{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VA5TRR4P6BTYWCTDKLZNDTEJSU","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":"41f4c2cdf07c2d90871438b324d26ef9128387962aed9bbcdbcb90b58fd575a9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-31T17:41:10Z","title_canon_sha256":"b13148723f55f58097ba86581f960c96143a855c64793ed7f4921715f67c141a"},"schema_version":"1.0","source":{"id":"1110.6869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6869","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6869v1","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6869","created_at":"2026-05-18T04:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"VA5TRR4P6BTY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VA5TRR4P6BTYWCTD","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VA5TRR4P","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:f995cd5e2092fcd33896a4e5c29ff4cb3ce6f9f250829a190bdb9ba5d906e406","target":"graph","created_at":"2026-05-18T04:09:54Z","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":"In this paper we examine spectral properties of a family of periodic singular Sturm-Liouville problems which are highly non-self-adjoint but have purely real spectrum. The problem originated from the study of the lubrication approximation of a viscous fluid film in the inner surface of a rotating cylinder and has received a substantial amount of attention in recent years. Our main focus will be the determination of Schatten class inclusions for the resolvent operator and regularity properties of the associated evolution equation.","authors_text":"David Rule, Lyonell Boulton, Marco Marletta","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-31T17:41:10Z","title":"On the stability of a forward-backward heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6869","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":"sha256:600b4a757cabf1f182ed82d395ee1dcbb1b041c81aa8bff1d1b9e362721b2a63","target":"record","created_at":"2026-05-18T04:09:54Z","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":"41f4c2cdf07c2d90871438b324d26ef9128387962aed9bbcdbcb90b58fd575a9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-10-31T17:41:10Z","title_canon_sha256":"b13148723f55f58097ba86581f960c96143a855c64793ed7f4921715f67c141a"},"schema_version":"1.0","source":{"id":"1110.6869","kind":"arxiv","version":1}},"canonical_sha256":"a83b38c78ff0678b0a6352f2d1cc89952568917e4db19f289269dc22c8abb1f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a83b38c78ff0678b0a6352f2d1cc89952568917e4db19f289269dc22c8abb1f9","first_computed_at":"2026-05-18T04:09:54.009346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:54.009346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZqQOwH6zwSnQbF6CZHiqxc0LXzkuEQBl94ZKbx5wI/fanWJEYm7Bz8eODOjbP4ySn6ihaZRMYKkss8Wv1afaBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:54.009947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:600b4a757cabf1f182ed82d395ee1dcbb1b041c81aa8bff1d1b9e362721b2a63","sha256:f995cd5e2092fcd33896a4e5c29ff4cb3ce6f9f250829a190bdb9ba5d906e406"],"state_sha256":"e9a66e4496a67a82de47e3cfa530a65f0baa4f58af2570fb60b147627fb6608a"}