{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JEYV5VA2I7RRJIXRJV5ECOSLQS","short_pith_number":"pith:JEYV5VA2","canonical_record":{"source":{"id":"1202.5425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-24T11:47:22Z","cross_cats_sorted":[],"title_canon_sha256":"c8bd6cada608bac96541ee1c9a545729a876b13dd44f698cb5ebac31739dad98","abstract_canon_sha256":"378eacc6f8b662ef35b0c14d2b53f714e605ff5e4f3d371603870197187e35b9"},"schema_version":"1.0"},"canonical_sha256":"49315ed41a47e314a2f14d7a413a4b84bf33aac5ad2ced243ba9eceed6d741c1","source":{"kind":"arxiv","id":"1202.5425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5425","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5425v1","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5425","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"JEYV5VA2I7RR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JEYV5VA2I7RRJIXR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JEYV5VA2","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JEYV5VA2I7RRJIXRJV5ECOSLQS","target":"record","payload":{"canonical_record":{"source":{"id":"1202.5425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-24T11:47:22Z","cross_cats_sorted":[],"title_canon_sha256":"c8bd6cada608bac96541ee1c9a545729a876b13dd44f698cb5ebac31739dad98","abstract_canon_sha256":"378eacc6f8b662ef35b0c14d2b53f714e605ff5e4f3d371603870197187e35b9"},"schema_version":"1.0"},"canonical_sha256":"49315ed41a47e314a2f14d7a413a4b84bf33aac5ad2ced243ba9eceed6d741c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:37.199134Z","signature_b64":"5ltpVBR1wZHitbWgvSwGUen6AN5i96/Xiilqc2gxtVxB1twypgQU+C5O24k4eECetsnf9SoT5W5PvBVUPEuRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49315ed41a47e314a2f14d7a413a4b84bf33aac5ad2ced243ba9eceed6d741c1","last_reissued_at":"2026-05-18T04:01:37.198412Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:37.198412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.5425","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":"2026-05-18T04:01:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ksVQAjuLll8jmyJytSUuIo/kjppeSpZFBN/RBAGwYKHN/4wMa6LyQa/6KJRF75+rlDCk6Oaol3JJ9fBgW/IBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:05:22.277700Z"},"content_sha256":"40b37645a4e7dee34bf80d1f38eb5cb078a8f0de775e311b35e9b4f5d0e5f51d","schema_version":"1.0","event_id":"sha256:40b37645a4e7dee34bf80d1f38eb5cb078a8f0de775e311b35e9b4f5d0e5f51d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JEYV5VA2I7RRJIXRJV5ECOSLQS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"N Dilations and Transference for Continuous One-Parameter Semigroups of Positive Contractions on $\\mathcal{L}^p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gero Fendler","submitted_at":"2012-02-24T11:47:22Z","abstract_excerpt":"These are the notes of a lecture given at the university of Wroclaw in 1996. We present results of semigroups of (sub)positive contractions on L^p-spaces. The dilation theorem of Akcoglue and sucheston is considered as a starting point. We construct a dilation of a strongly continuous semigroup of (sub)positive contractions on L^p-space, 1<p<infinity by a strongly continuous group of invertible isometries acting on some larger L^p-space. The transference results, for functions of the generators, are established as well as some square and maximal functions. This applies especially to sub-markov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5425","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":"2026-05-18T04:01:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WFiwwtqLK1eFFX4kzvHTYILkUIinRx4daMXJC+HBDCSgF/Ho2h8RlZQm5DcHZb+bw1/E0Wszi5WPIh8qhLhgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:05:22.278050Z"},"content_sha256":"62c20b43818801ed748e43802e2f26642f8270ed78ae81a0a4ea83ee092e278a","schema_version":"1.0","event_id":"sha256:62c20b43818801ed748e43802e2f26642f8270ed78ae81a0a4ea83ee092e278a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JEYV5VA2I7RRJIXRJV5ECOSLQS/bundle.json","state_url":"https://pith.science/pith/JEYV5VA2I7RRJIXRJV5ECOSLQS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JEYV5VA2I7RRJIXRJV5ECOSLQS/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":"2026-06-30T23:05:22Z","links":{"resolver":"https://pith.science/pith/JEYV5VA2I7RRJIXRJV5ECOSLQS","bundle":"https://pith.science/pith/JEYV5VA2I7RRJIXRJV5ECOSLQS/bundle.json","state":"https://pith.science/pith/JEYV5VA2I7RRJIXRJV5ECOSLQS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JEYV5VA2I7RRJIXRJV5ECOSLQS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JEYV5VA2I7RRJIXRJV5ECOSLQS","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":"378eacc6f8b662ef35b0c14d2b53f714e605ff5e4f3d371603870197187e35b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-24T11:47:22Z","title_canon_sha256":"c8bd6cada608bac96541ee1c9a545729a876b13dd44f698cb5ebac31739dad98"},"schema_version":"1.0","source":{"id":"1202.5425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5425","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5425v1","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5425","created_at":"2026-05-18T04:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"JEYV5VA2I7RR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JEYV5VA2I7RRJIXR","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JEYV5VA2","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:62c20b43818801ed748e43802e2f26642f8270ed78ae81a0a4ea83ee092e278a","target":"graph","created_at":"2026-05-18T04:01:37Z","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":"These are the notes of a lecture given at the university of Wroclaw in 1996. We present results of semigroups of (sub)positive contractions on L^p-spaces. The dilation theorem of Akcoglue and sucheston is considered as a starting point. We construct a dilation of a strongly continuous semigroup of (sub)positive contractions on L^p-space, 1<p<infinity by a strongly continuous group of invertible isometries acting on some larger L^p-space. The transference results, for functions of the generators, are established as well as some square and maximal functions. This applies especially to sub-markov","authors_text":"Gero Fendler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-24T11:47:22Z","title":"N Dilations and Transference for Continuous One-Parameter Semigroups of Positive Contractions on $\\mathcal{L}^p$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5425","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":"sha256:40b37645a4e7dee34bf80d1f38eb5cb078a8f0de775e311b35e9b4f5d0e5f51d","target":"record","created_at":"2026-05-18T04:01:37Z","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":"378eacc6f8b662ef35b0c14d2b53f714e605ff5e4f3d371603870197187e35b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-02-24T11:47:22Z","title_canon_sha256":"c8bd6cada608bac96541ee1c9a545729a876b13dd44f698cb5ebac31739dad98"},"schema_version":"1.0","source":{"id":"1202.5425","kind":"arxiv","version":1}},"canonical_sha256":"49315ed41a47e314a2f14d7a413a4b84bf33aac5ad2ced243ba9eceed6d741c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49315ed41a47e314a2f14d7a413a4b84bf33aac5ad2ced243ba9eceed6d741c1","first_computed_at":"2026-05-18T04:01:37.198412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:37.198412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ltpVBR1wZHitbWgvSwGUen6AN5i96/Xiilqc2gxtVxB1twypgQU+C5O24k4eECetsnf9SoT5W5PvBVUPEuRCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:37.199134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40b37645a4e7dee34bf80d1f38eb5cb078a8f0de775e311b35e9b4f5d0e5f51d","sha256:62c20b43818801ed748e43802e2f26642f8270ed78ae81a0a4ea83ee092e278a"],"state_sha256":"0cd0e18e095778e71cd67f3fd3c4122c48292c903e8efb2b7221d4839d07b988"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nb3l5foEDFjcxLAmsisaw8LRy2dOV7/pm9GYriW9pz55cBEYKfAWSKGPV2hLMvaX42R4qZogZ6mqpJxjiql0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:05:22.279978Z","bundle_sha256":"47e869e3b74a00edb721e2ecd0df795a8e4e1185ae590ee2d5e93181e1c9ef3a"}}