{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KRWDGP5QZQ54BJBHLRITKLOF4G","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":"66821636e20754792b04128ff85084684e0e685090d09c1414e3805318e54819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-07-20T10:32:21Z","title_canon_sha256":"d932433afdd0f1acb7f6ea44de851fb60a512a02af3979907963b096dc71a0d1"},"schema_version":"1.0","source":{"id":"2207.09802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.09802","created_at":"2026-07-05T04:54:04Z"},{"alias_kind":"arxiv_version","alias_value":"2207.09802v2","created_at":"2026-07-05T04:54:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.09802","created_at":"2026-07-05T04:54:04Z"},{"alias_kind":"pith_short_12","alias_value":"KRWDGP5QZQ54","created_at":"2026-07-05T04:54:04Z"},{"alias_kind":"pith_short_16","alias_value":"KRWDGP5QZQ54BJBH","created_at":"2026-07-05T04:54:04Z"},{"alias_kind":"pith_short_8","alias_value":"KRWDGP5Q","created_at":"2026-07-05T04:54:04Z"}],"graph_snapshots":[{"event_id":"sha256:aa9c51dd2e23c79e3aa1b446982a3cecc50b61d6b968ac5b75bab4c9e504ddc6","target":"graph","created_at":"2026-07-05T04:54:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.09802/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The class of Sturm-Liouville operators on the space of square integrable functions on a finite interval is considered. According to the Riesz-spectral property, the self-adjointness and the positivity of such unbounded linear operators on that space, a class of Hilbert spaces constructed as the domains of the positive (in particular, fractional) powers of any Sturm-Liouville operator is considered. On these spaces, it is shown that any Sturm-Liouville operator is a Riesz-spectral operator that possesses the same eigenvalues as the original ones, associated to rescaled eigenfunctions. This cons","authors_text":"Anthony Hastir, Joseph J. Winkin, Judica\\\"el Mohet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-07-20T10:32:21Z","title":"Well-posedness and observability of Sturm-Liouville systems on a class of Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.09802","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":"sha256:0b90cd64ff52e9759b2c1e5e57eb8c64f63ca9926dc15c816aa0eea8818545e6","target":"record","created_at":"2026-07-05T04:54:04Z","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":"66821636e20754792b04128ff85084684e0e685090d09c1414e3805318e54819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-07-20T10:32:21Z","title_canon_sha256":"d932433afdd0f1acb7f6ea44de851fb60a512a02af3979907963b096dc71a0d1"},"schema_version":"1.0","source":{"id":"2207.09802","kind":"arxiv","version":2}},"canonical_sha256":"546c333fb0cc3bc0a4275c51352dc5e196827fe6b8be1ca71e85961d2d3d1ec2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"546c333fb0cc3bc0a4275c51352dc5e196827fe6b8be1ca71e85961d2d3d1ec2","first_computed_at":"2026-07-05T04:54:04.159160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:54:04.159160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uaxLj7FyWb6A2CrYd1BvCBpZ5VsdI3FofLq93MZWtct86t4EFwHnNgnTzwD7DVwe95/jU1HiCdNLh0+vnIjjAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:54:04.159607Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.09802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b90cd64ff52e9759b2c1e5e57eb8c64f63ca9926dc15c816aa0eea8818545e6","sha256:aa9c51dd2e23c79e3aa1b446982a3cecc50b61d6b968ac5b75bab4c9e504ddc6"],"state_sha256":"e50914b2a7f3a9c61554af7c854f52de24a246b27c93370d9d59c3de772e3680"}