{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:LKNVT3UUCSZK2VDZSLYXPXE6KC","short_pith_number":"pith:LKNVT3UU","canonical_record":{"source":{"id":"math-ph/0101006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-01-05T19:49:11Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0f3f42db757eca7787262c8b29040a5f1915027f01901f5da447e451031823ba","abstract_canon_sha256":"5cba91d3df6930850ce32d7f6bfb38f201cf486e8f5ff5bca1d8e1f7483704bb"},"schema_version":"1.0"},"canonical_sha256":"5a9b59ee9414b2ad547992f177dc9e50bf1bba205772383b4fc2d796a682616b","source":{"kind":"arxiv","id":"math-ph/0101006","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:LKNVT3UUCSZK2VDZSLYXPXE6KC","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0101006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-01-05T19:49:11Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0f3f42db757eca7787262c8b29040a5f1915027f01901f5da447e451031823ba","abstract_canon_sha256":"5cba91d3df6930850ce32d7f6bfb38f201cf486e8f5ff5bca1d8e1f7483704bb"},"schema_version":"1.0"},"canonical_sha256":"5a9b59ee9414b2ad547992f177dc9e50bf1bba205772383b4fc2d796a682616b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:28:13.380377Z","signature_b64":"eWCrkvFjzlCa47EgEEyOEVuyFOERKNS2x+Z77yPsw1UFFSiuzo7xnFqjTaBpxleEqHHOTrlKsj5moGQTeWk+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a9b59ee9414b2ad547992f177dc9e50bf1bba205772383b4fc2d796a682616b","last_reissued_at":"2026-07-04T16:28:13.379973Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:28:13.379973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0101006","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxy1GH9wZBFmFRdZ1HJmbWrr627nKJhaVkJScoyBqQW+mJMsjAbKtUiEps+g1NlyKVMtBImaljiqkGj87CrJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T17:56:14.822741Z"},"content_sha256":"5d2695fa76d128d873cbec164487644590433b4392da718f9ba9b12fb160f8a4","schema_version":"1.0","event_id":"sha256:5d2695fa76d128d873cbec164487644590433b4392da718f9ba9b12fb160f8a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:LKNVT3UUCSZK2VDZSLYXPXE6KC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized spiked harmonic oscillator","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Attila B. von Keviczky, Nasser Saad, Richard L. Hall","submitted_at":"2001-01-05T19:49:11Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0101006","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0101006/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:28:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fCwivJGDsbxFdvT+dBmWptwWqVgMlWnZyO8RRjdymnq3JCahlpyAiSKai9wSWyEAeljmDOgeO953eDlZbEW0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T17:56:14.823450Z"},"content_sha256":"a44c4973b8be2e4d3b365bbd456adc5cc84f83cae91624b0cf780f2e7d162d85","schema_version":"1.0","event_id":"sha256:a44c4973b8be2e4d3b365bbd456adc5cc84f83cae91624b0cf780f2e7d162d85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LKNVT3UUCSZK2VDZSLYXPXE6KC/bundle.json","state_url":"https://pith.science/pith/LKNVT3UUCSZK2VDZSLYXPXE6KC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LKNVT3UUCSZK2VDZSLYXPXE6KC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-15T17:56:14Z","links":{"resolver":"https://pith.science/pith/LKNVT3UUCSZK2VDZSLYXPXE6KC","bundle":"https://pith.science/pith/LKNVT3UUCSZK2VDZSLYXPXE6KC/bundle.json","state":"https://pith.science/pith/LKNVT3UUCSZK2VDZSLYXPXE6KC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LKNVT3UUCSZK2VDZSLYXPXE6KC/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mT4t0Hh5Gz3JieieTGMEpkilJI2u61X75dFaZN8LMikYoiswKjfLmTg9HDWVW2GT9KCdIRQpSKpeekODVnC7DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T17:56:14.829415Z","bundle_sha256":"6c9ee6b033e6b099d23aa92594c9cc6e99815864d5a4297b6763749efe92d45b"}}