{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:B26G2JDWOC5GIGKQTGVJGEXOYF","short_pith_number":"pith:B26G2JDW","canonical_record":{"source":{"id":"0911.2443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-11-12T18:22:14Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"92f0b4c12294ff178477b8fa613c8e51bb371ca12f929544d85c5f552a006412","abstract_canon_sha256":"78055b52563c70ffbfb40942f4c40089cd0cc982ecfb134304d4131f3048604b"},"schema_version":"1.0"},"canonical_sha256":"0ebc6d247670ba64195099aa9312eec17eb2f36c95a37e0d49bf4f14b4c15ca8","source":{"kind":"arxiv","id":"0911.2443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2443","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2443v1","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2443","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"B26G2JDWOC5G","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"B26G2JDWOC5GIGKQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"B26G2JDW","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:B26G2JDWOC5GIGKQTGVJGEXOYF","target":"record","payload":{"canonical_record":{"source":{"id":"0911.2443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-11-12T18:22:14Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"92f0b4c12294ff178477b8fa613c8e51bb371ca12f929544d85c5f552a006412","abstract_canon_sha256":"78055b52563c70ffbfb40942f4c40089cd0cc982ecfb134304d4131f3048604b"},"schema_version":"1.0"},"canonical_sha256":"0ebc6d247670ba64195099aa9312eec17eb2f36c95a37e0d49bf4f14b4c15ca8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:15.354058Z","signature_b64":"OJR7RLp/+RTJS4neZiQiMFeDSZeYB5eWV4nb64K/as4oRRS87G9Gh140BacenflYu5COiDd5W/QSyqUryFzXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ebc6d247670ba64195099aa9312eec17eb2f36c95a37e0d49bf4f14b4c15ca8","last_reissued_at":"2026-05-18T04:41:15.353562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:15.353562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.2443","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":"2026-05-18T04:41:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+i+ikj3u4M9cEECswLgM9RInHzU6FLeyDObG5RZUm3OLWcWZ+FlrZK6JbnLIeCqCcIHTiu8ptZeppYFt5dNTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:19:24.748244Z"},"content_sha256":"5b22cae31ee5436a685b3db824404dc600aa8c26b0139add5e55c93c6922d925","schema_version":"1.0","event_id":"sha256:5b22cae31ee5436a685b3db824404dc600aa8c26b0139add5e55c93c6922d925"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:B26G2JDWOC5GIGKQTGVJGEXOYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.SP","authors_text":"Igor Lobanov, Igor Popov, Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik","submitted_at":"2009-11-12T18:22:14Z","abstract_excerpt":"In this note we investigate the asymptotic behaviour of the $s$-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain $\\Omega$ with smooth boundary $\\partial\\Omega$. For this we apply the recently introduced abstract notion of quasi boundary triples and Weyl functions from extension theory of symmetric operators together with Krein type resolvent formulae and well-known eigenvalue asymptotics of the Laplace-Beltrami operator on $\\partial\\Omega$. It will be shown that the resolvent difference of two "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2443","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":"2026-05-18T04:41:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CQawGwceNL6laHqFXxz6l9vAqm10xW7C6W27Wsxl7Z1vFXJ+HY1GmVH1pka0RQrdjraEJuWgJEIVJ1wtaOSBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:19:24.748609Z"},"content_sha256":"46279b24701f861605800af07faabe1addea5812fa7077f120e428e017482939","schema_version":"1.0","event_id":"sha256:46279b24701f861605800af07faabe1addea5812fa7077f120e428e017482939"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B26G2JDWOC5GIGKQTGVJGEXOYF/bundle.json","state_url":"https://pith.science/pith/B26G2JDWOC5GIGKQTGVJGEXOYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B26G2JDWOC5GIGKQTGVJGEXOYF/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":"2026-06-01T07:19:24Z","links":{"resolver":"https://pith.science/pith/B26G2JDWOC5GIGKQTGVJGEXOYF","bundle":"https://pith.science/pith/B26G2JDWOC5GIGKQTGVJGEXOYF/bundle.json","state":"https://pith.science/pith/B26G2JDWOC5GIGKQTGVJGEXOYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B26G2JDWOC5GIGKQTGVJGEXOYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:B26G2JDWOC5GIGKQTGVJGEXOYF","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":"78055b52563c70ffbfb40942f4c40089cd0cc982ecfb134304d4131f3048604b","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-11-12T18:22:14Z","title_canon_sha256":"92f0b4c12294ff178477b8fa613c8e51bb371ca12f929544d85c5f552a006412"},"schema_version":"1.0","source":{"id":"0911.2443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2443","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2443v1","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2443","created_at":"2026-05-18T04:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"B26G2JDWOC5G","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"B26G2JDWOC5GIGKQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"B26G2JDW","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:46279b24701f861605800af07faabe1addea5812fa7077f120e428e017482939","target":"graph","created_at":"2026-05-18T04:41:15Z","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":"In this note we investigate the asymptotic behaviour of the $s$-numbers of the resolvent difference of two generalized self-adjoint, maximal dissipative or maximal accumulative Robin Laplacians on a bounded domain $\\Omega$ with smooth boundary $\\partial\\Omega$. For this we apply the recently introduced abstract notion of quasi boundary triples and Weyl functions from extension theory of symmetric operators together with Krein type resolvent formulae and well-known eigenvalue asymptotics of the Laplace-Beltrami operator on $\\partial\\Omega$. It will be shown that the resolvent difference of two ","authors_text":"Igor Lobanov, Igor Popov, Jussi Behrndt, Matthias Langer, Vladimir Lotoreichik","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-11-12T18:22:14Z","title":"A remark on Schatten-von Neumann properties of resolvent differences of generalized Robin Laplacians on bounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2443","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":"sha256:5b22cae31ee5436a685b3db824404dc600aa8c26b0139add5e55c93c6922d925","target":"record","created_at":"2026-05-18T04:41:15Z","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":"78055b52563c70ffbfb40942f4c40089cd0cc982ecfb134304d4131f3048604b","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-11-12T18:22:14Z","title_canon_sha256":"92f0b4c12294ff178477b8fa613c8e51bb371ca12f929544d85c5f552a006412"},"schema_version":"1.0","source":{"id":"0911.2443","kind":"arxiv","version":1}},"canonical_sha256":"0ebc6d247670ba64195099aa9312eec17eb2f36c95a37e0d49bf4f14b4c15ca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ebc6d247670ba64195099aa9312eec17eb2f36c95a37e0d49bf4f14b4c15ca8","first_computed_at":"2026-05-18T04:41:15.353562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:15.353562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OJR7RLp/+RTJS4neZiQiMFeDSZeYB5eWV4nb64K/as4oRRS87G9Gh140BacenflYu5COiDd5W/QSyqUryFzXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:15.354058Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b22cae31ee5436a685b3db824404dc600aa8c26b0139add5e55c93c6922d925","sha256:46279b24701f861605800af07faabe1addea5812fa7077f120e428e017482939"],"state_sha256":"d76cb094633a4859bdf556a086c5d2ea83a168de4a61cf56d158e0e2608c7565"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ILdyIAipTIubUA/b1wCCa0slh4LS2jji0pIZNhFhQmg4GFR5AOlJLNWVGjRZ0JYrGIZ1R9XEhAwRshSOGFrBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:19:24.750571Z","bundle_sha256":"635ab66641919a5246859d67fb7cf2bdc8395c04e21201e10bbf85ee7e16d8fd"}}