{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:C44S6CMCLMMYOZQXXB2RKLNFTQ","short_pith_number":"pith:C44S6CMC","canonical_record":{"source":{"id":"1511.07828","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-11-24T18:59:23Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"79be791299e74a280375abf125b3fb52fb0f871605b175b79784be3b38eb4261","abstract_canon_sha256":"a785856ef607e4a2e2a72f51fc7daf06ca9847b00ea6f69a57271ccd7632046f"},"schema_version":"1.0"},"canonical_sha256":"17392f09825b19876617b875152da59c25b7ee513285565377c19ecfb60e6fb2","source":{"kind":"arxiv","id":"1511.07828","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07828","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07828v4","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07828","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"C44S6CMCLMMY","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C44S6CMCLMMYOZQX","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C44S6CMC","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:C44S6CMCLMMYOZQXXB2RKLNFTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07828","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-11-24T18:59:23Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"79be791299e74a280375abf125b3fb52fb0f871605b175b79784be3b38eb4261","abstract_canon_sha256":"a785856ef607e4a2e2a72f51fc7daf06ca9847b00ea6f69a57271ccd7632046f"},"schema_version":"1.0"},"canonical_sha256":"17392f09825b19876617b875152da59c25b7ee513285565377c19ecfb60e6fb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:53.743061Z","signature_b64":"iBxbeJO34TrwkJIBdT0QlhLsDJq1YAjE9FRNn94imZ0m74hZKynMss6OyyN1y2hk0C2hWLGKuccGF41oJm7zCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17392f09825b19876617b875152da59c25b7ee513285565377c19ecfb60e6fb2","last_reissued_at":"2026-05-18T01:22:53.742569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:53.742569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07828","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5IHsnxudOlSWqq6m1sKwyCOYYMTFY3ehJxU0N4TTr0jKNkE7yATovGo+WfaE0MPAWylLIY3SffO5NkmXEG2TDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:27:58.057451Z"},"content_sha256":"49416d3c9ecdea83b40483c12dedbcf996de22b74d875b4dba5d44ebafe0bfdd","schema_version":"1.0","event_id":"sha256:49416d3c9ecdea83b40483c12dedbcf996de22b74d875b4dba5d44ebafe0bfdd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:C44S6CMCLMMYOZQXXB2RKLNFTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue inequalities for Schr\\\"odinger operators on unbounded Lipschitz domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Jonathan Rohleder, Jussi Behrndt, Simon Stadler","submitted_at":"2015-11-24T18:59:23Z","abstract_excerpt":"Given a Schr\\\"odinger differential expression on an exterior Lipschitz domain we prove strict inequalities between the eigenvalues of the corresponding selfadjoint operators subject to Dirichlet and Neumann or Dirichlet and mixed boundary conditions, respectively. Moreover, we prove a strict inequality between the eigenvalues of two different elliptic differential operators on the same domain with Dirichlet boundary conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07828","kind":"arxiv","version":4},"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":"2026-05-18T01:22:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42pLSfn6Lq7XIWbcBxdEcP4XfNz7wRSGNj7O2bDqaF9NmWZT1r69iZ2DB2lYffj4ONeD5BiRkKTSf1YFhoSSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:27:58.057803Z"},"content_sha256":"fdc285cd6986ba4c7ccf917ce8c9b976921f927f379f7f62602ee765a45eae52","schema_version":"1.0","event_id":"sha256:fdc285cd6986ba4c7ccf917ce8c9b976921f927f379f7f62602ee765a45eae52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C44S6CMCLMMYOZQXXB2RKLNFTQ/bundle.json","state_url":"https://pith.science/pith/C44S6CMCLMMYOZQXXB2RKLNFTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C44S6CMCLMMYOZQXXB2RKLNFTQ/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":"2026-05-28T10:27:58Z","links":{"resolver":"https://pith.science/pith/C44S6CMCLMMYOZQXXB2RKLNFTQ","bundle":"https://pith.science/pith/C44S6CMCLMMYOZQXXB2RKLNFTQ/bundle.json","state":"https://pith.science/pith/C44S6CMCLMMYOZQXXB2RKLNFTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C44S6CMCLMMYOZQXXB2RKLNFTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C44S6CMCLMMYOZQXXB2RKLNFTQ","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":"a785856ef607e4a2e2a72f51fc7daf06ca9847b00ea6f69a57271ccd7632046f","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-11-24T18:59:23Z","title_canon_sha256":"79be791299e74a280375abf125b3fb52fb0f871605b175b79784be3b38eb4261"},"schema_version":"1.0","source":{"id":"1511.07828","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07828","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07828v4","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07828","created_at":"2026-05-18T01:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"C44S6CMCLMMY","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C44S6CMCLMMYOZQX","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C44S6CMC","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:fdc285cd6986ba4c7ccf917ce8c9b976921f927f379f7f62602ee765a45eae52","target":"graph","created_at":"2026-05-18T01:22:53Z","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":"Given a Schr\\\"odinger differential expression on an exterior Lipschitz domain we prove strict inequalities between the eigenvalues of the corresponding selfadjoint operators subject to Dirichlet and Neumann or Dirichlet and mixed boundary conditions, respectively. Moreover, we prove a strict inequality between the eigenvalues of two different elliptic differential operators on the same domain with Dirichlet boundary conditions.","authors_text":"Jonathan Rohleder, Jussi Behrndt, Simon Stadler","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-11-24T18:59:23Z","title":"Eigenvalue inequalities for Schr\\\"odinger operators on unbounded Lipschitz domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07828","kind":"arxiv","version":4},"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":"sha256:49416d3c9ecdea83b40483c12dedbcf996de22b74d875b4dba5d44ebafe0bfdd","target":"record","created_at":"2026-05-18T01:22:53Z","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":"a785856ef607e4a2e2a72f51fc7daf06ca9847b00ea6f69a57271ccd7632046f","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-11-24T18:59:23Z","title_canon_sha256":"79be791299e74a280375abf125b3fb52fb0f871605b175b79784be3b38eb4261"},"schema_version":"1.0","source":{"id":"1511.07828","kind":"arxiv","version":4}},"canonical_sha256":"17392f09825b19876617b875152da59c25b7ee513285565377c19ecfb60e6fb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17392f09825b19876617b875152da59c25b7ee513285565377c19ecfb60e6fb2","first_computed_at":"2026-05-18T01:22:53.742569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:53.742569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iBxbeJO34TrwkJIBdT0QlhLsDJq1YAjE9FRNn94imZ0m74hZKynMss6OyyN1y2hk0C2hWLGKuccGF41oJm7zCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:53.743061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07828","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49416d3c9ecdea83b40483c12dedbcf996de22b74d875b4dba5d44ebafe0bfdd","sha256:fdc285cd6986ba4c7ccf917ce8c9b976921f927f379f7f62602ee765a45eae52"],"state_sha256":"734039e258d8e0cec4b5ed35892b6eca03fc61de41cf80fd89df63b4e710655e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2a1a3142eZtqP1w7fYUXxOKEu4BA1hjaBZURYz+2LhwptdnMHbF4RelVM1cW3tCpbwk0xdGVTe1QezG1pj+mDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:27:58.059846Z","bundle_sha256":"926549d23d11101dfb5dfd745d8141c6c30bf74447450ee33ae103c1b4643786"}}