{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:EYXML63XNVOEOJH3ZPORYAOGZ7","short_pith_number":"pith:EYXML63X","schema_version":"1.0","canonical_sha256":"262ec5fb776d5c4724fbcbdd1c01c6cfc00631051d3ec048229b7ec7858464ad","source":{"kind":"arxiv","id":"1001.0495","version":1},"attestation_state":"computed","paper":{"title":"Ma-Xu quantization rule and exact WKB condition for translationally shape invariant potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alain Berard (FCN), Yves Grandati (FCN)","submitted_at":"2010-01-04T12:17:17Z","abstract_excerpt":"For translationally shape invariant potentials, the exact quantization rule proposed by Ma and Xu is a direct consequence of exactness of the modified WKB quantization condition proved by Barclay. We propose here a very direct alternative way to calculate the appropriate correction for the whole class of translationally shape invariant potentials."},"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":"1001.0495","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-01-04T12:17:17Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"e1d9278626482f5734e941138c67ab949eb6e24e4fa1660219c24c22e749343f","abstract_canon_sha256":"86f395498db111d9c151496bd7ee09c62f7e8b887b16f2e17d2cea309a073edf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:05.387680Z","signature_b64":"xKoDVHxbie45UXpq9scD6/N7Pnt7rTL0V9BsLCOHEMb/RequLc5jwOGYEOpSTK6n8yBDfi5cBbLZ1EBa1719Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"262ec5fb776d5c4724fbcbdd1c01c6cfc00631051d3ec048229b7ec7858464ad","last_reissued_at":"2026-05-18T02:10:05.387021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:05.387021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ma-Xu quantization rule and exact WKB condition for translationally shape invariant potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alain Berard (FCN), Yves Grandati (FCN)","submitted_at":"2010-01-04T12:17:17Z","abstract_excerpt":"For translationally shape invariant potentials, the exact quantization rule proposed by Ma and Xu is a direct consequence of exactness of the modified WKB quantization condition proved by Barclay. We propose here a very direct alternative way to calculate the appropriate correction for the whole class of translationally shape invariant potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0495","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":"1001.0495","created_at":"2026-05-18T02:10:05.387119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.0495v1","created_at":"2026-05-18T02:10:05.387119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0495","created_at":"2026-05-18T02:10:05.387119+00:00"},{"alias_kind":"pith_short_12","alias_value":"EYXML63XNVOE","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"EYXML63XNVOEOJH3","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"EYXML63X","created_at":"2026-05-18T12:26:06.534383+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/EYXML63XNVOEOJH3ZPORYAOGZ7","json":"https://pith.science/pith/EYXML63XNVOEOJH3ZPORYAOGZ7.json","graph_json":"https://pith.science/api/pith-number/EYXML63XNVOEOJH3ZPORYAOGZ7/graph.json","events_json":"https://pith.science/api/pith-number/EYXML63XNVOEOJH3ZPORYAOGZ7/events.json","paper":"https://pith.science/paper/EYXML63X"},"agent_actions":{"view_html":"https://pith.science/pith/EYXML63XNVOEOJH3ZPORYAOGZ7","download_json":"https://pith.science/pith/EYXML63XNVOEOJH3ZPORYAOGZ7.json","view_paper":"https://pith.science/paper/EYXML63X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.0495&json=true","fetch_graph":"https://pith.science/api/pith-number/EYXML63XNVOEOJH3ZPORYAOGZ7/graph.json","fetch_events":"https://pith.science/api/pith-number/EYXML63XNVOEOJH3ZPORYAOGZ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EYXML63XNVOEOJH3ZPORYAOGZ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EYXML63XNVOEOJH3ZPORYAOGZ7/action/storage_attestation","attest_author":"https://pith.science/pith/EYXML63XNVOEOJH3ZPORYAOGZ7/action/author_attestation","sign_citation":"https://pith.science/pith/EYXML63XNVOEOJH3ZPORYAOGZ7/action/citation_signature","submit_replication":"https://pith.science/pith/EYXML63XNVOEOJH3ZPORYAOGZ7/action/replication_record"}},"created_at":"2026-05-18T02:10:05.387119+00:00","updated_at":"2026-05-18T02:10:05.387119+00:00"}