{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HYVALAZ5GXPFQWTCB4E4XHU2YE","short_pith_number":"pith:HYVALAZ5","canonical_record":{"source":{"id":"1208.2744","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T01:20:49Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b1746c73891a0f044f8e66a0ea2caa0e5d4011c19351b94bd7f150496495eb29","abstract_canon_sha256":"04ec1b143c4f8025e01c8d8ad539f729dd80842ce0137a6603aa95bc4e262894"},"schema_version":"1.0"},"canonical_sha256":"3e2a05833d35de585a620f09cb9e9ac128e5d7da6361c1595bd13f7fac52d4b2","source":{"kind":"arxiv","id":"1208.2744","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2744","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2744v1","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2744","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"HYVALAZ5GXPF","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HYVALAZ5GXPFQWTC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HYVALAZ5","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HYVALAZ5GXPFQWTCB4E4XHU2YE","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2744","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T01:20:49Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"b1746c73891a0f044f8e66a0ea2caa0e5d4011c19351b94bd7f150496495eb29","abstract_canon_sha256":"04ec1b143c4f8025e01c8d8ad539f729dd80842ce0137a6603aa95bc4e262894"},"schema_version":"1.0"},"canonical_sha256":"3e2a05833d35de585a620f09cb9e9ac128e5d7da6361c1595bd13f7fac52d4b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:47.515448Z","signature_b64":"kk+8B26XnPK9wtFMXAWU/VsjUSwyg0ERExAnSAlYFunDM9hXh2zJ37Ky4Gef+D2ADqVBsTmY/v/C1jXfksB8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e2a05833d35de585a620f09cb9e9ac128e5d7da6361c1595bd13f7fac52d4b2","last_reissued_at":"2026-05-18T03:48:47.514737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:47.514737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2744","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":"2026-05-18T03:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D7YCuPIgw+Y6qP4yhTyfpgC2FWQDb1Ts9ViQvsOUGaHekDM17u03DbDVIF6Bo5bFF+xipf9fr2RjgE9xH6VuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T14:12:46.742569Z"},"content_sha256":"866b2de556ff4586828fdf5cf91b3c21d4c47032cc50d44d23213b97782f25ef","schema_version":"1.0","event_id":"sha256:866b2de556ff4586828fdf5cf91b3c21d4c47032cc50d44d23213b97782f25ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HYVALAZ5GXPFQWTCB4E4XHU2YE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Cornerstone Of Spin Statistics Connection: The SU(2)$\\times$ C $\\times$ T Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Biao Lian","submitted_at":"2012-08-14T01:20:49Z","abstract_excerpt":"We investigate the intrinsic reason for spin statistics connection. It is found that if a free field theory is rotationally (SU(2)) invariant, and has time reversal ($T$) and charge conjugation ($C$) symmetries, it obeys the spin statistics connection, except for a special case. Shr{\\\"o}dinger equation belongs to this special case, and does not obey spin statistics connection. Further we show that if the energy spectrum of a particle $E(p)$ takes the form of a square root, namely contains branch points in the complex $p$ plane, the particle cannot belong to this special case, and must obey the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2744","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":"2026-05-18T03:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpQ1UGFGUFqvGn2qcWo5sSObkWFwZd1K2PuhR6Pb4o3QJrMGV77V9HXeyBYYKHoihM0iYjLnrM5k5go5HhnPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T14:12:46.742924Z"},"content_sha256":"e845b3aa72739f52eb4384ebd181398d4e62599921d3fcd5c7a06af773baa34d","schema_version":"1.0","event_id":"sha256:e845b3aa72739f52eb4384ebd181398d4e62599921d3fcd5c7a06af773baa34d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYVALAZ5GXPFQWTCB4E4XHU2YE/bundle.json","state_url":"https://pith.science/pith/HYVALAZ5GXPFQWTCB4E4XHU2YE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYVALAZ5GXPFQWTCB4E4XHU2YE/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":"2026-07-02T14:12:46Z","links":{"resolver":"https://pith.science/pith/HYVALAZ5GXPFQWTCB4E4XHU2YE","bundle":"https://pith.science/pith/HYVALAZ5GXPFQWTCB4E4XHU2YE/bundle.json","state":"https://pith.science/pith/HYVALAZ5GXPFQWTCB4E4XHU2YE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYVALAZ5GXPFQWTCB4E4XHU2YE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HYVALAZ5GXPFQWTCB4E4XHU2YE","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":"04ec1b143c4f8025e01c8d8ad539f729dd80842ce0137a6603aa95bc4e262894","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T01:20:49Z","title_canon_sha256":"b1746c73891a0f044f8e66a0ea2caa0e5d4011c19351b94bd7f150496495eb29"},"schema_version":"1.0","source":{"id":"1208.2744","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2744","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2744v1","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2744","created_at":"2026-05-18T03:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"HYVALAZ5GXPF","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HYVALAZ5GXPFQWTC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HYVALAZ5","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:e845b3aa72739f52eb4384ebd181398d4e62599921d3fcd5c7a06af773baa34d","target":"graph","created_at":"2026-05-18T03:48:47Z","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 investigate the intrinsic reason for spin statistics connection. It is found that if a free field theory is rotationally (SU(2)) invariant, and has time reversal ($T$) and charge conjugation ($C$) symmetries, it obeys the spin statistics connection, except for a special case. Shr{\\\"o}dinger equation belongs to this special case, and does not obey spin statistics connection. Further we show that if the energy spectrum of a particle $E(p)$ takes the form of a square root, namely contains branch points in the complex $p$ plane, the particle cannot belong to this special case, and must obey the","authors_text":"Biao Lian","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T01:20:49Z","title":"The Cornerstone Of Spin Statistics Connection: The SU(2)$\\times$ C $\\times$ T Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2744","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":"sha256:866b2de556ff4586828fdf5cf91b3c21d4c47032cc50d44d23213b97782f25ef","target":"record","created_at":"2026-05-18T03:48:47Z","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":"04ec1b143c4f8025e01c8d8ad539f729dd80842ce0137a6603aa95bc4e262894","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-14T01:20:49Z","title_canon_sha256":"b1746c73891a0f044f8e66a0ea2caa0e5d4011c19351b94bd7f150496495eb29"},"schema_version":"1.0","source":{"id":"1208.2744","kind":"arxiv","version":1}},"canonical_sha256":"3e2a05833d35de585a620f09cb9e9ac128e5d7da6361c1595bd13f7fac52d4b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e2a05833d35de585a620f09cb9e9ac128e5d7da6361c1595bd13f7fac52d4b2","first_computed_at":"2026-05-18T03:48:47.514737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:47.514737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kk+8B26XnPK9wtFMXAWU/VsjUSwyg0ERExAnSAlYFunDM9hXh2zJ37Ky4Gef+D2ADqVBsTmY/v/C1jXfksB8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:47.515448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2744","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:866b2de556ff4586828fdf5cf91b3c21d4c47032cc50d44d23213b97782f25ef","sha256:e845b3aa72739f52eb4384ebd181398d4e62599921d3fcd5c7a06af773baa34d"],"state_sha256":"9c5339426c12a26f7a9dacdd58e19b77d6d29a332edfd4557718bee5956a7247"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IB6t+rP42xYSntLVa8e17/QfVSHxTIEglzJNy4vC2qYQbKgvH6qivjsP9Yi2nvdc0VuZ48MAphKdhEjY582cCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T14:12:46.744872Z","bundle_sha256":"56503f6a8a12ee3ebaa2896f6a23f22a655485e6e46288c5fd70bbea6039cbe6"}}