{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:77BBFU5NUCA4UVFXKOX523NSRB","short_pith_number":"pith:77BBFU5N","canonical_record":{"source":{"id":"1404.0922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-03T14:19:08Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"286491c312687160f6f4ca641f017bd292195556995d0b0c07de51cd3f71ceeb","abstract_canon_sha256":"4702e9d3a866c63265f5f574903a8ca5322b8a2a4f2bdecbed84d9e68bb85a48"},"schema_version":"1.0"},"canonical_sha256":"ffc212d3ada081ca54b753afdd6db288402f8d01a73c568a0fd75ad97fdf3d45","source":{"kind":"arxiv","id":"1404.0922","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0922","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0922v1","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0922","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"77BBFU5NUCA4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"77BBFU5NUCA4UVFX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"77BBFU5N","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:77BBFU5NUCA4UVFXKOX523NSRB","target":"record","payload":{"canonical_record":{"source":{"id":"1404.0922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-03T14:19:08Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"286491c312687160f6f4ca641f017bd292195556995d0b0c07de51cd3f71ceeb","abstract_canon_sha256":"4702e9d3a866c63265f5f574903a8ca5322b8a2a4f2bdecbed84d9e68bb85a48"},"schema_version":"1.0"},"canonical_sha256":"ffc212d3ada081ca54b753afdd6db288402f8d01a73c568a0fd75ad97fdf3d45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:03.492708Z","signature_b64":"UPamxrTIjV4xTa6VXX9EjPxiVG8sC+17QJYqDQq/Fulds4D7P7fkl2rNIhZUBf1POMF2i+DGFPHSsIo56BYyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffc212d3ada081ca54b753afdd6db288402f8d01a73c568a0fd75ad97fdf3d45","last_reissued_at":"2026-05-18T01:22:03.492104Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:03.492104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.0922","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":"2026-05-18T01:22:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xe8ihSZ2czMFCCuKzhbhe3Ch2HoCnO4LD/02OdR0Q2hHoEg19n/j+zLmrDetDw4QD+lzjZNnZHgdk8N3nqsfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T10:26:44.729657Z"},"content_sha256":"3eb21be1ec4bc24dc560981fbf88a3e322496cf737d3103082459036e4548466","schema_version":"1.0","event_id":"sha256:3eb21be1ec4bc24dc560981fbf88a3e322496cf737d3103082459036e4548466"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:77BBFU5NUCA4UVFXKOX523NSRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral analysis of selfadjoint elliptic differential operators, Dirichlet-to-Neumann maps, and abstract Weyl functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Jonathan Rohleder, Jussi Behrndt","submitted_at":"2014-04-03T14:19:08Z","abstract_excerpt":"The spectrum of a selfadjoint second order elliptic differential operator in $L^2(\\mathbb{R}^n)$ is described in terms of the limiting behavior of Dirichlet-to-Neumann maps, which arise in a multi-dimensional Glazman decomposition and correspond to an interior and an exterior boundary value problem. This leads to PDE analogs of renowned facts in spectral theory of ODEs. The main results in this paper are first derived in the more abstract context of extension theory of symmetric operators and corresponding Weyl functions, and are applied to the PDE setting afterwards."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0922","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":"2026-05-18T01:22:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aF3T7WQutxIJsg6skKgFlSi3nCn6ITruTXWGuasnofoCxIKxxF8J95a1RBLhLD8+hwsFi5XpFmTfVKOAS0uHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T10:26:44.730001Z"},"content_sha256":"c4846980c6d1c2ed7cdf176597a074cba4f1721908cc7274b4a0021290988afd","schema_version":"1.0","event_id":"sha256:c4846980c6d1c2ed7cdf176597a074cba4f1721908cc7274b4a0021290988afd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/77BBFU5NUCA4UVFXKOX523NSRB/bundle.json","state_url":"https://pith.science/pith/77BBFU5NUCA4UVFXKOX523NSRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/77BBFU5NUCA4UVFXKOX523NSRB/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":"2026-06-06T10:26:44Z","links":{"resolver":"https://pith.science/pith/77BBFU5NUCA4UVFXKOX523NSRB","bundle":"https://pith.science/pith/77BBFU5NUCA4UVFXKOX523NSRB/bundle.json","state":"https://pith.science/pith/77BBFU5NUCA4UVFXKOX523NSRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/77BBFU5NUCA4UVFXKOX523NSRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:77BBFU5NUCA4UVFXKOX523NSRB","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":"4702e9d3a866c63265f5f574903a8ca5322b8a2a4f2bdecbed84d9e68bb85a48","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-03T14:19:08Z","title_canon_sha256":"286491c312687160f6f4ca641f017bd292195556995d0b0c07de51cd3f71ceeb"},"schema_version":"1.0","source":{"id":"1404.0922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0922","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0922v1","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0922","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"77BBFU5NUCA4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"77BBFU5NUCA4UVFX","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"77BBFU5N","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:c4846980c6d1c2ed7cdf176597a074cba4f1721908cc7274b4a0021290988afd","target":"graph","created_at":"2026-05-18T01:22:03Z","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":"The spectrum of a selfadjoint second order elliptic differential operator in $L^2(\\mathbb{R}^n)$ is described in terms of the limiting behavior of Dirichlet-to-Neumann maps, which arise in a multi-dimensional Glazman decomposition and correspond to an interior and an exterior boundary value problem. This leads to PDE analogs of renowned facts in spectral theory of ODEs. The main results in this paper are first derived in the more abstract context of extension theory of symmetric operators and corresponding Weyl functions, and are applied to the PDE setting afterwards.","authors_text":"Jonathan Rohleder, Jussi Behrndt","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-03T14:19:08Z","title":"Spectral analysis of selfadjoint elliptic differential operators, Dirichlet-to-Neumann maps, and abstract Weyl functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0922","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":"sha256:3eb21be1ec4bc24dc560981fbf88a3e322496cf737d3103082459036e4548466","target":"record","created_at":"2026-05-18T01:22:03Z","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":"4702e9d3a866c63265f5f574903a8ca5322b8a2a4f2bdecbed84d9e68bb85a48","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-04-03T14:19:08Z","title_canon_sha256":"286491c312687160f6f4ca641f017bd292195556995d0b0c07de51cd3f71ceeb"},"schema_version":"1.0","source":{"id":"1404.0922","kind":"arxiv","version":1}},"canonical_sha256":"ffc212d3ada081ca54b753afdd6db288402f8d01a73c568a0fd75ad97fdf3d45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffc212d3ada081ca54b753afdd6db288402f8d01a73c568a0fd75ad97fdf3d45","first_computed_at":"2026-05-18T01:22:03.492104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:03.492104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UPamxrTIjV4xTa6VXX9EjPxiVG8sC+17QJYqDQq/Fulds4D7P7fkl2rNIhZUBf1POMF2i+DGFPHSsIo56BYyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:03.492708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eb21be1ec4bc24dc560981fbf88a3e322496cf737d3103082459036e4548466","sha256:c4846980c6d1c2ed7cdf176597a074cba4f1721908cc7274b4a0021290988afd"],"state_sha256":"b1e9685028a9024c396c3380afddb292691afdc01fe3fb7f38f776d3ef5e9351"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MqXaTl5gq+fb+4vjG7cdnFZaJCi9KY3QeEv/AU+4tq0Qd+yIFg90pzxFRiojc5kjRIh5gEZllTJtFJYgmryoBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T10:26:44.732099Z","bundle_sha256":"826470e48380d222a6c378d5385b61f0f9600fd0ea414f47b2917c6f5c7accaf"}}