{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:72P3WXWU5J65GPHNMQNJC6PLSC","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":"e1b81bbd172f030ba4f8b00103d46240c32d6e353efc102f9855235fe4024131","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2018-03-03T21:37:32Z","title_canon_sha256":"979957944110146bd6ae88a5614e4bd9d2d95b5bc8acc8db739d4dfbc0161324"},"schema_version":"1.0","source":{"id":"1803.01247","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01247","created_at":"2026-05-18T00:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01247v4","created_at":"2026-05-18T00:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01247","created_at":"2026-05-18T00:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"72P3WXWU5J65","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"72P3WXWU5J65GPHN","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"72P3WXWU","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:4b94cbcf99c5aa9f7a7081f3408e9315e5657b7ef8a92e7dba3a61576c753782","target":"graph","created_at":"2026-05-18T00:05:23Z","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":"In this paper we start with proving that the Schr\\\"odinger equation (SE) with the classical $12-6$ Lennard-Jones (L-J) potential is nonintegrable in the sense of the differential Galois theory (DGT), for any value of energy; i.e., there are no solutions in closed form for such differential equation. We study the $10-6$ potential through DGT and SUSYQM; being it one of the two partner potentials built with a superpotential of the form $w(r)\\propto 1/r^5$. We also find that it is integrable in the sense of DGT for zero energy. A first analysis of the applicability and physical consequences of th","authors_text":"Erick Tuir\\'an, Manuel F. Acosta-Hum\\'anez, Primitivo B. Acosta-Hum\\'anez","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2018-03-03T21:37:32Z","title":"Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01247","kind":"arxiv","version":4},"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:b98e3e6ead2031b679a7734851851b4cd857ab40728811b6d59e419eda0fd861","target":"record","created_at":"2026-05-18T00:05:23Z","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":"e1b81bbd172f030ba4f8b00103d46240c32d6e353efc102f9855235fe4024131","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2018-03-03T21:37:32Z","title_canon_sha256":"979957944110146bd6ae88a5614e4bd9d2d95b5bc8acc8db739d4dfbc0161324"},"schema_version":"1.0","source":{"id":"1803.01247","kind":"arxiv","version":4}},"canonical_sha256":"fe9fbb5ed4ea7dd33ced641a9179eb90a12707fff6d1437cdf638f7ac6bec581","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe9fbb5ed4ea7dd33ced641a9179eb90a12707fff6d1437cdf638f7ac6bec581","first_computed_at":"2026-05-18T00:05:23.754935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:23.754935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fD8PUqfm6tXeNGnC2qyDQ243QxULa7i6nbLW+CPE2PE9J7H4dFIYVYfkeGeqeJxa4vfhFvH3uSYnL8nqikzFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:23.755408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01247","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b98e3e6ead2031b679a7734851851b4cd857ab40728811b6d59e419eda0fd861","sha256:4b94cbcf99c5aa9f7a7081f3408e9315e5657b7ef8a92e7dba3a61576c753782"],"state_sha256":"a3413b6f49d09631c11b0f0ab747a3ee7a36a690dab1c738a5853e4a8ae4b7cb"}