{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MJD5PQCHDHXI5F6A6DBF74CYXX","short_pith_number":"pith:MJD5PQCH","canonical_record":{"source":{"id":"1212.5438","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-21T13:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"fa16721f7444ca80696164fed43c82fbbe770fe7a6234b51a1d600abb8108565","abstract_canon_sha256":"701ba7c1c838fb2e4223507b997df877e2dae1f14143d5b09289db130fa99469"},"schema_version":"1.0"},"canonical_sha256":"6247d7c04719ee8e97c0f0c25ff058bdc65da6cd66d252cc23e11a010e6cb70e","source":{"kind":"arxiv","id":"1212.5438","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5438","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5438v3","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5438","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"MJD5PQCHDHXI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MJD5PQCHDHXI5F6A","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MJD5PQCH","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MJD5PQCHDHXI5F6A6DBF74CYXX","target":"record","payload":{"canonical_record":{"source":{"id":"1212.5438","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-21T13:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"fa16721f7444ca80696164fed43c82fbbe770fe7a6234b51a1d600abb8108565","abstract_canon_sha256":"701ba7c1c838fb2e4223507b997df877e2dae1f14143d5b09289db130fa99469"},"schema_version":"1.0"},"canonical_sha256":"6247d7c04719ee8e97c0f0c25ff058bdc65da6cd66d252cc23e11a010e6cb70e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:57.828031Z","signature_b64":"SXOWb17EMzzE2IBLb2IH9ebUTpyOSvdjg1YbAxkZYi7cfycfVwWq9NsDRlDYD8QxDahhXTGk5ZSIADJgwQjhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6247d7c04719ee8e97c0f0c25ff058bdc65da6cd66d252cc23e11a010e6cb70e","last_reissued_at":"2026-05-18T03:12:57.827399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:57.827399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.5438","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d4reqMIbbpyNQQBooikzJZ4tyQ4WIZ2JSN/4bE8Wc2YNqXC323hLLDX2ydKOT1hryZ/j3E2P5wzpyi/hSYc0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:45:00.028534Z"},"content_sha256":"06de25a100f69e490aecc7ae9549e93bd32e2102621b1c5cc2b6e885b3a46bc7","schema_version":"1.0","event_id":"sha256:06de25a100f69e490aecc7ae9549e93bd32e2102621b1c5cc2b6e885b3a46bc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MJD5PQCHDHXI5F6A6DBF74CYXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A duality between the metric projection onto a convex cone and the metric projection onto its dual in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"S. Z. N\\'emeth","submitted_at":"2012-12-21T13:55:12Z","abstract_excerpt":"If $K$ and $L$ are mutually dual closed convex cones in a Hilbert space with the metric projections onto them denoted by $P_K$ and $P_L$ respectively, then the following two assertions are equivalent: (i) $P_K$ is isotone with respect to the order induced by $K$ (i. e. $v-u\\in K$ implies $P_Kv-P_Ku\\in K$); (ii) $P_L$ is subadditive with respect to the order induced by $L$ (i. e. $P_Lu+P_Lv-P_L(u+v)\\in L$ for any $u, v \\in \\R^n$). This extends the similar result of A. B. N\\'emeth and the author for Euclidean spaces. The extension is essential because the proof of the result for Euclidean spaces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5438","kind":"arxiv","version":3},"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":"2026-05-18T03:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GS9cGR0OtWU1uSNB4OgCXBo3p/sUHxlUFQyo48OExQhaG+nvc1bawdp79ToKaXJd58ZoSCIOB7cARHo6DrrwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:45:00.029216Z"},"content_sha256":"443ebc4decd4f466578d760cdbefb148719c7bf5683765ed08e6a191125b3a21","schema_version":"1.0","event_id":"sha256:443ebc4decd4f466578d760cdbefb148719c7bf5683765ed08e6a191125b3a21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MJD5PQCHDHXI5F6A6DBF74CYXX/bundle.json","state_url":"https://pith.science/pith/MJD5PQCHDHXI5F6A6DBF74CYXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MJD5PQCHDHXI5F6A6DBF74CYXX/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":"2026-05-26T03:45:00Z","links":{"resolver":"https://pith.science/pith/MJD5PQCHDHXI5F6A6DBF74CYXX","bundle":"https://pith.science/pith/MJD5PQCHDHXI5F6A6DBF74CYXX/bundle.json","state":"https://pith.science/pith/MJD5PQCHDHXI5F6A6DBF74CYXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MJD5PQCHDHXI5F6A6DBF74CYXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MJD5PQCHDHXI5F6A6DBF74CYXX","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":"701ba7c1c838fb2e4223507b997df877e2dae1f14143d5b09289db130fa99469","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-21T13:55:12Z","title_canon_sha256":"fa16721f7444ca80696164fed43c82fbbe770fe7a6234b51a1d600abb8108565"},"schema_version":"1.0","source":{"id":"1212.5438","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.5438","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1212.5438v3","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5438","created_at":"2026-05-18T03:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"MJD5PQCHDHXI","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MJD5PQCHDHXI5F6A","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MJD5PQCH","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:443ebc4decd4f466578d760cdbefb148719c7bf5683765ed08e6a191125b3a21","target":"graph","created_at":"2026-05-18T03:12:57Z","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":"If $K$ and $L$ are mutually dual closed convex cones in a Hilbert space with the metric projections onto them denoted by $P_K$ and $P_L$ respectively, then the following two assertions are equivalent: (i) $P_K$ is isotone with respect to the order induced by $K$ (i. e. $v-u\\in K$ implies $P_Kv-P_Ku\\in K$); (ii) $P_L$ is subadditive with respect to the order induced by $L$ (i. e. $P_Lu+P_Lv-P_L(u+v)\\in L$ for any $u, v \\in \\R^n$). This extends the similar result of A. B. N\\'emeth and the author for Euclidean spaces. The extension is essential because the proof of the result for Euclidean spaces","authors_text":"S. Z. N\\'emeth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-21T13:55:12Z","title":"A duality between the metric projection onto a convex cone and the metric projection onto its dual in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5438","kind":"arxiv","version":3},"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":"sha256:06de25a100f69e490aecc7ae9549e93bd32e2102621b1c5cc2b6e885b3a46bc7","target":"record","created_at":"2026-05-18T03:12:57Z","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":"701ba7c1c838fb2e4223507b997df877e2dae1f14143d5b09289db130fa99469","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-12-21T13:55:12Z","title_canon_sha256":"fa16721f7444ca80696164fed43c82fbbe770fe7a6234b51a1d600abb8108565"},"schema_version":"1.0","source":{"id":"1212.5438","kind":"arxiv","version":3}},"canonical_sha256":"6247d7c04719ee8e97c0f0c25ff058bdc65da6cd66d252cc23e11a010e6cb70e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6247d7c04719ee8e97c0f0c25ff058bdc65da6cd66d252cc23e11a010e6cb70e","first_computed_at":"2026-05-18T03:12:57.827399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:57.827399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SXOWb17EMzzE2IBLb2IH9ebUTpyOSvdjg1YbAxkZYi7cfycfVwWq9NsDRlDYD8QxDahhXTGk5ZSIADJgwQjhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:57.828031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.5438","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06de25a100f69e490aecc7ae9549e93bd32e2102621b1c5cc2b6e885b3a46bc7","sha256:443ebc4decd4f466578d760cdbefb148719c7bf5683765ed08e6a191125b3a21"],"state_sha256":"5d6ef323a40d53a7967a6f074a88ba602e12da36f47a6b9705c9a0cb7282c80d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"odWOu28F9Nf+58lCGYHWZsnpaWkFj8/4TS/5q7ZaLioC5oWoFcneA21ROpXFXq3kQxMUBWP1iRdDMXu/maD1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:45:00.033003Z","bundle_sha256":"31697bbaf2f4396769015a3d6c27698be7dcb01379de0e4aac2edd89e9a5e1d0"}}