{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:VVXTNZCNXWCNABTW4IBAZB5KBQ","short_pith_number":"pith:VVXTNZCN","canonical_record":{"source":{"id":"math-ph/0101030","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-01-27T08:51:24Z","cross_cats_sorted":["cs.NA","math.MP","math.NA"],"title_canon_sha256":"11d08efad951a622fb5d4dd3a531b37bf8016a6b2af692710bd2f88b4370e225","abstract_canon_sha256":"fba043c8cf2aa1ffc8276648d25f648a8cfc4e2b7d8c79063106aac736f7ca93"},"schema_version":"1.0"},"canonical_sha256":"ad6f36e44dbd84d00676e2020c87aa0c2f3af3604c510f2021563d0b0183a03c","source":{"kind":"arxiv","id":"math-ph/0101030","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0101030","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0101030v2","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0101030","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_12","alias_value":"VVXTNZCNXWCN","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_16","alias_value":"VVXTNZCNXWCNABTW","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_8","alias_value":"VVXTNZCN","created_at":"2026-06-03T22:06:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:VVXTNZCNXWCNABTW4IBAZB5KBQ","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0101030","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2001-01-27T08:51:24Z","cross_cats_sorted":["cs.NA","math.MP","math.NA"],"title_canon_sha256":"11d08efad951a622fb5d4dd3a531b37bf8016a6b2af692710bd2f88b4370e225","abstract_canon_sha256":"fba043c8cf2aa1ffc8276648d25f648a8cfc4e2b7d8c79063106aac736f7ca93"},"schema_version":"1.0"},"canonical_sha256":"ad6f36e44dbd84d00676e2020c87aa0c2f3af3604c510f2021563d0b0183a03c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:14.227028Z","signature_b64":"Imlov9EX+3z5WxGvrgGwz5QOObMzxCJzg6xxl/2fZWkxrelDLSqKrlxKJYb33rU6NUhFqgVIxws8ccbzQaHlCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad6f36e44dbd84d00676e2020c87aa0c2f3af3604c510f2021563d0b0183a03c","last_reissued_at":"2026-06-03T22:06:14.226603Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:14.226603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0101030","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T22:06:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+VIVTOrk1tcuSo7x7ZxVSo1xVINs6beF+FPhZEjahWK6e3v0vfe3sCd2eHwf3EizwUhBRrLWthn4QSK+QioDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:06:05.400437Z"},"content_sha256":"83d99205e17f2ef9625f8461a2856a6866fe86c124c9144beda233359f7aa7fd","schema_version":"1.0","event_id":"sha256:83d99205e17f2ef9625f8461a2856a6866fe86c124c9144beda233359f7aa7fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:VVXTNZCNXWCNABTW4IBAZB5KBQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfined","license":"","headline":"","cross_cats":["cs.NA","math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Omar Mustafa","submitted_at":"2001-01-27T08:51:24Z","abstract_excerpt":"The D -dimensional quasi - exact solutions for the singular even - power anharmonic potential $V(q)=aq^2+bq^{-4}+cq^{-6}$ are reported. We show that whilst Dong and Ma's [5] quasi - exact ground - state solution (in D=2) is beyond doubt, their solution for the first excited state is exotic. Quasi - exact solutions for the ground and first excited states are also given for the above potential confined to an impenetrable cylindrical (D=2) or spherical (D=3) wall."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0101030","kind":"arxiv","version":2},"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/0101030/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":"2026-06-03T22:06:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALVYe1tcxLp4y93AuMRHni9dVK2MneCcCr+7I9Q4mrJp3KdpSIe+lq91C3k62QMyu2cORGzeACUCOiY8SmavBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:06:05.400816Z"},"content_sha256":"4e4a7ffb780f0ee1d35ea4027f2adf57f22e884b31d607a25e4d3c2c2aa9be01","schema_version":"1.0","event_id":"sha256:4e4a7ffb780f0ee1d35ea4027f2adf57f22e884b31d607a25e4d3c2c2aa9be01"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVXTNZCNXWCNABTW4IBAZB5KBQ/bundle.json","state_url":"https://pith.science/pith/VVXTNZCNXWCNABTW4IBAZB5KBQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVXTNZCNXWCNABTW4IBAZB5KBQ/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":"2026-06-22T16:06:05Z","links":{"resolver":"https://pith.science/pith/VVXTNZCNXWCNABTW4IBAZB5KBQ","bundle":"https://pith.science/pith/VVXTNZCNXWCNABTW4IBAZB5KBQ/bundle.json","state":"https://pith.science/pith/VVXTNZCNXWCNABTW4IBAZB5KBQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVXTNZCNXWCNABTW4IBAZB5KBQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:VVXTNZCNXWCNABTW4IBAZB5KBQ","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":"fba043c8cf2aa1ffc8276648d25f648a8cfc4e2b7d8c79063106aac736f7ca93","cross_cats_sorted":["cs.NA","math.MP","math.NA"],"license":"","primary_cat":"math-ph","submitted_at":"2001-01-27T08:51:24Z","title_canon_sha256":"11d08efad951a622fb5d4dd3a531b37bf8016a6b2af692710bd2f88b4370e225"},"schema_version":"1.0","source":{"id":"math-ph/0101030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0101030","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0101030v2","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0101030","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_12","alias_value":"VVXTNZCNXWCN","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_16","alias_value":"VVXTNZCNXWCNABTW","created_at":"2026-06-03T22:06:14Z"},{"alias_kind":"pith_short_8","alias_value":"VVXTNZCN","created_at":"2026-06-03T22:06:14Z"}],"graph_snapshots":[{"event_id":"sha256:4e4a7ffb780f0ee1d35ea4027f2adf57f22e884b31d607a25e4d3c2c2aa9be01","target":"graph","created_at":"2026-06-03T22:06:14Z","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/0101030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The D -dimensional quasi - exact solutions for the singular even - power anharmonic potential $V(q)=aq^2+bq^{-4}+cq^{-6}$ are reported. We show that whilst Dong and Ma's [5] quasi - exact ground - state solution (in D=2) is beyond doubt, their solution for the first excited state is exotic. Quasi - exact solutions for the ground and first excited states are also given for the above potential confined to an impenetrable cylindrical (D=2) or spherical (D=3) wall.","authors_text":"Omar Mustafa","cross_cats":["cs.NA","math.MP","math.NA"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2001-01-27T08:51:24Z","title":"On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfined"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0101030","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":"sha256:83d99205e17f2ef9625f8461a2856a6866fe86c124c9144beda233359f7aa7fd","target":"record","created_at":"2026-06-03T22:06:14Z","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":"fba043c8cf2aa1ffc8276648d25f648a8cfc4e2b7d8c79063106aac736f7ca93","cross_cats_sorted":["cs.NA","math.MP","math.NA"],"license":"","primary_cat":"math-ph","submitted_at":"2001-01-27T08:51:24Z","title_canon_sha256":"11d08efad951a622fb5d4dd3a531b37bf8016a6b2af692710bd2f88b4370e225"},"schema_version":"1.0","source":{"id":"math-ph/0101030","kind":"arxiv","version":2}},"canonical_sha256":"ad6f36e44dbd84d00676e2020c87aa0c2f3af3604c510f2021563d0b0183a03c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad6f36e44dbd84d00676e2020c87aa0c2f3af3604c510f2021563d0b0183a03c","first_computed_at":"2026-06-03T22:06:14.226603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:14.226603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Imlov9EX+3z5WxGvrgGwz5QOObMzxCJzg6xxl/2fZWkxrelDLSqKrlxKJYb33rU6NUhFqgVIxws8ccbzQaHlCw==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:14.227028Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0101030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83d99205e17f2ef9625f8461a2856a6866fe86c124c9144beda233359f7aa7fd","sha256:4e4a7ffb780f0ee1d35ea4027f2adf57f22e884b31d607a25e4d3c2c2aa9be01"],"state_sha256":"567db8401c25dfe94c98c7d28fd6261560db70b727b9e5a6bef66dacbdce5d60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lrAo0FYbMtfcsto0FFBOPLFmvcgQGucJcXC+26+O/o7ykA+c7HRr6jIQEC567tQCcw7llDXbcjFIkZ/4/ilQBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:06:05.402784Z","bundle_sha256":"ff77455f46cd424bd172c858fdaa20ecd92c5164352a14a66e11fe51dd06d79e"}}