{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:RZWJ6GLCSHMZR6ZATB6OW6WTEQ","short_pith_number":"pith:RZWJ6GLC","canonical_record":{"source":{"id":"math-ph/9811026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1998-11-28T00:24:52Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e82013059148136b77eb817c8bcd80f737eb08328649763fd14850153bd5c4bd","abstract_canon_sha256":"37675d192c723fa4e12213cb6959ba796f7a6044c3933cb7a1fefdad6b3e4be9"},"schema_version":"1.0"},"canonical_sha256":"8e6c9f196291d998fb20987ceb7ad32405df71e219980b961f296bc8299a81e1","source":{"kind":"arxiv","id":"math-ph/9811026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9811026","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9811026v1","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9811026","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"RZWJ6GLCSHMZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"RZWJ6GLCSHMZR6ZA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"RZWJ6GLC","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:RZWJ6GLCSHMZR6ZATB6OW6WTEQ","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/9811026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1998-11-28T00:24:52Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"e82013059148136b77eb817c8bcd80f737eb08328649763fd14850153bd5c4bd","abstract_canon_sha256":"37675d192c723fa4e12213cb6959ba796f7a6044c3933cb7a1fefdad6b3e4be9"},"schema_version":"1.0"},"canonical_sha256":"8e6c9f196291d998fb20987ceb7ad32405df71e219980b961f296bc8299a81e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:29.943702Z","signature_b64":"FZztADIE8rvtPYCWqvrBCYHeLL+o8IFOSaK8wJFaT4e4L1Rd6MHPCb/FilxmY3jyXS+Ew3/YN5aexLYENNK7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e6c9f196291d998fb20987ceb7ad32405df71e219980b961f296bc8299a81e1","last_reissued_at":"2026-05-18T01:05:29.942873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:29.942873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/9811026","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":"2026-05-18T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PF5xYY6Bv7OJK6CwqfEL1/pH2+tMGT49EJ3flzcb2C4w9cANlYvr57iXnwJM37w2sSZHSlhkdTyHqtwxIjWhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:37:00.046367Z"},"content_sha256":"543a27bae33258c36639fa76be94ff367cc43e2f1a90454e6849efd8b9f39766","schema_version":"1.0","event_id":"sha256:543a27bae33258c36639fa76be94ff367cc43e2f1a90454e6849efd8b9f39766"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:RZWJ6GLCSHMZR6ZATB6OW6WTEQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Irreducible bases and correlations of spin states for double point groups","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Shi-Hai Dong, Xi-Wen Hou, Zhong-Qi Ma","submitted_at":"1998-11-28T00:24:52Z","abstract_excerpt":"In terms of the irreducible bases of the group space of the octahedral double group {\\bf O'}, an analytic formula is obtained to combine the spin states $|j,\\mu \\rangle$ into the symmetrical adapted bases, belonging to a given row of a given irreducible representation of {\\bf O'}. This method is effective for all double point groups. However, for the subgroups of {\\bf O'}, there is another way to obtain those combinations. As an example, the correlations of spin states for the tetrahedral double group {\\bf T'} are calculated explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9811026","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":"2026-05-18T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2DptvZqnWD3BHi81T6rX78bzYF/gKQK1TGLK1po85EBODSAPkh+d7esLMUVdhyQvWo8V2yie2X+hw0dA1xEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:37:00.046717Z"},"content_sha256":"af43f4b73e4aed83f8ad28bf40feeb9bd55bfa53e724385c382017d99af069f1","schema_version":"1.0","event_id":"sha256:af43f4b73e4aed83f8ad28bf40feeb9bd55bfa53e724385c382017d99af069f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZWJ6GLCSHMZR6ZATB6OW6WTEQ/bundle.json","state_url":"https://pith.science/pith/RZWJ6GLCSHMZR6ZATB6OW6WTEQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZWJ6GLCSHMZR6ZATB6OW6WTEQ/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":"2026-06-06T18:37:00Z","links":{"resolver":"https://pith.science/pith/RZWJ6GLCSHMZR6ZATB6OW6WTEQ","bundle":"https://pith.science/pith/RZWJ6GLCSHMZR6ZATB6OW6WTEQ/bundle.json","state":"https://pith.science/pith/RZWJ6GLCSHMZR6ZATB6OW6WTEQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZWJ6GLCSHMZR6ZATB6OW6WTEQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:RZWJ6GLCSHMZR6ZATB6OW6WTEQ","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":"37675d192c723fa4e12213cb6959ba796f7a6044c3933cb7a1fefdad6b3e4be9","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1998-11-28T00:24:52Z","title_canon_sha256":"e82013059148136b77eb817c8bcd80f737eb08328649763fd14850153bd5c4bd"},"schema_version":"1.0","source":{"id":"math-ph/9811026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9811026","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9811026v1","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9811026","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"RZWJ6GLCSHMZ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"RZWJ6GLCSHMZR6ZA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"RZWJ6GLC","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:af43f4b73e4aed83f8ad28bf40feeb9bd55bfa53e724385c382017d99af069f1","target":"graph","created_at":"2026-05-18T01:05:29Z","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 terms of the irreducible bases of the group space of the octahedral double group {\\bf O'}, an analytic formula is obtained to combine the spin states $|j,\\mu \\rangle$ into the symmetrical adapted bases, belonging to a given row of a given irreducible representation of {\\bf O'}. This method is effective for all double point groups. However, for the subgroups of {\\bf O'}, there is another way to obtain those combinations. As an example, the correlations of spin states for the tetrahedral double group {\\bf T'} are calculated explicitly.","authors_text":"Shi-Hai Dong, Xi-Wen Hou, Zhong-Qi Ma","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"1998-11-28T00:24:52Z","title":"Irreducible bases and correlations of spin states for double point groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9811026","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":"sha256:543a27bae33258c36639fa76be94ff367cc43e2f1a90454e6849efd8b9f39766","target":"record","created_at":"2026-05-18T01:05:29Z","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":"37675d192c723fa4e12213cb6959ba796f7a6044c3933cb7a1fefdad6b3e4be9","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"1998-11-28T00:24:52Z","title_canon_sha256":"e82013059148136b77eb817c8bcd80f737eb08328649763fd14850153bd5c4bd"},"schema_version":"1.0","source":{"id":"math-ph/9811026","kind":"arxiv","version":1}},"canonical_sha256":"8e6c9f196291d998fb20987ceb7ad32405df71e219980b961f296bc8299a81e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e6c9f196291d998fb20987ceb7ad32405df71e219980b961f296bc8299a81e1","first_computed_at":"2026-05-18T01:05:29.942873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:29.942873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FZztADIE8rvtPYCWqvrBCYHeLL+o8IFOSaK8wJFaT4e4L1Rd6MHPCb/FilxmY3jyXS+Ew3/YN5aexLYENNK7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:29.943702Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/9811026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:543a27bae33258c36639fa76be94ff367cc43e2f1a90454e6849efd8b9f39766","sha256:af43f4b73e4aed83f8ad28bf40feeb9bd55bfa53e724385c382017d99af069f1"],"state_sha256":"66085d5b35b5d4a2d14a54116c3063bb2c24578072e1b256d3c7af8b8bbb717c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RYg38uytOw0VIHdt5d0gWAvG5cusnb3Fs36iaS6FrD7kA4F2XLSgQqyL9VP7bAWotRP6nJforMxZiji3WNpUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:37:00.048742Z","bundle_sha256":"28764036793fc17ee39dba9227f6d114c54f7670a93433135693e54866e7d73b"}}