{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZTJHSJPTCIFX5V5IHDHP6OK6QY","short_pith_number":"pith:ZTJHSJPT","schema_version":"1.0","canonical_sha256":"ccd27925f3120b7ed7a838ceff395e863a77fa02db64066a1f235f19bd1fb439","source":{"kind":"arxiv","id":"1806.09873","version":1},"attestation_state":"computed","paper":{"title":"Temperature-reflection II: Modular Invariance and T-reflection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"David A. McGady","submitted_at":"2018-06-26T09:41:45Z","abstract_excerpt":"In this paper, we present robust evidence that general finite temperature quantum field theory (QFT) path integrals are invariant under reflecting temperatures to negative values (T-reflection), up to a possible anomaly phase. Our main focus is on two-dimensional conformal field theories (2d CFTs) on the two-torus. Modular invariance for 2d CFT path integrals follows from demanding invariance under redundant encodings of the two-torus shape in the path integral. We emphasize that identical logic implies 2d CFTs are invariant under T-reflection, up to phases. We compute T-reflection anomaly pha"},"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":"1806.09873","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-26T09:41:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e397300def33e550a95663ea4b345c3b2c046fe560c97e7122f2f9072bb2c3e0","abstract_canon_sha256":"8391d6bd901b7e85aebbadb5bcf40c05f400365a5a62336154f1eb5f0bc49e33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:23.027693Z","signature_b64":"0rzfynfBeHma+tv+o1JA4dadJP06N0+xGL4midYhZrufynr4tQqhwR7021YDGsViSq9RMmEA5MPTc8x0j0B2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccd27925f3120b7ed7a838ceff395e863a77fa02db64066a1f235f19bd1fb439","last_reissued_at":"2026-05-18T00:12:23.027072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:23.027072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Temperature-reflection II: Modular Invariance and T-reflection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"David A. McGady","submitted_at":"2018-06-26T09:41:45Z","abstract_excerpt":"In this paper, we present robust evidence that general finite temperature quantum field theory (QFT) path integrals are invariant under reflecting temperatures to negative values (T-reflection), up to a possible anomaly phase. Our main focus is on two-dimensional conformal field theories (2d CFTs) on the two-torus. Modular invariance for 2d CFT path integrals follows from demanding invariance under redundant encodings of the two-torus shape in the path integral. We emphasize that identical logic implies 2d CFTs are invariant under T-reflection, up to phases. We compute T-reflection anomaly pha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09873","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.09873","created_at":"2026-05-18T00:12:23.027187+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.09873v1","created_at":"2026-05-18T00:12:23.027187+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09873","created_at":"2026-05-18T00:12:23.027187+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZTJHSJPTCIFX","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZTJHSJPTCIFX5V5I","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZTJHSJPT","created_at":"2026-05-18T12:33:07.085635+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/ZTJHSJPTCIFX5V5IHDHP6OK6QY","json":"https://pith.science/pith/ZTJHSJPTCIFX5V5IHDHP6OK6QY.json","graph_json":"https://pith.science/api/pith-number/ZTJHSJPTCIFX5V5IHDHP6OK6QY/graph.json","events_json":"https://pith.science/api/pith-number/ZTJHSJPTCIFX5V5IHDHP6OK6QY/events.json","paper":"https://pith.science/paper/ZTJHSJPT"},"agent_actions":{"view_html":"https://pith.science/pith/ZTJHSJPTCIFX5V5IHDHP6OK6QY","download_json":"https://pith.science/pith/ZTJHSJPTCIFX5V5IHDHP6OK6QY.json","view_paper":"https://pith.science/paper/ZTJHSJPT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.09873&json=true","fetch_graph":"https://pith.science/api/pith-number/ZTJHSJPTCIFX5V5IHDHP6OK6QY/graph.json","fetch_events":"https://pith.science/api/pith-number/ZTJHSJPTCIFX5V5IHDHP6OK6QY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZTJHSJPTCIFX5V5IHDHP6OK6QY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZTJHSJPTCIFX5V5IHDHP6OK6QY/action/storage_attestation","attest_author":"https://pith.science/pith/ZTJHSJPTCIFX5V5IHDHP6OK6QY/action/author_attestation","sign_citation":"https://pith.science/pith/ZTJHSJPTCIFX5V5IHDHP6OK6QY/action/citation_signature","submit_replication":"https://pith.science/pith/ZTJHSJPTCIFX5V5IHDHP6OK6QY/action/replication_record"}},"created_at":"2026-05-18T00:12:23.027187+00:00","updated_at":"2026-05-18T00:12:23.027187+00:00"}