{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DQF4J6R4YXNZKIZDM7IW52LVLK","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":"c8647f7150ec4fd5c5765ad286220d8bd1961c1622ca5a152ead4a599628ac08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-23T15:00:04Z","title_canon_sha256":"3c5972cf145ac1d8820d03dd02845ff0a606a39965dc6f95ad06154c2c740e0e"},"schema_version":"1.0","source":{"id":"1106.4747","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4747","created_at":"2026-05-18T04:19:23Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4747v1","created_at":"2026-05-18T04:19:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4747","created_at":"2026-05-18T04:19:23Z"},{"alias_kind":"pith_short_12","alias_value":"DQF4J6R4YXNZ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DQF4J6R4YXNZKIZD","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DQF4J6R4","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:d27a23c6a153cd0a0b4acb132c752b0df3408770cf2549065aed6e4f68d3d651","target":"graph","created_at":"2026-05-18T04:19:23Z","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 the linear eigenvalue problem \\tag{1}\n  -u\" = \\lambda u, \\quad \\text{on $(-1,1)$}, where $\\lambda \\in \\mathbb{R}$, together with the general multi-point boundary conditions \\tag{2} \\alpha_0^\\pm u(\\pm 1) + \\beta_0^\\pm u'(\\pm 1) = \\sum^{m^\\pm}_{i=1} \\alpha^\\pm_i u(\\eta^\\pm_i)\n  + \\sum_{i=1}^{m^\\pm} \\beta^\\pm_i u'(\\eta^\\pm_i). We also suppose that: \\alpha_0^\\pm \\ge 0, \\quad \\alpha_0^\\pm + |\\beta_0^\\pm| > 0, \\tag{3}  \\pm \\beta_0^\\pm \\ge 0, \\tag{4} (\\frac{\\sum_{i=1}^{m^\\pm} |\\alpha_i^\\pm|}{\\alpha_0^\\pm})^2\n  + (\\frac{\\sum_{i=1}^{m^\\pm} |\\beta_i^\\pm|}{\\beta_0^\\pm})^2\n  < 1, \\tag{5} with ","authors_text":"Bryan P. Rynne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-23T15:00:04Z","title":"Linear, second-order problems with Sturm-Liouville-type multi-point boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4747","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":"sha256:61870367cfb826e7c78ae8f9a31a6bda477c4f26827badd8a93d12ad9e21ff89","target":"record","created_at":"2026-05-18T04:19:23Z","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":"c8647f7150ec4fd5c5765ad286220d8bd1961c1622ca5a152ead4a599628ac08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-23T15:00:04Z","title_canon_sha256":"3c5972cf145ac1d8820d03dd02845ff0a606a39965dc6f95ad06154c2c740e0e"},"schema_version":"1.0","source":{"id":"1106.4747","kind":"arxiv","version":1}},"canonical_sha256":"1c0bc4fa3cc5db95232367d16ee9755a8adf526261775e84cc41e0e01dc36931","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c0bc4fa3cc5db95232367d16ee9755a8adf526261775e84cc41e0e01dc36931","first_computed_at":"2026-05-18T04:19:23.731378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:23.731378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wGy6zNq4YV+7biOIFqIeH9JHQHjZ1c+S8cY9Hk3D7Y/xe4pZiO6qifbUtId6Zq3neoKhe/IIX7OG82Qpl0HWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:23.731759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4747","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61870367cfb826e7c78ae8f9a31a6bda477c4f26827badd8a93d12ad9e21ff89","sha256:d27a23c6a153cd0a0b4acb132c752b0df3408770cf2549065aed6e4f68d3d651"],"state_sha256":"798f679f0a32229fecf5fe5f6e520c8074fff6bb883d926c9d558dff27f35554"}