:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"04c7a25fd972df308ec4d4887744522ee451ecf815813d181c477c1116f864aa","abstract_canon_sha256":"07a5f77ce20c83b18eee7f189f59fa38f8c58821ece0928c7c5a8cd02797a3b1"},"schema_version":"1.0"},"canonical_sha256":"14a6eaf4ccf23ac0aed81e1b4d46d7675c7395e6411e776051c79f259aa66243","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:15.895497Z","signature_b64":"8jhqX23NjxiYmGv71Tj2w3I7ntwZVURD7KOdPZi4D18iAC2rat1Ar4vVhS/5c9KSaZd2sBVsE+bwDW9zes26Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14a6eaf4ccf23ac0aed81e1b4d46d7675c7395e6411e776051c79f259aa66243","last_reissued_at":"2026-05-18T04:27:15.894967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:15.894967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1409","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":"2026-05-18T04:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ms51QmPNTcKT/xNWMctRcmPGwhUhUHC1zSCfRdZeuRS0hcow5nIqWkMkIXlvNt/eodgwrCQJYx6zPE679OyQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T02:28:08.670108Z"},"content_sha256":"e9651bb5c3f69a4841d3bde61f61e137587760cf91921f551cf3b4b0a015af17","schema_version":"1.0","event_id":"sha256:e9651bb5c3f69a4841d3bde61f61e137587760cf91921f551cf3b4b0a015af17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CSTOV5GM6I5MBLWYDYNU2RWXM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximally Monotone Linear Subspace Extensions of Monotone Subspaces: Explicit Constructions and Characterizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Liangjin Yao, Xianfu Wang","submitted_at":"2011-03-08T01:05:30Z","abstract_excerpt":"Monotone linear relations play important roles in variational inequality problems and quadratic optimizations. In this paper, we give explicit maximally monotone linear subspace extensions of a monotone linear relation in finite dimensional spaces. Examples are provided to illustrate our extensions. Our results generalize a recent result by Crouzeix and Anaya."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1409","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":"2026-05-18T04:27:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A8qiBegjN1m0P+WIxB4tef84cYRZBGmyCZyeI6UmWv2xMc1BKmLm7G/gNnA6yrSDAjsMYAPU3+6MtDmel9EOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T02:28:08.670741Z"},"content_sha256":"e85ee8555445fc6ff7c1d71220d9f0103720e2e65cc2bae3230766b16d773e20","schema_version":"1.0","event_id":"sha256:e85ee8555445fc6ff7c1d71220d9f0103720e2e65cc2bae3230766b16d773e20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CSTOV5GM6I5MBLWYDYNU2RWXM5/bundle.json","state_url":"https://pith.science/pith/CSTOV5GM6I5MBLWYDYNU2RWXM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CSTOV5GM6I5MBLWYDYNU2RWXM5/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":"2026-06-08T02:28:08Z","links":{"resolver":"https://pith.science/pith/CSTOV5GM6I5MBLWYDYNU2RWXM5","bundle":"https://pith.science/pith/CSTOV5GM6I5MBLWYDYNU2RWXM5/bundle.json","state":"https://pith.science/pith/CSTOV5GM6I5MBLWYDYNU2RWXM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CSTOV5GM6I5MBLWYDYNU2RWXM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CSTOV5GM6I5MBLWYDYNU2RWXM5","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":"07a5f77ce20c83b18eee7f189f59fa38f8c58821ece0928c7c5a8cd02797a3b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-08T01:05:30Z","title_canon_sha256":"04c7a25fd972df308ec4d4887744522ee451ecf815813d181c477c1116f864aa"},"schema_version":"1.0","source":{"id":"1103.1409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1409","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1409v1","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1409","created_at":"2026-05-18T04:27:15Z"},{"alias_kind":"pith_short_12","alias_value":"CSTOV5GM6I5M","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CSTOV5GM6I5MBLWY","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CSTOV5GM","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:e85ee8555445fc6ff7c1d71220d9f0103720e2e65cc2bae3230766b16d773e20","target":"graph","created_at":"2026-05-18T04:27:15Z","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":"Monotone linear relations play important roles in variational inequality problems and quadratic optimizations. In this paper, we give explicit maximally monotone linear subspace extensions of a monotone linear relation in finite dimensional spaces. Examples are provided to illustrate our extensions. Our results generalize a recent result by Crouzeix and Anaya.","authors_text":"Liangjin Yao, Xianfu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-08T01:05:30Z","title":"Maximally Monotone Linear Subspace Extensions of Monotone Subspaces: Explicit Constructions and Characterizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1409","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:e9651bb5c3f69a4841d3bde61f61e137587760cf91921f551cf3b4b0a015af17","target":"record","created_at":"2026-05-18T04:27:15Z","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":"07a5f77ce20c83b18eee7f189f59fa38f8c58821ece0928c7c5a8cd02797a3b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-08T01:05:30Z","title_canon_sha256":"04c7a25fd972df308ec4d4887744522ee451ecf815813d181c477c1116f864aa"},"schema_version":"1.0","source":{"id":"1103.1409","kind":"arxiv","version":1}},"canonical_sha256":"14a6eaf4ccf23ac0aed81e1b4d46d7675c7395e6411e776051c79f259aa66243","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14a6eaf4ccf23ac0aed81e1b4d46d7675c7395e6411e776051c79f259aa66243","first_computed_at":"2026-05-18T04:27:15.894967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:15.894967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8jhqX23NjxiYmGv71Tj2w3I7ntwZVURD7KOdPZi4D18iAC2rat1Ar4vVhS/5c9KSaZd2sBVsE+bwDW9zes26Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:15.895497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9651bb5c3f69a4841d3bde61f61e137587760cf91921f551cf3b4b0a015af17","sha256:e85ee8555445fc6ff7c1d71220d9f0103720e2e65cc2bae3230766b16d773e20"],"state_sha256":"1c09666bff4ba5bae182bde881cfca08775f89b6f669f8fff6afa3d39ff0a0f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mtn1TmCpki1CUzlxJLMmN8hc3tIErKM9bYM/NPnq73oSpstFkA+hmGasUw6oHIzsSQlFDkHm7fHDSaVqAfGkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T02:28:08.673962Z","bundle_sha256":"7fc0347e0d629c9b9fb96752ae1e7659986d3474787cff3e11a0b593e20d6edd"}}