{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZLPNHVLUZ5U3G2Z32NVFZMV4O7","short_pith_number":"pith:ZLPNHVLU","canonical_record":{"source":{"id":"1204.2615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-12T04:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"af36e835ddf5851aab5fad86a856d2ae127aa49ba2536b09b67a234ee7984a7a","abstract_canon_sha256":"ca0a1cd2e1ea5e224e46303172324643eebed9fdbcaf42bb9fb1e6029cea82ca"},"schema_version":"1.0"},"canonical_sha256":"caded3d574cf69b36b3bd36a5cb2bc77fa4008f6b36e7b898d2b4f88c8f0463a","source":{"kind":"arxiv","id":"1204.2615","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2615","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2615v1","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2615","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZLPNHVLUZ5U3","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZLPNHVLUZ5U3G2Z3","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZLPNHVLU","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZLPNHVLUZ5U3G2Z32NVFZMV4O7","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-12T04:21:57Z","cross_cats_sorted":[],"title_canon_sha256":"af36e835ddf5851aab5fad86a856d2ae127aa49ba2536b09b67a234ee7984a7a","abstract_canon_sha256":"ca0a1cd2e1ea5e224e46303172324643eebed9fdbcaf42bb9fb1e6029cea82ca"},"schema_version":"1.0"},"canonical_sha256":"caded3d574cf69b36b3bd36a5cb2bc77fa4008f6b36e7b898d2b4f88c8f0463a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:53.291580Z","signature_b64":"frSOcDpPGHEv0wQ8HjnOtvZ49ngr96wQ8AHp5K9ILY/gFhsdzdIAtEsB8Opdh0+qMAw1ZM+SI5bijBgvPwbGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"caded3d574cf69b36b3bd36a5cb2bc77fa4008f6b36e7b898d2b4f88c8f0463a","last_reissued_at":"2026-05-18T01:57:53.290854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:53.290854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2615","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":"2026-05-18T01:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lxhQ40mUzjxWybF/swGQxPRg9Pu+Birs9H1Xak3KA0ZsmcZkRSa/QI+M4o8qy157UW1O98ujw/6AJsCYPY0hCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:32:07.564610Z"},"content_sha256":"fd7888fa809bd85da7c09cad8bf0ffac63fc00966c7b6ce583c71d52c5e6a949","schema_version":"1.0","event_id":"sha256:fd7888fa809bd85da7c09cad8bf0ffac63fc00966c7b6ce583c71d52c5e6a949"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZLPNHVLUZ5U3G2Z32NVFZMV4O7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric coupling of four spin-1/2 systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Berthold-Georg Englert, Jun Suzuki","submitted_at":"2012-04-12T04:21:57Z","abstract_excerpt":"We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2615","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":"2026-05-18T01:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUDKDtL5UoPbLapII9SiUN8QFOjOB6c/uzgOZZ1e7wqVSmywXux0GiFnOkTmEFEhUqB2kt9lKeszXwEICqqHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:32:07.565033Z"},"content_sha256":"c8a678b2d03b52c08a206fdc61b2822532a7b4f34027f7f6aa7d41ea9547d253","schema_version":"1.0","event_id":"sha256:c8a678b2d03b52c08a206fdc61b2822532a7b4f34027f7f6aa7d41ea9547d253"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZLPNHVLUZ5U3G2Z32NVFZMV4O7/bundle.json","state_url":"https://pith.science/pith/ZLPNHVLUZ5U3G2Z32NVFZMV4O7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZLPNHVLUZ5U3G2Z32NVFZMV4O7/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":"2026-05-31T08:32:07Z","links":{"resolver":"https://pith.science/pith/ZLPNHVLUZ5U3G2Z32NVFZMV4O7","bundle":"https://pith.science/pith/ZLPNHVLUZ5U3G2Z32NVFZMV4O7/bundle.json","state":"https://pith.science/pith/ZLPNHVLUZ5U3G2Z32NVFZMV4O7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZLPNHVLUZ5U3G2Z32NVFZMV4O7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZLPNHVLUZ5U3G2Z32NVFZMV4O7","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":"ca0a1cd2e1ea5e224e46303172324643eebed9fdbcaf42bb9fb1e6029cea82ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-12T04:21:57Z","title_canon_sha256":"af36e835ddf5851aab5fad86a856d2ae127aa49ba2536b09b67a234ee7984a7a"},"schema_version":"1.0","source":{"id":"1204.2615","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2615","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2615v1","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2615","created_at":"2026-05-18T01:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"ZLPNHVLUZ5U3","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZLPNHVLUZ5U3G2Z3","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZLPNHVLU","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:c8a678b2d03b52c08a206fdc61b2822532a7b4f34027f7f6aa7d41ea9547d253","target":"graph","created_at":"2026-05-18T01:57:53Z","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"},"paper":{"abstract_excerpt":"We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems.","authors_text":"Berthold-Georg Englert, Jun Suzuki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-12T04:21:57Z","title":"Symmetric coupling of four spin-1/2 systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2615","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:fd7888fa809bd85da7c09cad8bf0ffac63fc00966c7b6ce583c71d52c5e6a949","target":"record","created_at":"2026-05-18T01:57:53Z","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":"ca0a1cd2e1ea5e224e46303172324643eebed9fdbcaf42bb9fb1e6029cea82ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-04-12T04:21:57Z","title_canon_sha256":"af36e835ddf5851aab5fad86a856d2ae127aa49ba2536b09b67a234ee7984a7a"},"schema_version":"1.0","source":{"id":"1204.2615","kind":"arxiv","version":1}},"canonical_sha256":"caded3d574cf69b36b3bd36a5cb2bc77fa4008f6b36e7b898d2b4f88c8f0463a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caded3d574cf69b36b3bd36a5cb2bc77fa4008f6b36e7b898d2b4f88c8f0463a","first_computed_at":"2026-05-18T01:57:53.290854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:53.290854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"frSOcDpPGHEv0wQ8HjnOtvZ49ngr96wQ8AHp5K9ILY/gFhsdzdIAtEsB8Opdh0+qMAw1ZM+SI5bijBgvPwbGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:53.291580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2615","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd7888fa809bd85da7c09cad8bf0ffac63fc00966c7b6ce583c71d52c5e6a949","sha256:c8a678b2d03b52c08a206fdc61b2822532a7b4f34027f7f6aa7d41ea9547d253"],"state_sha256":"e2188030b7f3eae8723b8d16ffae2adbcc5632053849c1f69d329098563fec73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mYtZN9Ug41icAa92+3Jd92Paj9xLU2DzKhUr8ZjgxazaaAweprZz/Qgm8VzUv1pB2jwKA01tJBwraickqpJEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:32:07.568650Z","bundle_sha256":"8a064a4a5af144a522789803f802ef19641710e3d0e71965a1836a96edda1c86"}}