{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:LKNVT3UUCSZK2VDZSLYXPXE6KC","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":"5cba91d3df6930850ce32d7f6bfb38f201cf486e8f5ff5bca1d8e1f7483704bb","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-01-05T19:49:11Z","title_canon_sha256":"0f3f42db757eca7787262c8b29040a5f1915027f01901f5da447e451031823ba"},"schema_version":"1.0","source":{"id":"math-ph/0101006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0101006","created_at":"2026-07-04T16:28:13Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0101006v1","created_at":"2026-07-04T16:28:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0101006","created_at":"2026-07-04T16:28:13Z"},{"alias_kind":"pith_short_12","alias_value":"LKNVT3UUCSZK","created_at":"2026-07-04T16:28:13Z"},{"alias_kind":"pith_short_16","alias_value":"LKNVT3UUCSZK2VDZ","created_at":"2026-07-04T16:28:13Z"},{"alias_kind":"pith_short_8","alias_value":"LKNVT3UU","created_at":"2026-07-04T16:28:13Z"}],"graph_snapshots":[{"event_id":"sha256:a44c4973b8be2e4d3b365bbd456adc5cc84f83cae91624b0cf780f2e7d162d85","target":"graph","created_at":"2026-07-04T16:28:13Z","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/math-ph/0101006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = -(d/dx)^2 + B x^2 + A/x^2 + lambda/x^alpha, where B > 0, A >= 0, and alpha and lambda denote two real positive parameters. The method makes use of the function space spanned by the solutions |n> of Schroedinger's equation for the potential V(x)= B x^2 + A/x^2. Compact closed-form expressions are obtained for the matrix elements <m|H|n>, and a first-order perturbation series is derived for the wave function. The results are given in terms of generalized hypergeometric fun","authors_text":"Attila B. von Keviczky, Nasser Saad, Richard L. Hall","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2001-01-05T19:49:11Z","title":"Generalized spiked harmonic oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0101006","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":"sha256:5d2695fa76d128d873cbec164487644590433b4392da718f9ba9b12fb160f8a4","target":"record","created_at":"2026-07-04T16:28:13Z","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":"5cba91d3df6930850ce32d7f6bfb38f201cf486e8f5ff5bca1d8e1f7483704bb","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2001-01-05T19:49:11Z","title_canon_sha256":"0f3f42db757eca7787262c8b29040a5f1915027f01901f5da447e451031823ba"},"schema_version":"1.0","source":{"id":"math-ph/0101006","kind":"arxiv","version":1}},"canonical_sha256":"5a9b59ee9414b2ad547992f177dc9e50bf1bba205772383b4fc2d796a682616b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a9b59ee9414b2ad547992f177dc9e50bf1bba205772383b4fc2d796a682616b","first_computed_at":"2026-07-04T16:28:13.379973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:28:13.379973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eWCrkvFjzlCa47EgEEyOEVuyFOERKNS2x+Z77yPsw1UFFSiuzo7xnFqjTaBpxleEqHHOTrlKsj5moGQTeWk+BQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:28:13.380377Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0101006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d2695fa76d128d873cbec164487644590433b4392da718f9ba9b12fb160f8a4","sha256:a44c4973b8be2e4d3b365bbd456adc5cc84f83cae91624b0cf780f2e7d162d85"],"state_sha256":"3f38dd3dcbfc23936bc694e1bd3cd8fb8e3c9687b9c78b937234cf7db9470b77"}