{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QFW3OBYH2IIPFTJN4MY3N4BIN2","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":"e51f1f2b25adb837c226c2bd1dd7bbe17d409db04cf8472287f7d799ec193c22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-08-06T17:49:43Z","title_canon_sha256":"74536d18ae7d7b41cdab5ea6cd9b9beecf720ceb816d09eecf252b4cfe1479a9"},"schema_version":"1.0","source":{"id":"2608.06339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06339","created_at":"2026-08-07T01:41:23Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06339v1","created_at":"2026-08-07T01:41:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06339","created_at":"2026-08-07T01:41:23Z"},{"alias_kind":"pith_short_12","alias_value":"QFW3OBYH2IIP","created_at":"2026-08-07T01:41:23Z"},{"alias_kind":"pith_short_16","alias_value":"QFW3OBYH2IIPFTJN","created_at":"2026-08-07T01:41:23Z"},{"alias_kind":"pith_short_8","alias_value":"QFW3OBYH","created_at":"2026-08-07T01:41:23Z"}],"graph_snapshots":[{"event_id":"sha256:ae9c226a4911a9d9138fad01258e920b938c4ff28b7e88801874702ffd612f91","target":"graph","created_at":"2026-08-07T01:41:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.06339/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Nuclear-spin statistical weights and selection rules in molecular spectroscopy are governed by the permutation symmetry of identical nuclei, although rigid and semi-rigid molecules typically realize only a proper subgroup of the full symmetric group. Building on the Schur-Weyl framework of Schmiedt, Jensen, and Schlemmer, we extend this approach to molecular geometries whose rovibrational motion realizes cyclic and dihedral permutation subgroups. By combining the Schur-Weyl decomposition of the $n$-spin Hilbert space with the Kra\\'skiewicz-Weyman-Adin-Roichman major-index branching rule for th","authors_text":"Eric Kubischta, Ian Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-08-06T17:49:43Z","title":"Nuclear-Spin Statistical Weights from Young Diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06339","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":"sha256:571ffff5df958d5dc21f72ced79fb1e6681207b3b0cfc6429660fe117221d078","target":"record","created_at":"2026-08-07T01:41:23Z","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":"e51f1f2b25adb837c226c2bd1dd7bbe17d409db04cf8472287f7d799ec193c22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-08-06T17:49:43Z","title_canon_sha256":"74536d18ae7d7b41cdab5ea6cd9b9beecf720ceb816d09eecf252b4cfe1479a9"},"schema_version":"1.0","source":{"id":"2608.06339","kind":"arxiv","version":1}},"canonical_sha256":"816db70707d210f2cd2de331b6f0286e9826e57c405a2e8566ea96dd4e1164d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"816db70707d210f2cd2de331b6f0286e9826e57c405a2e8566ea96dd4e1164d6","first_computed_at":"2026-08-07T01:41:23.751118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T01:41:23.751118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fyFCz1kDSgcEyk+zlm5yTqtIrlnh6fTNOhUW4WpdnHanEgLxMFf1VHedPDmC7gyJDCGZ5uaMf3MsX2Sn+DOzBQ==","signature_status":"signed_v1","signed_at":"2026-08-07T01:41:23.752685Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:571ffff5df958d5dc21f72ced79fb1e6681207b3b0cfc6429660fe117221d078","sha256:ae9c226a4911a9d9138fad01258e920b938c4ff28b7e88801874702ffd612f91"],"state_sha256":"18766dbcce0eae308feb6c522479801af3b5375af7f1c7dc1f11d3433bc426c3"}