{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5LQG7PKWZVISSIAVVOEJAO2MVT","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":"2b1aa5de88c0d83624e89f8b04803cef35b834d8eb4d5d2f79b559bb00dcd7a7","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-17T04:38:34Z","title_canon_sha256":"616d1b2a363bb4d914ee05520426571aecadefe24d101cc9e54bd634c8a3317c"},"schema_version":"1.0","source":{"id":"1301.3980","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3980","created_at":"2026-05-18T01:52:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3980v2","created_at":"2026-05-18T01:52:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3980","created_at":"2026-05-18T01:52:06Z"},{"alias_kind":"pith_short_12","alias_value":"5LQG7PKWZVIS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5LQG7PKWZVISSIAV","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5LQG7PKW","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:b9f06ee4101814006c6d95d0686b3554e0fccf7ce5b37ba30a27fb70d74645e5","target":"graph","created_at":"2026-05-18T01:52:06Z","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 address the problem of rational extensions of six examples of shape-invariant potentials having finitely many discrete eigenstates. The overshoot eigenfunctions are proposed as candidates unique in this group for the virtual state wavefunctions, which are an essential ingredient for multi-indexed and iso-spectral extensions of these potentials. They have exactly the same form as the eigenfunctions but their degrees are much higher than n_{max} so that their energies are lower than the groundstate energy.","authors_text":"Ryu Sasaki, Satoru Odake","cross_cats":["hep-th","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-17T04:38:34Z","title":"Extensions of solvable potentials with finitely many discrete eigenstates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3980","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":"sha256:56e8e6ccbd085574df2a9e93733e531c1ea42551a82a75e7de9e409026c874a6","target":"record","created_at":"2026-05-18T01:52:06Z","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":"2b1aa5de88c0d83624e89f8b04803cef35b834d8eb4d5d2f79b559bb00dcd7a7","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-17T04:38:34Z","title_canon_sha256":"616d1b2a363bb4d914ee05520426571aecadefe24d101cc9e54bd634c8a3317c"},"schema_version":"1.0","source":{"id":"1301.3980","kind":"arxiv","version":2}},"canonical_sha256":"eae06fbd56cd51292015ab88903b4cacecdc8ad85606e756dc129e221bae47ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eae06fbd56cd51292015ab88903b4cacecdc8ad85606e756dc129e221bae47ba","first_computed_at":"2026-05-18T01:52:06.371058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:06.371058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vS4mqJf8pAGVDxFAQNv+e32LxN9E46R7bGL9XK7M+PPHcYymnSfUOikWNsgJlEGeK/dSO1+lNHGaE06PV1brBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:06.371502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3980","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56e8e6ccbd085574df2a9e93733e531c1ea42551a82a75e7de9e409026c874a6","sha256:b9f06ee4101814006c6d95d0686b3554e0fccf7ce5b37ba30a27fb70d74645e5"],"state_sha256":"fcad249788fe0ce924cc619ed23f2fda77a446169eb96631c77d806568640b95"}