{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NUJ6MUU5PU2WBX3JUTD3Y6MZ2E","short_pith_number":"pith:NUJ6MUU5","canonical_record":{"source":{"id":"1507.03929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-14T17:06:54Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"143ec06d482f836f5ffe8f74611d148996c2815c248d3249fe74adc082058a39","abstract_canon_sha256":"3b5d6cee020cd463d69549dd0ff6105b66edc4d97a856a9b1e749ea974b75d44"},"schema_version":"1.0"},"canonical_sha256":"6d13e6529d7d3560df69a4c7bc7999d1233e7cb8fc0e4bef77f364b1543f3628","source":{"kind":"arxiv","id":"1507.03929","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03929","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03929v1","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03929","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"pith_short_12","alias_value":"NUJ6MUU5PU2W","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NUJ6MUU5PU2WBX3J","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NUJ6MUU5","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NUJ6MUU5PU2WBX3JUTD3Y6MZ2E","target":"record","payload":{"canonical_record":{"source":{"id":"1507.03929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-14T17:06:54Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"143ec06d482f836f5ffe8f74611d148996c2815c248d3249fe74adc082058a39","abstract_canon_sha256":"3b5d6cee020cd463d69549dd0ff6105b66edc4d97a856a9b1e749ea974b75d44"},"schema_version":"1.0"},"canonical_sha256":"6d13e6529d7d3560df69a4c7bc7999d1233e7cb8fc0e4bef77f364b1543f3628","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:52.204392Z","signature_b64":"3mi2p/u3rZPKIPN35Wb651OWC2g4bpNxA8jZgbnGvWLfauJ+MwVQMUzbtHCm3JHDOm8P01PmbEk0D72piaaCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d13e6529d7d3560df69a4c7bc7999d1233e7cb8fc0e4bef77f364b1543f3628","last_reissued_at":"2026-05-18T01:36:52.203783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:52.203783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.03929","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":"2026-05-18T01:36:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q3qiHYHkcHynNDz3rHVPF03mqmEdNrb+62Vgzn9nlk9AYDmtBXpCaCKfXfsun7qRNr4Rl1SQHK7kpN0nB7XbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:08:39.189546Z"},"content_sha256":"9c5a62b8b7a527bc79f0fdb25f3945077656f6caaf18e5f80c6d0b5e894fa01c","schema_version":"1.0","event_id":"sha256:9c5a62b8b7a527bc79f0fdb25f3945077656f6caaf18e5f80c6d0b5e894fa01c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NUJ6MUU5PU2WBX3JUTD3Y6MZ2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alonso Contreras-Astorga, Axel Schulze-Halberg","submitted_at":"2015-07-14T17:06:54Z","abstract_excerpt":"We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential representation are obtained using this relationship. Furthermore, it is used to find normalization constants of wave functions of quantum systems that feature energy-dependent potentials. Additionally, this relationship is used to express certain integrals involving functions that are solution of Schrodinger equations through derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03929","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":"2026-05-18T01:36:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8HhhfQDZSOCk8GJRWtskJEhL6hw5KnMHqpiZD1pKqsTJfyiEZzzazGavxtKhFyeZL4s96GHxi/FJtgCrdicBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:08:39.190109Z"},"content_sha256":"55324b8f71e26c86b3301a3be758eb13cc5c6ab278fcd6389ff784137b57de7e","schema_version":"1.0","event_id":"sha256:55324b8f71e26c86b3301a3be758eb13cc5c6ab278fcd6389ff784137b57de7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NUJ6MUU5PU2WBX3JUTD3Y6MZ2E/bundle.json","state_url":"https://pith.science/pith/NUJ6MUU5PU2WBX3JUTD3Y6MZ2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NUJ6MUU5PU2WBX3JUTD3Y6MZ2E/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":"2026-05-31T21:08:39Z","links":{"resolver":"https://pith.science/pith/NUJ6MUU5PU2WBX3JUTD3Y6MZ2E","bundle":"https://pith.science/pith/NUJ6MUU5PU2WBX3JUTD3Y6MZ2E/bundle.json","state":"https://pith.science/pith/NUJ6MUU5PU2WBX3JUTD3Y6MZ2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NUJ6MUU5PU2WBX3JUTD3Y6MZ2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NUJ6MUU5PU2WBX3JUTD3Y6MZ2E","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":"3b5d6cee020cd463d69549dd0ff6105b66edc4d97a856a9b1e749ea974b75d44","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-14T17:06:54Z","title_canon_sha256":"143ec06d482f836f5ffe8f74611d148996c2815c248d3249fe74adc082058a39"},"schema_version":"1.0","source":{"id":"1507.03929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.03929","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"arxiv_version","alias_value":"1507.03929v1","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03929","created_at":"2026-05-18T01:36:52Z"},{"alias_kind":"pith_short_12","alias_value":"NUJ6MUU5PU2W","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NUJ6MUU5PU2WBX3J","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NUJ6MUU5","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:55324b8f71e26c86b3301a3be758eb13cc5c6ab278fcd6389ff784137b57de7e","target":"graph","created_at":"2026-05-18T01:36:52Z","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 construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential representation are obtained using this relationship. Furthermore, it is used to find normalization constants of wave functions of quantum systems that feature energy-dependent potentials. Additionally, this relationship is used to express certain integrals involving functions that are solution of Schrodinger equations through derivatives.","authors_text":"Alonso Contreras-Astorga, Axel Schulze-Halberg","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-14T17:06:54Z","title":"On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03929","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":"sha256:9c5a62b8b7a527bc79f0fdb25f3945077656f6caaf18e5f80c6d0b5e894fa01c","target":"record","created_at":"2026-05-18T01:36:52Z","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":"3b5d6cee020cd463d69549dd0ff6105b66edc4d97a856a9b1e749ea974b75d44","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-14T17:06:54Z","title_canon_sha256":"143ec06d482f836f5ffe8f74611d148996c2815c248d3249fe74adc082058a39"},"schema_version":"1.0","source":{"id":"1507.03929","kind":"arxiv","version":1}},"canonical_sha256":"6d13e6529d7d3560df69a4c7bc7999d1233e7cb8fc0e4bef77f364b1543f3628","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d13e6529d7d3560df69a4c7bc7999d1233e7cb8fc0e4bef77f364b1543f3628","first_computed_at":"2026-05-18T01:36:52.203783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:52.203783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3mi2p/u3rZPKIPN35Wb651OWC2g4bpNxA8jZgbnGvWLfauJ+MwVQMUzbtHCm3JHDOm8P01PmbEk0D72piaaCBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:52.204392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.03929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c5a62b8b7a527bc79f0fdb25f3945077656f6caaf18e5f80c6d0b5e894fa01c","sha256:55324b8f71e26c86b3301a3be758eb13cc5c6ab278fcd6389ff784137b57de7e"],"state_sha256":"04e9ba0351d87295bb025b00caee38b809d185ec8c40525503e669695dde5096"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f8YHDQK1l1Y75eF5I5zUJgLf10jWVDzS983PSZhZT3SNhFkKOr2HiMqDnP3hEFIX632bJEmtzN0ZoPAMSYw9BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:08:39.193281Z","bundle_sha256":"7832489213c1fdd49cf1319a9e6271498b3c91c7bba3f8116a4037638a33d3b9"}}