{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XG3JC3TJLUVEAJJD5GGGRQ4NVN","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":"0b6360237c4aa9fac5943442b065d817d7fa657f0b0579f4a2eae3aad41e6873","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-29T06:12:35Z","title_canon_sha256":"f235ebe28a7cf9f13f4b610e1594355de33d50a71bda5352eddbf858d54b4089"},"schema_version":"1.0","source":{"id":"2407.19723","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.19723","created_at":"2026-07-05T09:56:53Z"},{"alias_kind":"arxiv_version","alias_value":"2407.19723v2","created_at":"2026-07-05T09:56:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.19723","created_at":"2026-07-05T09:56:53Z"},{"alias_kind":"pith_short_12","alias_value":"XG3JC3TJLUVE","created_at":"2026-07-05T09:56:53Z"},{"alias_kind":"pith_short_16","alias_value":"XG3JC3TJLUVEAJJD","created_at":"2026-07-05T09:56:53Z"},{"alias_kind":"pith_short_8","alias_value":"XG3JC3TJ","created_at":"2026-07-05T09:56:53Z"}],"graph_snapshots":[{"event_id":"sha256:d591e47c3b6c700cae5fede95305d5a6e99215a33e0f3a5dafbc5b0b5795a377","target":"graph","created_at":"2026-07-05T09:56:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.19723/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The L\\'evy-Leblond equation with free potential admits a symmetry algebra that is a $ \\mathbb{Z}_2\\times\\mathbb{Z}_2 $-graded colour Lie superalgebra (see arXiv:1609.08224). We extend this result in two directions by considering a time-independent version of the L\\'evy-Leblond equation. First, we construct a $ \\mathbb{Z}_2^3 $-graded colour Lie superalgebra containing operators that leave the eigenspaces invariant and demonstrate the utility of this algebra in constructing general solutions for the free equation. Second, we find that the ladder operators for the harmonic oscillator generate a ","authors_text":"Mitchell Ryan","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-29T06:12:35Z","title":"Graded colour Lie superalgebras for solving L\\'evy-Leblond equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.19723","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":"sha256:6ad05180b1cb3c3c76d5a79827a6afd929e760aef1990ab9a509cc405ad245f3","target":"record","created_at":"2026-07-05T09:56:53Z","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":"0b6360237c4aa9fac5943442b065d817d7fa657f0b0579f4a2eae3aad41e6873","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-07-29T06:12:35Z","title_canon_sha256":"f235ebe28a7cf9f13f4b610e1594355de33d50a71bda5352eddbf858d54b4089"},"schema_version":"1.0","source":{"id":"2407.19723","kind":"arxiv","version":2}},"canonical_sha256":"b9b6916e695d2a402523e98c68c38dab61550c0b915b7cb4fd0f96d6198f060b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9b6916e695d2a402523e98c68c38dab61550c0b915b7cb4fd0f96d6198f060b","first_computed_at":"2026-07-05T09:56:53.276349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:53.276349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TJUK3ZK3QCM20ZoKw7Uq1LPB2uoP4IhMabJ3lmJD+i02XwpU7J2SyTWJgPKi2B7TlC2Nisn8C4RaWKY3C+opBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:53.276823Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.19723","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ad05180b1cb3c3c76d5a79827a6afd929e760aef1990ab9a509cc405ad245f3","sha256:d591e47c3b6c700cae5fede95305d5a6e99215a33e0f3a5dafbc5b0b5795a377"],"state_sha256":"ccb4a73996fbc1012d07f4a1241b000c792ed20726383f81a21f31c5173d648d"}