{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:IINX6VJAO27DDVJBQPSXBXC7ZC","short_pith_number":"pith:IINX6VJA","schema_version":"1.0","canonical_sha256":"421b7f552076be31d52183e570dc5fc891914ef28e3f4732be02aa8635ddfd14","source":{"kind":"arxiv","id":"2507.21655","version":1},"attestation_state":"computed","paper":{"title":"Constructive Quantum Field Theory on Curved Surfaces and Related Topics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.DG","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Jiasheng Lin","submitted_at":"2025-07-29T10:11:56Z","abstract_excerpt":"This is the Ph.D. thesis of the author. In this thesis, we construct the $ P(\\phi)_2 $ Quantum Field Theory (QFT) model on curved surfaces and show that it satisfies Segal's axioms (arXiv:2403.12804). An important ingredient in this construction is the use of a local regularization procedure to define the interaction as a random variable with respect to the Gaussian Free Field (GFF). We provide a counterexample demonstrating that spectral truncation regularization violates locality (arXiv:2312.15511). We then explain how Segal's formalism can be extended to the gluing of surfaces with slits, w"},"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":"2507.21655","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-07-29T10:11:56Z","cross_cats_sorted":["hep-th","math-ph","math.DG","math.MP","math.PR"],"title_canon_sha256":"0f0848c169e317eb9df72a6ae3e0d1b0435f73a24cd66f68355604cd8fd80b7d","abstract_canon_sha256":"9f76744ed85d2c2d334c4bf4929477ffccf9480c558961b2bdcc408a82950217"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:45:03.998246Z","signature_b64":"O6hwNpC1W/mov5tmKi+5QGoS4ykpe0uKEeKfuOUmUnTJwBRC425DsZzeTDsuAAPypP+3z68d/RrtLF16wZwLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"421b7f552076be31d52183e570dc5fc891914ef28e3f4732be02aa8635ddfd14","last_reissued_at":"2026-07-05T11:45:03.997832Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:45:03.997832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructive Quantum Field Theory on Curved Surfaces and Related Topics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.DG","math.MP","math.PR"],"primary_cat":"quant-ph","authors_text":"Jiasheng Lin","submitted_at":"2025-07-29T10:11:56Z","abstract_excerpt":"This is the Ph.D. thesis of the author. In this thesis, we construct the $ P(\\phi)_2 $ Quantum Field Theory (QFT) model on curved surfaces and show that it satisfies Segal's axioms (arXiv:2403.12804). An important ingredient in this construction is the use of a local regularization procedure to define the interaction as a random variable with respect to the Gaussian Free Field (GFF). We provide a counterexample demonstrating that spectral truncation regularization violates locality (arXiv:2312.15511). We then explain how Segal's formalism can be extended to the gluing of surfaces with slits, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.21655","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.21655/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.21655","created_at":"2026-07-05T11:45:03.997887+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.21655v1","created_at":"2026-07-05T11:45:03.997887+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.21655","created_at":"2026-07-05T11:45:03.997887+00:00"},{"alias_kind":"pith_short_12","alias_value":"IINX6VJAO27D","created_at":"2026-07-05T11:45:03.997887+00:00"},{"alias_kind":"pith_short_16","alias_value":"IINX6VJAO27DDVJB","created_at":"2026-07-05T11:45:03.997887+00:00"},{"alias_kind":"pith_short_8","alias_value":"IINX6VJA","created_at":"2026-07-05T11:45:03.997887+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/IINX6VJAO27DDVJBQPSXBXC7ZC","json":"https://pith.science/pith/IINX6VJAO27DDVJBQPSXBXC7ZC.json","graph_json":"https://pith.science/api/pith-number/IINX6VJAO27DDVJBQPSXBXC7ZC/graph.json","events_json":"https://pith.science/api/pith-number/IINX6VJAO27DDVJBQPSXBXC7ZC/events.json","paper":"https://pith.science/paper/IINX6VJA"},"agent_actions":{"view_html":"https://pith.science/pith/IINX6VJAO27DDVJBQPSXBXC7ZC","download_json":"https://pith.science/pith/IINX6VJAO27DDVJBQPSXBXC7ZC.json","view_paper":"https://pith.science/paper/IINX6VJA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.21655&json=true","fetch_graph":"https://pith.science/api/pith-number/IINX6VJAO27DDVJBQPSXBXC7ZC/graph.json","fetch_events":"https://pith.science/api/pith-number/IINX6VJAO27DDVJBQPSXBXC7ZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IINX6VJAO27DDVJBQPSXBXC7ZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IINX6VJAO27DDVJBQPSXBXC7ZC/action/storage_attestation","attest_author":"https://pith.science/pith/IINX6VJAO27DDVJBQPSXBXC7ZC/action/author_attestation","sign_citation":"https://pith.science/pith/IINX6VJAO27DDVJBQPSXBXC7ZC/action/citation_signature","submit_replication":"https://pith.science/pith/IINX6VJAO27DDVJBQPSXBXC7ZC/action/replication_record"}},"created_at":"2026-07-05T11:45:03.997887+00:00","updated_at":"2026-07-05T11:45:03.997887+00:00"}