{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IUXMUAAERZMTROONKBSI2ZIIT2","short_pith_number":"pith:IUXMUAAE","canonical_record":{"source":{"id":"1802.00091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-31T22:55:34Z","cross_cats_sorted":[],"title_canon_sha256":"26410de44165e53a5f5700949764feca014601e8ea9eb405e4ed9189fac65b64","abstract_canon_sha256":"97066657a2dce3547df35c9a350f65f1c05edd616884f92361b7fa4b601b855f"},"schema_version":"1.0"},"canonical_sha256":"452eca00048e5938b9cd50648d65089eb667103c54431451d391298f106bc8cc","source":{"kind":"arxiv","id":"1802.00091","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00091","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00091v1","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00091","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"IUXMUAAERZMT","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IUXMUAAERZMTROON","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IUXMUAAE","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IUXMUAAERZMTROONKBSI2ZIIT2","target":"record","payload":{"canonical_record":{"source":{"id":"1802.00091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-31T22:55:34Z","cross_cats_sorted":[],"title_canon_sha256":"26410de44165e53a5f5700949764feca014601e8ea9eb405e4ed9189fac65b64","abstract_canon_sha256":"97066657a2dce3547df35c9a350f65f1c05edd616884f92361b7fa4b601b855f"},"schema_version":"1.0"},"canonical_sha256":"452eca00048e5938b9cd50648d65089eb667103c54431451d391298f106bc8cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:36.829282Z","signature_b64":"J7wmUJEtXHa0+yQSA2OR5g9srSp0s8zIngTgRhSqWoHrwtOYl52e6GNL/JTDOjexFCcaTk1fQ3p5a5CVeeBSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"452eca00048e5938b9cd50648d65089eb667103c54431451d391298f106bc8cc","last_reissued_at":"2026-05-18T00:24:36.828691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:36.828691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.00091","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":"2026-05-18T00:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/HZhudVy/3EiMlJe22hIHkjMk17SSx7Hd5/CPR5C1XGw+qgm44chTYvokY8I0guJ9SXpNn9kWOFz25avjeKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:40:38.219507Z"},"content_sha256":"9fbd5e37e7c8f649e86e6ca227c019bbfdad245a5d973879e7bb7e17bfb16a03","schema_version":"1.0","event_id":"sha256:9fbd5e37e7c8f649e86e6ca227c019bbfdad245a5d973879e7bb7e17bfb16a03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IUXMUAAERZMTROONKBSI2ZIIT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiplicities of Eigenvalues of the Diffusion Operator with Random Jumps from the Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Guoliang Shi, Jun Yan","submitted_at":"2018-01-31T22:55:34Z","abstract_excerpt":"This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebraic multiplicity of an eigenvalue is equal to its order as a zero of the characteristic function $\\Delta(\\lambda) $. This can be used to determine the multiplicities of eigenvalues for concrete operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00091","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":"2026-05-18T00:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CUAve6gKzfwIMjBpVY5wXBpWteBIy6Oq/EAvvWrn+5/Ah2K+p0ZtCn4ILfdljjFOt0hYY1RO1p2Uv9t5eltCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:40:38.219866Z"},"content_sha256":"830f0d7a0bcbd0547c7b448547baded3a5f522cc39951262be90cfddb01837bc","schema_version":"1.0","event_id":"sha256:830f0d7a0bcbd0547c7b448547baded3a5f522cc39951262be90cfddb01837bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUXMUAAERZMTROONKBSI2ZIIT2/bundle.json","state_url":"https://pith.science/pith/IUXMUAAERZMTROONKBSI2ZIIT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUXMUAAERZMTROONKBSI2ZIIT2/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":"2026-05-21T12:40:38Z","links":{"resolver":"https://pith.science/pith/IUXMUAAERZMTROONKBSI2ZIIT2","bundle":"https://pith.science/pith/IUXMUAAERZMTROONKBSI2ZIIT2/bundle.json","state":"https://pith.science/pith/IUXMUAAERZMTROONKBSI2ZIIT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUXMUAAERZMTROONKBSI2ZIIT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IUXMUAAERZMTROONKBSI2ZIIT2","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":"97066657a2dce3547df35c9a350f65f1c05edd616884f92361b7fa4b601b855f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-31T22:55:34Z","title_canon_sha256":"26410de44165e53a5f5700949764feca014601e8ea9eb405e4ed9189fac65b64"},"schema_version":"1.0","source":{"id":"1802.00091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00091","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00091v1","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00091","created_at":"2026-05-18T00:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"IUXMUAAERZMT","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IUXMUAAERZMTROON","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IUXMUAAE","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:830f0d7a0bcbd0547c7b448547baded3a5f522cc39951262be90cfddb01837bc","target":"graph","created_at":"2026-05-18T00:24:36Z","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":"This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebraic multiplicity of an eigenvalue is equal to its order as a zero of the characteristic function $\\Delta(\\lambda) $. This can be used to determine the multiplicities of eigenvalues for concrete operators.","authors_text":"Guoliang Shi, Jun Yan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-31T22:55:34Z","title":"Multiplicities of Eigenvalues of the Diffusion Operator with Random Jumps from the Boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00091","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":"sha256:9fbd5e37e7c8f649e86e6ca227c019bbfdad245a5d973879e7bb7e17bfb16a03","target":"record","created_at":"2026-05-18T00:24:36Z","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":"97066657a2dce3547df35c9a350f65f1c05edd616884f92361b7fa4b601b855f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-01-31T22:55:34Z","title_canon_sha256":"26410de44165e53a5f5700949764feca014601e8ea9eb405e4ed9189fac65b64"},"schema_version":"1.0","source":{"id":"1802.00091","kind":"arxiv","version":1}},"canonical_sha256":"452eca00048e5938b9cd50648d65089eb667103c54431451d391298f106bc8cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"452eca00048e5938b9cd50648d65089eb667103c54431451d391298f106bc8cc","first_computed_at":"2026-05-18T00:24:36.828691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:36.828691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J7wmUJEtXHa0+yQSA2OR5g9srSp0s8zIngTgRhSqWoHrwtOYl52e6GNL/JTDOjexFCcaTk1fQ3p5a5CVeeBSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:36.829282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fbd5e37e7c8f649e86e6ca227c019bbfdad245a5d973879e7bb7e17bfb16a03","sha256:830f0d7a0bcbd0547c7b448547baded3a5f522cc39951262be90cfddb01837bc"],"state_sha256":"07dddae4812fc2d7cdae381b382814db363ed8badb87dec64b330876eba62c39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OegNv6LAaFrOXw+NZJRiwx/P0J+lQBS/r/xo5rPAcNc2fDn2lKeVdN320S1J+KxE4jMm4SJI2kiGfgu8I8gPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T12:40:38.221855Z","bundle_sha256":"9e4635801d7b67c4e0cd96e1f92721c0c846e8603ae1cdcd004619b4b8b69ae3"}}