{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GFDPRVHXWAORPPQ6NBQZEQ3AA6","short_pith_number":"pith:GFDPRVHX","canonical_record":{"source":{"id":"1008.1528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-09T15:23:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0dd4cbe4a7d011a6df46f68c137738fc2eb2f84c46020bfc7ef3e4d2d5adde6e","abstract_canon_sha256":"c135e738b70f4b86f098d229a551d779b2cf9bff710fd027f0052bccd04d4644"},"schema_version":"1.0"},"canonical_sha256":"3146f8d4f7b01d17be1e686192436007849188654a8c63a0fe03b2ae4ccd81f2","source":{"kind":"arxiv","id":"1008.1528","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1528","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1528v1","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1528","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"GFDPRVHXWAOR","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GFDPRVHXWAORPPQ6","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GFDPRVHX","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GFDPRVHXWAORPPQ6NBQZEQ3AA6","target":"record","payload":{"canonical_record":{"source":{"id":"1008.1528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-09T15:23:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0dd4cbe4a7d011a6df46f68c137738fc2eb2f84c46020bfc7ef3e4d2d5adde6e","abstract_canon_sha256":"c135e738b70f4b86f098d229a551d779b2cf9bff710fd027f0052bccd04d4644"},"schema_version":"1.0"},"canonical_sha256":"3146f8d4f7b01d17be1e686192436007849188654a8c63a0fe03b2ae4ccd81f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:51.122993Z","signature_b64":"odKOF5VVf+5D8IvWwO00xs0jFvQqhpXhiW1mcEXA+Hf9uVq9rsLWdonTJezQ2QIL4um9hzODb6OY/Jp7XcjFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3146f8d4f7b01d17be1e686192436007849188654a8c63a0fe03b2ae4ccd81f2","last_reissued_at":"2026-05-18T04:36:51.122326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:51.122326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.1528","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":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7pn5GI+tcwRDcjMVsNWdIRuo9oHHmDNxVPrc5vofPwCRYRcimmpYgNw4z1leqeqTgyYjwKDpuIPlRdYFNbIjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:44:08.031495Z"},"content_sha256":"ff17a806218ab75ffee45a5b7f682938cbd57b5ece228f762e488afe173ca881","schema_version":"1.0","event_id":"sha256:ff17a806218ab75ffee45a5b7f682938cbd57b5ece228f762e488afe173ca881"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GFDPRVHXWAORPPQ6NBQZEQ3AA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isospectral Potentials from Modified Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Micheal S. Berger, Nail S. Ussembayev","submitted_at":"2010-08-09T15:23:47Z","abstract_excerpt":"Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1528","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Kb3P8jRH3ftwmJYlGsFHjtPM08tNzPOvFlBTn8ObFhpf6H22v06nOSlZ8v4oaozPMNE9sBOIRH0AVUURmUjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:44:08.031837Z"},"content_sha256":"394e6673300a3435dd6307312cc5c019e79168b6b74eaefa41891f31006540df","schema_version":"1.0","event_id":"sha256:394e6673300a3435dd6307312cc5c019e79168b6b74eaefa41891f31006540df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFDPRVHXWAORPPQ6NBQZEQ3AA6/bundle.json","state_url":"https://pith.science/pith/GFDPRVHXWAORPPQ6NBQZEQ3AA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFDPRVHXWAORPPQ6NBQZEQ3AA6/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":"2026-06-27T13:44:08Z","links":{"resolver":"https://pith.science/pith/GFDPRVHXWAORPPQ6NBQZEQ3AA6","bundle":"https://pith.science/pith/GFDPRVHXWAORPPQ6NBQZEQ3AA6/bundle.json","state":"https://pith.science/pith/GFDPRVHXWAORPPQ6NBQZEQ3AA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFDPRVHXWAORPPQ6NBQZEQ3AA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GFDPRVHXWAORPPQ6NBQZEQ3AA6","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":"c135e738b70f4b86f098d229a551d779b2cf9bff710fd027f0052bccd04d4644","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-09T15:23:47Z","title_canon_sha256":"0dd4cbe4a7d011a6df46f68c137738fc2eb2f84c46020bfc7ef3e4d2d5adde6e"},"schema_version":"1.0","source":{"id":"1008.1528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1528","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1528v1","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1528","created_at":"2026-05-18T04:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"GFDPRVHXWAOR","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GFDPRVHXWAORPPQ6","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GFDPRVHX","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:394e6673300a3435dd6307312cc5c019e79168b6b74eaefa41891f31006540df","target":"graph","created_at":"2026-05-18T04:36:51Z","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":"Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such","authors_text":"Micheal S. Berger, Nail S. Ussembayev","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-09T15:23:47Z","title":"Isospectral Potentials from Modified Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1528","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:ff17a806218ab75ffee45a5b7f682938cbd57b5ece228f762e488afe173ca881","target":"record","created_at":"2026-05-18T04:36:51Z","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":"c135e738b70f4b86f098d229a551d779b2cf9bff710fd027f0052bccd04d4644","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-08-09T15:23:47Z","title_canon_sha256":"0dd4cbe4a7d011a6df46f68c137738fc2eb2f84c46020bfc7ef3e4d2d5adde6e"},"schema_version":"1.0","source":{"id":"1008.1528","kind":"arxiv","version":1}},"canonical_sha256":"3146f8d4f7b01d17be1e686192436007849188654a8c63a0fe03b2ae4ccd81f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3146f8d4f7b01d17be1e686192436007849188654a8c63a0fe03b2ae4ccd81f2","first_computed_at":"2026-05-18T04:36:51.122326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:51.122326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"odKOF5VVf+5D8IvWwO00xs0jFvQqhpXhiW1mcEXA+Hf9uVq9rsLWdonTJezQ2QIL4um9hzODb6OY/Jp7XcjFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:51.122993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff17a806218ab75ffee45a5b7f682938cbd57b5ece228f762e488afe173ca881","sha256:394e6673300a3435dd6307312cc5c019e79168b6b74eaefa41891f31006540df"],"state_sha256":"4701fd7b338ce6d334e4c107b2370df712b2a01e474685470d75d04e4eb41a98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEStKaImOIiiWwP2/gZA28V6ZK2QV3lI+7Cjjvy4mRgukp0XSbzgZZfbj3qqTeKZzUY4RwEqANwXigadZi0LAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:44:08.033716Z","bundle_sha256":"2f6e1d75fe51999adf531f39f74f16270ea9470fc0b4abed351e0d4ba275e507"}}