{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:NXCQQ3TRGKKSDCCOPAEHCMLUJB","short_pith_number":"pith:NXCQQ3TR","schema_version":"1.0","canonical_sha256":"6dc5086e71329521884e78087131744854fe63e2789679a0928f469af26d1c80","source":{"kind":"arxiv","id":"hep-th/0412060","version":4},"attestation_state":"computed","paper":{"title":"Spin, Statistics, and Reflections, I. Rotation Invariance","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bernd Kuckert","submitted_at":"2004-12-07T13:43:46Z","abstract_excerpt":"The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry, which is referred to as \"modular P_1CT-symmetry (Bisognano, Wichmann, 1975, 1976, and Guido, Longo, [funct-an/9406005]). This symmetry is used to construct a representation of G_R by pairs of modular P_1CT-operators. The representation thus obtained satisfies Pauli's spin-statistics relation."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-th/0412060","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-12-07T13:43:46Z","cross_cats_sorted":[],"title_canon_sha256":"f530584eb73e60bc80fe55c68ebe2bf8269b6f799a50d2e22c177464cf0fb6a7","abstract_canon_sha256":"1ceea6d2e1f82f4cfd07af48b259bb5c01e47a2330c9c4f0298ff3ef8a82618f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:22.971383Z","signature_b64":"TjdGe9t2nDdxnfwsto5xXXoIDFcWE28UInVQ7CTpGVc2BSzauTx31IyC6oSRnuh1xrolI/vea4eDPRoRQsGIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dc5086e71329521884e78087131744854fe63e2789679a0928f469af26d1c80","last_reissued_at":"2026-05-18T04:35:22.970913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:22.970913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spin, Statistics, and Reflections, I. Rotation Invariance","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bernd Kuckert","submitted_at":"2004-12-07T13:43:46Z","abstract_excerpt":"The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry, which is referred to as \"modular P_1CT-symmetry (Bisognano, Wichmann, 1975, 1976, and Guido, Longo, [funct-an/9406005]). This symmetry is used to construct a representation of G_R by pairs of modular P_1CT-operators. The representation thus obtained satisfies Pauli's spin-statistics relation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0412060","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0412060","created_at":"2026-05-18T04:35:22.970997+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0412060v4","created_at":"2026-05-18T04:35:22.970997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0412060","created_at":"2026-05-18T04:35:22.970997+00:00"},{"alias_kind":"pith_short_12","alias_value":"NXCQQ3TRGKKS","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"NXCQQ3TRGKKSDCCO","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"NXCQQ3TR","created_at":"2026-05-18T12:25:52.687210+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB","json":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB.json","graph_json":"https://pith.science/api/pith-number/NXCQQ3TRGKKSDCCOPAEHCMLUJB/graph.json","events_json":"https://pith.science/api/pith-number/NXCQQ3TRGKKSDCCOPAEHCMLUJB/events.json","paper":"https://pith.science/paper/NXCQQ3TR"},"agent_actions":{"view_html":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB","download_json":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB.json","view_paper":"https://pith.science/paper/NXCQQ3TR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0412060&json=true","fetch_graph":"https://pith.science/api/pith-number/NXCQQ3TRGKKSDCCOPAEHCMLUJB/graph.json","fetch_events":"https://pith.science/api/pith-number/NXCQQ3TRGKKSDCCOPAEHCMLUJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB/action/storage_attestation","attest_author":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB/action/author_attestation","sign_citation":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB/action/citation_signature","submit_replication":"https://pith.science/pith/NXCQQ3TRGKKSDCCOPAEHCMLUJB/action/replication_record"}},"created_at":"2026-05-18T04:35:22.970997+00:00","updated_at":"2026-05-18T04:35:22.970997+00:00"}