{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OENPR6B5QTD4J5N2DGWBLPK7ST","short_pith_number":"pith:OENPR6B5","canonical_record":{"source":{"id":"1711.02422","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-07T12:00:00Z","cross_cats_sorted":["hep-th","nlin.SI"],"title_canon_sha256":"852f6411baad83654746171a6dd6bf4eb78c97ff66180437fa5dd91bb3241c01","abstract_canon_sha256":"288f79cf39a8eda2c887dc3f7a88e3fd16c83bd0f2c12a892447d63b037eb4cf"},"schema_version":"1.0"},"canonical_sha256":"711af8f83d84c7c4f5ba19ac15bd5f94e17658ca1f888bafbdaffbd5db34fbf2","source":{"kind":"arxiv","id":"1711.02422","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02422","created_at":"2026-05-18T00:26:49Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02422v2","created_at":"2026-05-18T00:26:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02422","created_at":"2026-05-18T00:26:49Z"},{"alias_kind":"pith_short_12","alias_value":"OENPR6B5QTD4","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OENPR6B5QTD4J5N2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OENPR6B5","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OENPR6B5QTD4J5N2DGWBLPK7ST","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02422","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-07T12:00:00Z","cross_cats_sorted":["hep-th","nlin.SI"],"title_canon_sha256":"852f6411baad83654746171a6dd6bf4eb78c97ff66180437fa5dd91bb3241c01","abstract_canon_sha256":"288f79cf39a8eda2c887dc3f7a88e3fd16c83bd0f2c12a892447d63b037eb4cf"},"schema_version":"1.0"},"canonical_sha256":"711af8f83d84c7c4f5ba19ac15bd5f94e17658ca1f888bafbdaffbd5db34fbf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:49.096924Z","signature_b64":"XBELHxsllIAiZ+gOxDndHmrwzo/avYUd1jhsJ3AOO7sAtFQ2QXrP7DIkZhJ4qbZDal6XrzwZwBelEqsN+yEyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"711af8f83d84c7c4f5ba19ac15bd5f94e17658ca1f888bafbdaffbd5db34fbf2","last_reissued_at":"2026-05-18T00:26:49.096399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:49.096399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02422","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":"2026-05-18T00:26:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGDjl7KeSocl6afNsbLACCNTEZgkAwVy9r2aPAUAbr41zpS/E3JqKivsCahFK8wr0ioBVixGBusdspQ9YRdoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:36:08.765302Z"},"content_sha256":"8a979b65f58e88711ddc29181d9c9be528821b7f2677d471942160aa07bdda5f","schema_version":"1.0","event_id":"sha256:8a979b65f58e88711ddc29181d9c9be528821b7f2677d471942160aa07bdda5f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OENPR6B5QTD4J5N2DGWBLPK7ST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Description of Shape Invariance Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","nlin.SI"],"primary_cat":"quant-ph","authors_text":"Satoshi Ohya","submitted_at":"2017-11-07T12:00:00Z","abstract_excerpt":"We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler problem in hyperbolic space, and the Rosen-Morse potential problem. Following the prescription given by Gangopadhyaya et al., we first introduce certain nonlinear algebraic systems. We then show that, if the model parameters are appropriately quantized, the bound-state problems can be solved solely by means of representation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02422","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":""},"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":"2026-05-18T00:26:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NKUaOjH4GSZKt87B+GGfupx/GOi0kTZ76ZP4QOcVKxcUUxTnRqcoVutYvW7FYieY4uueSk2uk2dS0RNgsE8bAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:36:08.765875Z"},"content_sha256":"43c635a6808b3400465a00c36b14b5a541411bf2c9eb55ad73687cc0d1ef2e71","schema_version":"1.0","event_id":"sha256:43c635a6808b3400465a00c36b14b5a541411bf2c9eb55ad73687cc0d1ef2e71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OENPR6B5QTD4J5N2DGWBLPK7ST/bundle.json","state_url":"https://pith.science/pith/OENPR6B5QTD4J5N2DGWBLPK7ST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OENPR6B5QTD4J5N2DGWBLPK7ST/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":"2026-06-07T15:36:08Z","links":{"resolver":"https://pith.science/pith/OENPR6B5QTD4J5N2DGWBLPK7ST","bundle":"https://pith.science/pith/OENPR6B5QTD4J5N2DGWBLPK7ST/bundle.json","state":"https://pith.science/pith/OENPR6B5QTD4J5N2DGWBLPK7ST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OENPR6B5QTD4J5N2DGWBLPK7ST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OENPR6B5QTD4J5N2DGWBLPK7ST","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":"288f79cf39a8eda2c887dc3f7a88e3fd16c83bd0f2c12a892447d63b037eb4cf","cross_cats_sorted":["hep-th","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-07T12:00:00Z","title_canon_sha256":"852f6411baad83654746171a6dd6bf4eb78c97ff66180437fa5dd91bb3241c01"},"schema_version":"1.0","source":{"id":"1711.02422","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02422","created_at":"2026-05-18T00:26:49Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02422v2","created_at":"2026-05-18T00:26:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02422","created_at":"2026-05-18T00:26:49Z"},{"alias_kind":"pith_short_12","alias_value":"OENPR6B5QTD4","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OENPR6B5QTD4J5N2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OENPR6B5","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:43c635a6808b3400465a00c36b14b5a541411bf2c9eb55ad73687cc0d1ef2e71","target":"graph","created_at":"2026-05-18T00:26:49Z","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 revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler problem in hyperbolic space, and the Rosen-Morse potential problem. Following the prescription given by Gangopadhyaya et al., we first introduce certain nonlinear algebraic systems. We then show that, if the model parameters are appropriately quantized, the bound-state problems can be solved solely by means of representation theory.","authors_text":"Satoshi Ohya","cross_cats":["hep-th","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-07T12:00:00Z","title":"Algebraic Description of Shape Invariance Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02422","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":"sha256:8a979b65f58e88711ddc29181d9c9be528821b7f2677d471942160aa07bdda5f","target":"record","created_at":"2026-05-18T00:26:49Z","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":"288f79cf39a8eda2c887dc3f7a88e3fd16c83bd0f2c12a892447d63b037eb4cf","cross_cats_sorted":["hep-th","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-11-07T12:00:00Z","title_canon_sha256":"852f6411baad83654746171a6dd6bf4eb78c97ff66180437fa5dd91bb3241c01"},"schema_version":"1.0","source":{"id":"1711.02422","kind":"arxiv","version":2}},"canonical_sha256":"711af8f83d84c7c4f5ba19ac15bd5f94e17658ca1f888bafbdaffbd5db34fbf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"711af8f83d84c7c4f5ba19ac15bd5f94e17658ca1f888bafbdaffbd5db34fbf2","first_computed_at":"2026-05-18T00:26:49.096399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:49.096399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XBELHxsllIAiZ+gOxDndHmrwzo/avYUd1jhsJ3AOO7sAtFQ2QXrP7DIkZhJ4qbZDal6XrzwZwBelEqsN+yEyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:49.096924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02422","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a979b65f58e88711ddc29181d9c9be528821b7f2677d471942160aa07bdda5f","sha256:43c635a6808b3400465a00c36b14b5a541411bf2c9eb55ad73687cc0d1ef2e71"],"state_sha256":"9076606602ebef25d199eb1e663781c38e0e89ea7a7c7797ee2628b54b29d8f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zJv587JLIq3SyToFn0EoD3eSjBdm6sL9E+1ZsyXhjRyLB9zP4zxvnhS00bUo07c3MetMK7Qmcj0d5f5t/5FwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T15:36:08.769137Z","bundle_sha256":"5205c7bad6d1409c7112d65a4d842e0f86471d27f234db578f6aa01508107556"}}