{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6IG6OZCQ4IDE55NGEVPSELHYOH","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":"cc6c0d8d275b86bc305b28d6d8a88ef430f86829658bab240e1c708e9703f740","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-04-07T14:43:58Z","title_canon_sha256":"a377e306170065d3ea2758bed0e7ab1bda7676ce49126a3d0349b1e7e64eae70"},"schema_version":"1.0","source":{"id":"1904.03662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03662","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03662v1","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03662","created_at":"2026-05-17T23:49:12Z"},{"alias_kind":"pith_short_12","alias_value":"6IG6OZCQ4IDE","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6IG6OZCQ4IDE55NG","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6IG6OZCQ","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:958d3ef8d065366197b99f609ddfa81b41bf2380c807999918c1baaf8d270aaf","target":"graph","created_at":"2026-05-17T23:49:12Z","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 study spectral properties of two-dimensional canonical systems $y'(t)=zJH(t)y(t)$, $t\\in[a,b)$, where the Hamiltonian $H$ is locally integrable on $[a,b)$, positive semidefinite, and Weyl's limit point case takes place at $b$. We answer the following questions explicitly in terms of $H$:\n  Is the spectrum of the associated selfadjoint operator discrete ?\n  If it is discrete, what is its asymptotic distribution ?\n  Here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast. Making an analogy with complex analysis, t","authors_text":"Harald Woracek, Roman Romanov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-04-07T14:43:58Z","title":"Canonical systems with discrete spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03662","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:e4e0500659326aa74e00877b8449d15dc645f51eda9a1c0a0948c09611948903","target":"record","created_at":"2026-05-17T23:49:12Z","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":"cc6c0d8d275b86bc305b28d6d8a88ef430f86829658bab240e1c708e9703f740","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-04-07T14:43:58Z","title_canon_sha256":"a377e306170065d3ea2758bed0e7ab1bda7676ce49126a3d0349b1e7e64eae70"},"schema_version":"1.0","source":{"id":"1904.03662","kind":"arxiv","version":1}},"canonical_sha256":"f20de76450e2064ef5a6255f222cf871deac4994160222c68dcf5aea0a0f0ac9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f20de76450e2064ef5a6255f222cf871deac4994160222c68dcf5aea0a0f0ac9","first_computed_at":"2026-05-17T23:49:12.596336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:12.596336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XeY9D9yAkDA2xjuA7NQPLYV1dSk5iLUGLxDR7MiWm+Ak+vGrvqkp8sjnuZg8wTBmUn8pfl21GJPRI/YdD/6PDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:12.597119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4e0500659326aa74e00877b8449d15dc645f51eda9a1c0a0948c09611948903","sha256:958d3ef8d065366197b99f609ddfa81b41bf2380c807999918c1baaf8d270aaf"],"state_sha256":"5c5af6898c279480aefce9ef108a54f7e9bd6eac8e1afefabde875cf4a6c13c6"}