{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:P7HDSL23PO5EX3BKCGAEEIGSUB","short_pith_number":"pith:P7HDSL23","canonical_record":{"source":{"id":"1902.09827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T09:49:41Z","cross_cats_sorted":[],"title_canon_sha256":"081d57b4747ab154abec3cfde4f27ddb099f76956309152ae30dcc067acca760","abstract_canon_sha256":"b5d84147d960be9eea304120003052dcfbeb2983fae23da777db92d126364056"},"schema_version":"1.0"},"canonical_sha256":"7fce392f5b7bba4bec2a11804220d2a07b2fb80ec571e5bb6ee743466fb2e05e","source":{"kind":"arxiv","id":"1902.09827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09827","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09827v1","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09827","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"P7HDSL23PO5E","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"P7HDSL23PO5EX3BK","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"P7HDSL23","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:P7HDSL23PO5EX3BKCGAEEIGSUB","target":"record","payload":{"canonical_record":{"source":{"id":"1902.09827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T09:49:41Z","cross_cats_sorted":[],"title_canon_sha256":"081d57b4747ab154abec3cfde4f27ddb099f76956309152ae30dcc067acca760","abstract_canon_sha256":"b5d84147d960be9eea304120003052dcfbeb2983fae23da777db92d126364056"},"schema_version":"1.0"},"canonical_sha256":"7fce392f5b7bba4bec2a11804220d2a07b2fb80ec571e5bb6ee743466fb2e05e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:35.241902Z","signature_b64":"7SufpACJ3y6jSKifjXPwiyZjOxK8tBo31U7+PCp9vdqAuln4sZf0iZh7BOXa2HDxulzp1HcE8ALr7IETax2dDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fce392f5b7bba4bec2a11804220d2a07b2fb80ec571e5bb6ee743466fb2e05e","last_reissued_at":"2026-05-17T23:52:35.241428Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:35.241428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.09827","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":"2026-05-17T23:52:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dtybRV6whBzPWV31DEAgRtSyV2BJpSMur2Pt9EPNbxRTdizidBJygshViMgzU0JDcLbiAlbpVfNac1N47blECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:49:28.206207Z"},"content_sha256":"4f83a66233099560461a1b6aec9376a8460c10ce9f4e1d84326f2fe255975e86","schema_version":"1.0","event_id":"sha256:4f83a66233099560461a1b6aec9376a8460c10ce9f4e1d84326f2fe255975e86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:P7HDSL23PO5EX3BKCGAEEIGSUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized monotone operators and their averaged resolvents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Heinz H. Bauschke, Walaa M. Moursi, Xianfu Wang","submitted_at":"2019-02-26T09:49:41Z","abstract_excerpt":"The correspondence between the monotonicity of a (possibly) set-valued operator and the firm nonexpansiveness of its resolvent is a key ingredient in the convergence analysis of many optimization algorithms. Firmly nonexpansive operators form a proper subclass of the more general - but still pleasant from an algorithmic perspective - class of averaged operators. In this paper, we introduce the new notion of conically nonexpansive operators which generalize nonexpansive mappings. We characterize averaged operators as being resolvents of comonotone operators under appropriate scaling. As a conse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09827","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":"2026-05-17T23:52:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aUivIZ2YUcfAcYszzse9H6O8HQ46A7rm9Q+UB2Toyz36S0SABMBIF6zudze8voncuAFdoUhlqm7FBdxGRHoiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:49:28.206945Z"},"content_sha256":"01360abb7e7d8cbfedf1482f8b23b2cbda8035fbfb4610e21bf0135861a1d968","schema_version":"1.0","event_id":"sha256:01360abb7e7d8cbfedf1482f8b23b2cbda8035fbfb4610e21bf0135861a1d968"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7HDSL23PO5EX3BKCGAEEIGSUB/bundle.json","state_url":"https://pith.science/pith/P7HDSL23PO5EX3BKCGAEEIGSUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7HDSL23PO5EX3BKCGAEEIGSUB/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":"2026-06-09T15:49:28Z","links":{"resolver":"https://pith.science/pith/P7HDSL23PO5EX3BKCGAEEIGSUB","bundle":"https://pith.science/pith/P7HDSL23PO5EX3BKCGAEEIGSUB/bundle.json","state":"https://pith.science/pith/P7HDSL23PO5EX3BKCGAEEIGSUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7HDSL23PO5EX3BKCGAEEIGSUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:P7HDSL23PO5EX3BKCGAEEIGSUB","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":"b5d84147d960be9eea304120003052dcfbeb2983fae23da777db92d126364056","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T09:49:41Z","title_canon_sha256":"081d57b4747ab154abec3cfde4f27ddb099f76956309152ae30dcc067acca760"},"schema_version":"1.0","source":{"id":"1902.09827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09827","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09827v1","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09827","created_at":"2026-05-17T23:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"P7HDSL23PO5E","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"P7HDSL23PO5EX3BK","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"P7HDSL23","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:01360abb7e7d8cbfedf1482f8b23b2cbda8035fbfb4610e21bf0135861a1d968","target":"graph","created_at":"2026-05-17T23:52:35Z","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 correspondence between the monotonicity of a (possibly) set-valued operator and the firm nonexpansiveness of its resolvent is a key ingredient in the convergence analysis of many optimization algorithms. Firmly nonexpansive operators form a proper subclass of the more general - but still pleasant from an algorithmic perspective - class of averaged operators. In this paper, we introduce the new notion of conically nonexpansive operators which generalize nonexpansive mappings. We characterize averaged operators as being resolvents of comonotone operators under appropriate scaling. As a conse","authors_text":"Heinz H. Bauschke, Walaa M. Moursi, Xianfu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T09:49:41Z","title":"Generalized monotone operators and their averaged resolvents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09827","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":"sha256:4f83a66233099560461a1b6aec9376a8460c10ce9f4e1d84326f2fe255975e86","target":"record","created_at":"2026-05-17T23:52:35Z","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":"b5d84147d960be9eea304120003052dcfbeb2983fae23da777db92d126364056","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T09:49:41Z","title_canon_sha256":"081d57b4747ab154abec3cfde4f27ddb099f76956309152ae30dcc067acca760"},"schema_version":"1.0","source":{"id":"1902.09827","kind":"arxiv","version":1}},"canonical_sha256":"7fce392f5b7bba4bec2a11804220d2a07b2fb80ec571e5bb6ee743466fb2e05e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fce392f5b7bba4bec2a11804220d2a07b2fb80ec571e5bb6ee743466fb2e05e","first_computed_at":"2026-05-17T23:52:35.241428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:35.241428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7SufpACJ3y6jSKifjXPwiyZjOxK8tBo31U7+PCp9vdqAuln4sZf0iZh7BOXa2HDxulzp1HcE8ALr7IETax2dDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:35.241902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f83a66233099560461a1b6aec9376a8460c10ce9f4e1d84326f2fe255975e86","sha256:01360abb7e7d8cbfedf1482f8b23b2cbda8035fbfb4610e21bf0135861a1d968"],"state_sha256":"353c28231b7632b86f0931def7a879a7583807f78cd479c255ed0a79c03463a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wz9Xpfd4jXk7a8m8//nSGFn6LkC5ov/OohZRYXueDFWXTuFzcBjFMlNzKmgOlch2p+Q060AuTXSEALAfxvMLBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:49:28.211129Z","bundle_sha256":"ba4d03979f84d89eb00310258795ccfa6b80c601506ff711e76a58a4f65d1e76"}}