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We prove that \\calM(V_0) is connected."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0307007","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2003-07-01T12:02:08Z","cross_cats_sorted":[],"title_canon_sha256":"c42e15250f7e0f26a4963a72297b734c8fd6c11309088649f20e402b45b67d1e","abstract_canon_sha256":"cdb895731af5b8a6fe197655a06cd47776cb51d38c3df800d7319d6341bf3f56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:28.985580Z","signature_b64":"uUsOlyNjxTlOEE4lRlks6Z+FsQDZPh/7/rEwkaXTVV5reFJ8K8bJRyByIhgThl3aY97ID1N0MdylGFvHE76gCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbb7e570f3d22c80218d382664636d76012bbd4d6f34a4973484bea265846fb7","last_reissued_at":"2026-05-18T01:38:28.984861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:28.984861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schr\\\"odinger Operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Barry Simon, Fritz Gesztesy","submitted_at":"2003-07-01T12:02:08Z","abstract_excerpt":"Let V_0 be a real-valued function on [0,\\infty) and V\\in L^1([0,R]) for all R>0 so that H(V_0)= -\\f{d^2}{dx^2}+V_0 in L^2([0,\\infty)) with u(0)=0 boundary conditions has discrete spectrum bounded from below. Let \\calM (V_0) be the set of V so that H(V) and H(V_0) have the same spectrum. We prove that \\calM(V_0) is connected."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307007","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0307007","created_at":"2026-05-18T01:38:28.984979+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0307007v1","created_at":"2026-05-18T01:38:28.984979+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307007","created_at":"2026-05-18T01:38:28.984979+00:00"},{"alias_kind":"pith_short_12","alias_value":"XO36K4HT2IWI","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"XO36K4HT2IWIAIMN","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"XO36K4HT","created_at":"2026-05-18T12:25:52.051335+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY","json":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY.json","graph_json":"https://pith.science/api/pith-number/XO36K4HT2IWIAIMNHATGIY3NOY/graph.json","events_json":"https://pith.science/api/pith-number/XO36K4HT2IWIAIMNHATGIY3NOY/events.json","paper":"https://pith.science/paper/XO36K4HT"},"agent_actions":{"view_html":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY","download_json":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY.json","view_paper":"https://pith.science/paper/XO36K4HT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0307007&json=true","fetch_graph":"https://pith.science/api/pith-number/XO36K4HT2IWIAIMNHATGIY3NOY/graph.json","fetch_events":"https://pith.science/api/pith-number/XO36K4HT2IWIAIMNHATGIY3NOY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY/action/storage_attestation","attest_author":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY/action/author_attestation","sign_citation":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY/action/citation_signature","submit_replication":"https://pith.science/pith/XO36K4HT2IWIAIMNHATGIY3NOY/action/replication_record"}},"created_at":"2026-05-18T01:38:28.984979+00:00","updated_at":"2026-05-18T01:38:28.984979+00:00"}