{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JOQCWLLAIN5C67IK7YC47PDGW6","short_pith_number":"pith:JOQCWLLA","canonical_record":{"source":{"id":"1012.4195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-19T19:12:09Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"4dd02f34cc5f626753bd59e353f695401012cb349270abe9d9a1c8d7477d9f68","abstract_canon_sha256":"5a353687596e20726dd6b6a740667340dd94a782d118600a9cc752627f4d341e"},"schema_version":"1.0"},"canonical_sha256":"4ba02b2d60437a2f7d0afe05cfbc66b7b86505836e0a68a596b5afd9b37b7c2b","source":{"kind":"arxiv","id":"1012.4195","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4195","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4195v2","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4195","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"pith_short_12","alias_value":"JOQCWLLAIN5C","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JOQCWLLAIN5C67IK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JOQCWLLA","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JOQCWLLAIN5C67IK7YC47PDGW6","target":"record","payload":{"canonical_record":{"source":{"id":"1012.4195","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-19T19:12:09Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"4dd02f34cc5f626753bd59e353f695401012cb349270abe9d9a1c8d7477d9f68","abstract_canon_sha256":"5a353687596e20726dd6b6a740667340dd94a782d118600a9cc752627f4d341e"},"schema_version":"1.0"},"canonical_sha256":"4ba02b2d60437a2f7d0afe05cfbc66b7b86505836e0a68a596b5afd9b37b7c2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:21.797965Z","signature_b64":"U3Uw8B1KyG+dArmYjuOxts5l+hRRL4698CqStE9Ip1/nGsTYBwiXEAWXLtQ6zcY8NVC6F40zO6XYXi1SYO1hAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ba02b2d60437a2f7d0afe05cfbc66b7b86505836e0a68a596b5afd9b37b7c2b","last_reissued_at":"2026-05-18T03:55:21.797341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:21.797341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.4195","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"snfKdJ1UrOCuGj6f0/7i5jg7KNGWLDFSIHEqTLonIppeECfL6k6vXS1uMOGbUOAhLlKVgJgW6TG9W8TqZqrNAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:44.775099Z"},"content_sha256":"9505b45e7a4e7735620cad340a7836d5839e47c9880cc4fda9bce270a319ac80","schema_version":"1.0","event_id":"sha256:9505b45e7a4e7735620cad340a7836d5839e47c9880cc4fda9bce270a319ac80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JOQCWLLAIN5C67IK7YC47PDGW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalue estimates for singular left-definite Sturm-Liouville operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.SP","authors_text":"Carsten Trunk, Jussi Behrndt, Roland Moews","submitted_at":"2010-12-19T19:12:09Z","abstract_excerpt":"The spectral properties of a singular left-definite Sturm-Liouville operator $JA$ are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart $A$ which is obtained by substituting the indefinite weight function by its absolute value. The spectrum of the $J$-selfadjoint operator $JA$ is real and it follows that an interval $(a,b)\\subset\\mathbb R^+$ is a gap in the essential spectrum of $A$ if and only if both intervals $(-b,-a)$ and $(a,b)$ are gaps in the essential spectrum of the $J$-selfadjoint operator $JA$. As one of the main results it is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4195","kind":"arxiv","version":2},"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":"2026-05-18T03:55:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A9dM/9SQ4vx1M1oFpGAGdVEAcTQEN6pTjQ1umvOo3cPIstN68sbVKtI5BJJFjox/B0jTFQWWpUOH3FavtqSfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:44.775521Z"},"content_sha256":"068fab78fca6b351b6c2483a9a8931e1cfaf1766bbceaaea9d4a76b0a7c30d53","schema_version":"1.0","event_id":"sha256:068fab78fca6b351b6c2483a9a8931e1cfaf1766bbceaaea9d4a76b0a7c30d53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOQCWLLAIN5C67IK7YC47PDGW6/bundle.json","state_url":"https://pith.science/pith/JOQCWLLAIN5C67IK7YC47PDGW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOQCWLLAIN5C67IK7YC47PDGW6/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":"2026-06-01T18:39:44Z","links":{"resolver":"https://pith.science/pith/JOQCWLLAIN5C67IK7YC47PDGW6","bundle":"https://pith.science/pith/JOQCWLLAIN5C67IK7YC47PDGW6/bundle.json","state":"https://pith.science/pith/JOQCWLLAIN5C67IK7YC47PDGW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOQCWLLAIN5C67IK7YC47PDGW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JOQCWLLAIN5C67IK7YC47PDGW6","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":"5a353687596e20726dd6b6a740667340dd94a782d118600a9cc752627f4d341e","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-19T19:12:09Z","title_canon_sha256":"4dd02f34cc5f626753bd59e353f695401012cb349270abe9d9a1c8d7477d9f68"},"schema_version":"1.0","source":{"id":"1012.4195","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4195","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4195v2","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4195","created_at":"2026-05-18T03:55:21Z"},{"alias_kind":"pith_short_12","alias_value":"JOQCWLLAIN5C","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JOQCWLLAIN5C67IK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JOQCWLLA","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:068fab78fca6b351b6c2483a9a8931e1cfaf1766bbceaaea9d4a76b0a7c30d53","target":"graph","created_at":"2026-05-18T03:55:21Z","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 spectral properties of a singular left-definite Sturm-Liouville operator $JA$ are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart $A$ which is obtained by substituting the indefinite weight function by its absolute value. The spectrum of the $J$-selfadjoint operator $JA$ is real and it follows that an interval $(a,b)\\subset\\mathbb R^+$ is a gap in the essential spectrum of $A$ if and only if both intervals $(-b,-a)$ and $(a,b)$ are gaps in the essential spectrum of the $J$-selfadjoint operator $JA$. As one of the main results it is ","authors_text":"Carsten Trunk, Jussi Behrndt, Roland Moews","cross_cats":["math.CA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-19T19:12:09Z","title":"Eigenvalue estimates for singular left-definite Sturm-Liouville operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4195","kind":"arxiv","version":2},"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":"sha256:9505b45e7a4e7735620cad340a7836d5839e47c9880cc4fda9bce270a319ac80","target":"record","created_at":"2026-05-18T03:55:21Z","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":"5a353687596e20726dd6b6a740667340dd94a782d118600a9cc752627f4d341e","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-12-19T19:12:09Z","title_canon_sha256":"4dd02f34cc5f626753bd59e353f695401012cb349270abe9d9a1c8d7477d9f68"},"schema_version":"1.0","source":{"id":"1012.4195","kind":"arxiv","version":2}},"canonical_sha256":"4ba02b2d60437a2f7d0afe05cfbc66b7b86505836e0a68a596b5afd9b37b7c2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ba02b2d60437a2f7d0afe05cfbc66b7b86505836e0a68a596b5afd9b37b7c2b","first_computed_at":"2026-05-18T03:55:21.797341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:21.797341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U3Uw8B1KyG+dArmYjuOxts5l+hRRL4698CqStE9Ip1/nGsTYBwiXEAWXLtQ6zcY8NVC6F40zO6XYXi1SYO1hAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:21.797965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4195","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9505b45e7a4e7735620cad340a7836d5839e47c9880cc4fda9bce270a319ac80","sha256:068fab78fca6b351b6c2483a9a8931e1cfaf1766bbceaaea9d4a76b0a7c30d53"],"state_sha256":"c565c108a2bf7ebe4d48ef06a6b9951fe68bb847517cff295b61795b69d0ecb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EQzL2n1zpYIMohgYWxp0W+yVEErtPmMxoOioZyB+7KaPvZGYD52yo2QoLEsQlxxyLjsTu6q0xu51eqPa9G7rDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:39:44.777540Z","bundle_sha256":"6516a6f5a1a4c10fdd5b15f9c0708d2e7e9d4dae63ea80811f209222a1429aad"}}