{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:D46KI4UBLZRS5THUOBMSP52PRW","short_pith_number":"pith:D46KI4UB","canonical_record":{"source":{"id":"1505.01336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-06T12:15:35Z","cross_cats_sorted":[],"title_canon_sha256":"54bd8269ded2d674b94af39d4b83ca8ae370005c7e073490f233a01969e5c754","abstract_canon_sha256":"248821a04798cfc2ebbc66d802ef4fef24aee052edfaa1b22a5d987cae894da3"},"schema_version":"1.0"},"canonical_sha256":"1f3ca472815e632eccf4705927f74f8d9443575d42d0a602a6691e781ec688fb","source":{"kind":"arxiv","id":"1505.01336","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01336","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01336v1","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01336","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"D46KI4UBLZRS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D46KI4UBLZRS5THU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D46KI4UB","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:D46KI4UBLZRS5THUOBMSP52PRW","target":"record","payload":{"canonical_record":{"source":{"id":"1505.01336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-06T12:15:35Z","cross_cats_sorted":[],"title_canon_sha256":"54bd8269ded2d674b94af39d4b83ca8ae370005c7e073490f233a01969e5c754","abstract_canon_sha256":"248821a04798cfc2ebbc66d802ef4fef24aee052edfaa1b22a5d987cae894da3"},"schema_version":"1.0"},"canonical_sha256":"1f3ca472815e632eccf4705927f74f8d9443575d42d0a602a6691e781ec688fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:49.734571Z","signature_b64":"i7oSV7PtbRQcU0oFN/ea7zbu1NW/2Lbk9ZnIxyd50cZtuOMU63UJgXwIWenujWh1Uu9bB71WoUJOF5jV0dsuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f3ca472815e632eccf4705927f74f8d9443575d42d0a602a6691e781ec688fb","last_reissued_at":"2026-05-18T02:16:49.733841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:49.733841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.01336","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":"2026-05-18T02:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rMI3ynbLBiAH4Mu1z2IFKw1Vfy2qp5yD2eq0OS2FM33BXOdLeZjHEhJXLIAj5oqlkISc+5/ghCDkVEX/+F3mBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:37:29.667425Z"},"content_sha256":"82768bc15aa8e79eea1bf5bacc33562d3774729e0fa2213bd45f3632cddfc882","schema_version":"1.0","event_id":"sha256:82768bc15aa8e79eea1bf5bacc33562d3774729e0fa2213bd45f3632cddfc882"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:D46KI4UBLZRS5THUOBMSP52PRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbation of Analytic Semigroups and Applications to Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Klaus-Jochen Engel, Martin Adler, Miriam Bombieri","submitted_at":"2015-05-06T12:15:35Z","abstract_excerpt":"In a recent paper we presented a general perturbation result for generators of $C_0$-semigroups. The aim of the present paper is to replace, in case the unperturbed semigroup is analytic, the various conditions appearing in this result by simpler assumptions on the domain and range of the operators involved. The power of our result to treat classes of PDE's systematically is illustrated by considering a generic example, a degenerate differential operator with generalized Wentzell boundary conditions and a reaction diffusion equation subject to Neumann boundary conditions with distributed unbou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01336","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":"2026-05-18T02:16:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"harOdhImLRzXfDGlRxCeXOwjN8/05aWR92vuIZh1u1M89hgMsdcUstlsLnqt9yVXx4oz6G7CUaFn45CEaw3mAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:37:29.667756Z"},"content_sha256":"0ab40fdd27b6bc22a62e6fdd3ff29487a9c66c857423e7c08ca9f672025c72c1","schema_version":"1.0","event_id":"sha256:0ab40fdd27b6bc22a62e6fdd3ff29487a9c66c857423e7c08ca9f672025c72c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D46KI4UBLZRS5THUOBMSP52PRW/bundle.json","state_url":"https://pith.science/pith/D46KI4UBLZRS5THUOBMSP52PRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D46KI4UBLZRS5THUOBMSP52PRW/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":"2026-06-07T04:37:29Z","links":{"resolver":"https://pith.science/pith/D46KI4UBLZRS5THUOBMSP52PRW","bundle":"https://pith.science/pith/D46KI4UBLZRS5THUOBMSP52PRW/bundle.json","state":"https://pith.science/pith/D46KI4UBLZRS5THUOBMSP52PRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D46KI4UBLZRS5THUOBMSP52PRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:D46KI4UBLZRS5THUOBMSP52PRW","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":"248821a04798cfc2ebbc66d802ef4fef24aee052edfaa1b22a5d987cae894da3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-06T12:15:35Z","title_canon_sha256":"54bd8269ded2d674b94af39d4b83ca8ae370005c7e073490f233a01969e5c754"},"schema_version":"1.0","source":{"id":"1505.01336","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01336","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01336v1","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01336","created_at":"2026-05-18T02:16:49Z"},{"alias_kind":"pith_short_12","alias_value":"D46KI4UBLZRS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"D46KI4UBLZRS5THU","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"D46KI4UB","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:0ab40fdd27b6bc22a62e6fdd3ff29487a9c66c857423e7c08ca9f672025c72c1","target":"graph","created_at":"2026-05-18T02:16:49Z","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":"In a recent paper we presented a general perturbation result for generators of $C_0$-semigroups. The aim of the present paper is to replace, in case the unperturbed semigroup is analytic, the various conditions appearing in this result by simpler assumptions on the domain and range of the operators involved. The power of our result to treat classes of PDE's systematically is illustrated by considering a generic example, a degenerate differential operator with generalized Wentzell boundary conditions and a reaction diffusion equation subject to Neumann boundary conditions with distributed unbou","authors_text":"Klaus-Jochen Engel, Martin Adler, Miriam Bombieri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-06T12:15:35Z","title":"Perturbation of Analytic Semigroups and Applications to Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01336","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":"sha256:82768bc15aa8e79eea1bf5bacc33562d3774729e0fa2213bd45f3632cddfc882","target":"record","created_at":"2026-05-18T02:16:49Z","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":"248821a04798cfc2ebbc66d802ef4fef24aee052edfaa1b22a5d987cae894da3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-06T12:15:35Z","title_canon_sha256":"54bd8269ded2d674b94af39d4b83ca8ae370005c7e073490f233a01969e5c754"},"schema_version":"1.0","source":{"id":"1505.01336","kind":"arxiv","version":1}},"canonical_sha256":"1f3ca472815e632eccf4705927f74f8d9443575d42d0a602a6691e781ec688fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f3ca472815e632eccf4705927f74f8d9443575d42d0a602a6691e781ec688fb","first_computed_at":"2026-05-18T02:16:49.733841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:49.733841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7oSV7PtbRQcU0oFN/ea7zbu1NW/2Lbk9ZnIxyd50cZtuOMU63UJgXwIWenujWh1Uu9bB71WoUJOF5jV0dsuCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:49.734571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01336","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82768bc15aa8e79eea1bf5bacc33562d3774729e0fa2213bd45f3632cddfc882","sha256:0ab40fdd27b6bc22a62e6fdd3ff29487a9c66c857423e7c08ca9f672025c72c1"],"state_sha256":"b11b1fdd653b34fee463bbfd4472a44ba670098ec401521ce8518614279bc8c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1Llq649OmE3aqFhnmy1tOd/JvRySD0moGHjYVfsIbOnQhEgQ0R3Qh43Y+iq5cAnD+b4+1Mldw96o7wao78EAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:37:29.669617Z","bundle_sha256":"d38b7c20ce72c5ef843488fa5b64451dcf52bb3ee042ae00fc64e49b2936e113"}}