{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:JJ5TUKOWNO4HOYOZLDLPO2XNIP","short_pith_number":"pith:JJ5TUKOW","canonical_record":{"source":{"id":"0705.4161","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2007-05-29T08:41:59Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"41394db028a327a25fab4566aad3421b24943c6414289708411f609c38634688","abstract_canon_sha256":"dfc35098fed8193c70ecc3e8a5814839d42c3a9abb0ae2aa30bae0b0fbe6a413"},"schema_version":"1.0"},"canonical_sha256":"4a7b3a29d66bb87761d958d6f76aed43d3a654a1ceaec616ec8fb4cadd58a7d4","source":{"kind":"arxiv","id":"0705.4161","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.4161","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"0705.4161v1","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.4161","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"JJ5TUKOWNO4H","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JJ5TUKOWNO4HOYOZ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JJ5TUKOW","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:JJ5TUKOWNO4HOYOZLDLPO2XNIP","target":"record","payload":{"canonical_record":{"source":{"id":"0705.4161","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2007-05-29T08:41:59Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"41394db028a327a25fab4566aad3421b24943c6414289708411f609c38634688","abstract_canon_sha256":"dfc35098fed8193c70ecc3e8a5814839d42c3a9abb0ae2aa30bae0b0fbe6a413"},"schema_version":"1.0"},"canonical_sha256":"4a7b3a29d66bb87761d958d6f76aed43d3a654a1ceaec616ec8fb4cadd58a7d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:04.652430Z","signature_b64":"zQS7c3FMzfMgb8ZgXjHY/pdKhF2nxr0nKjiaBFBUTO9g5/yTUkJQCdltntY75GBsdmPAHOmazuY69RP6W0H7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a7b3a29d66bb87761d958d6f76aed43d3a654a1ceaec616ec8fb4cadd58a7d4","last_reissued_at":"2026-05-18T03:54:04.651785Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:04.651785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0705.4161","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":"2026-05-18T03:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9npJ0940gVGjJkfbjgCII+2lFzA8TPv6lNCrko0l7ZdFHMNj9gY7SeEnau5B6Z/kpywvv2NyswaRCrxBzBPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:24:43.562133Z"},"content_sha256":"b8952f5ca545449d20384a9d7641296f282b9a2f5cc56369d9cb2644ca32d600","schema_version":"1.0","event_id":"sha256:b8952f5ca545449d20384a9d7641296f282b9a2f5cc56369d9cb2644ca32d600"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:JJ5TUKOWNO4HOYOZLDLPO2XNIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riesz Bases of Root Vectors of Indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, I","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Branko \\'Curgus, Paul Binding","submitted_at":"2007-05-29T08:41:59Z","abstract_excerpt":"We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.4161","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":"2026-05-18T03:54:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8oEI/cSiVRSRhwQbHnAhCRPLNEW7k8EQBqjIVNHBeyqzLEl14FqnkDXmqm9gQphrDV7A9G8R+g6NLjIRfvxqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:24:43.562878Z"},"content_sha256":"70d65dfd1c925594d36951154e9abfa16d53e5619f4dc9a01a70b075a429c98b","schema_version":"1.0","event_id":"sha256:70d65dfd1c925594d36951154e9abfa16d53e5619f4dc9a01a70b075a429c98b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JJ5TUKOWNO4HOYOZLDLPO2XNIP/bundle.json","state_url":"https://pith.science/pith/JJ5TUKOWNO4HOYOZLDLPO2XNIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JJ5TUKOWNO4HOYOZLDLPO2XNIP/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":"2026-06-12T04:24:43Z","links":{"resolver":"https://pith.science/pith/JJ5TUKOWNO4HOYOZLDLPO2XNIP","bundle":"https://pith.science/pith/JJ5TUKOWNO4HOYOZLDLPO2XNIP/bundle.json","state":"https://pith.science/pith/JJ5TUKOWNO4HOYOZLDLPO2XNIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JJ5TUKOWNO4HOYOZLDLPO2XNIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:JJ5TUKOWNO4HOYOZLDLPO2XNIP","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":"dfc35098fed8193c70ecc3e8a5814839d42c3a9abb0ae2aa30bae0b0fbe6a413","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.CA","submitted_at":"2007-05-29T08:41:59Z","title_canon_sha256":"41394db028a327a25fab4566aad3421b24943c6414289708411f609c38634688"},"schema_version":"1.0","source":{"id":"0705.4161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.4161","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"0705.4161v1","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.4161","created_at":"2026-05-18T03:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"JJ5TUKOWNO4H","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JJ5TUKOWNO4HOYOZ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JJ5TUKOW","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:70d65dfd1c925594d36951154e9abfa16d53e5619f4dc9a01a70b075a429c98b","target":"graph","created_at":"2026-05-18T03:54:04Z","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":"We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.","authors_text":"Branko \\'Curgus, Paul Binding","cross_cats":["math.FA"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2007-05-29T08:41:59Z","title":"Riesz Bases of Root Vectors of Indefinite Sturm-Liouville problems with eigenparameter dependent boundary conditions, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.4161","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:b8952f5ca545449d20384a9d7641296f282b9a2f5cc56369d9cb2644ca32d600","target":"record","created_at":"2026-05-18T03:54:04Z","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":"dfc35098fed8193c70ecc3e8a5814839d42c3a9abb0ae2aa30bae0b0fbe6a413","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.CA","submitted_at":"2007-05-29T08:41:59Z","title_canon_sha256":"41394db028a327a25fab4566aad3421b24943c6414289708411f609c38634688"},"schema_version":"1.0","source":{"id":"0705.4161","kind":"arxiv","version":1}},"canonical_sha256":"4a7b3a29d66bb87761d958d6f76aed43d3a654a1ceaec616ec8fb4cadd58a7d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a7b3a29d66bb87761d958d6f76aed43d3a654a1ceaec616ec8fb4cadd58a7d4","first_computed_at":"2026-05-18T03:54:04.651785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:04.651785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zQS7c3FMzfMgb8ZgXjHY/pdKhF2nxr0nKjiaBFBUTO9g5/yTUkJQCdltntY75GBsdmPAHOmazuY69RP6W0H7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:04.652430Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.4161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8952f5ca545449d20384a9d7641296f282b9a2f5cc56369d9cb2644ca32d600","sha256:70d65dfd1c925594d36951154e9abfa16d53e5619f4dc9a01a70b075a429c98b"],"state_sha256":"e4c0db5ac4d102baa202da7d4bb642a3cb21724c064557d0af9fca235e773ee7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LjjLA0IDlXh3ituDCsqMAf0RktGxVYGgpNw/MeBq3yPnFNncmZyPqaAFY5VP8rmyZvN0Jb6oFfjFhWkBnkRUAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:24:43.567151Z","bundle_sha256":"3c4054af220b052436aeb8978399a886d57d2a31a5fa2a13ca5c4bf3c3317773"}}