{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:4VC56FQVNNPHAYSJPBXRMMAPKC","short_pith_number":"pith:4VC56FQV","schema_version":"1.0","canonical_sha256":"e545df16156b5e706249786f16300f50aa31dffbe5cb37187488c405c3228fee","source":{"kind":"arxiv","id":"2504.06203","version":1},"attestation_state":"computed","paper":{"title":"Factorizing Defects from Generalized Pinning Fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math.OA"],"primary_cat":"hep-th","authors_text":"Fedor K. Popov, Yifan Wang","submitted_at":"2025-04-08T16:47:34Z","abstract_excerpt":"We introduce generalized pinning fields in conformal field theory that model a large class of critical impurities at large distance, enriching the familiar universality classes. We provide a rigorous definition of such defects as certain unbounded operators on the Hilbert space and prove that when inserted on codimension-one surfaces they factorize the spacetime into two halves. The factorization channels are further constrained by symmetries in the bulk. As a corollary, we solve such critical impurities in the 2d minimal models and establish the factorization phenomena previously observed for"},"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":"2504.06203","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-04-08T16:47:34Z","cross_cats_sorted":["cond-mat.str-el","math.OA"],"title_canon_sha256":"ec59f0f3d6b4fdf7c9b1cd9a84d1ee824fe975ea2599cddafb816ed6fc69f7b4","abstract_canon_sha256":"7c7c54db80e7976708bee2be0bbd81b03d2b306f9c02352d29379dc9a433ef94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:46:17.077564Z","signature_b64":"/kkP52EXr3ja28UeMkq3GtL9MP1s7SWvnhenYUNTF5lMVcqnypEQCA6HfWWQg+frBC83NuBeeQojoCBX9Dl1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e545df16156b5e706249786f16300f50aa31dffbe5cb37187488c405c3228fee","last_reissued_at":"2026-07-05T10:46:17.077059Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:46:17.077059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factorizing Defects from Generalized Pinning Fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math.OA"],"primary_cat":"hep-th","authors_text":"Fedor K. Popov, Yifan Wang","submitted_at":"2025-04-08T16:47:34Z","abstract_excerpt":"We introduce generalized pinning fields in conformal field theory that model a large class of critical impurities at large distance, enriching the familiar universality classes. We provide a rigorous definition of such defects as certain unbounded operators on the Hilbert space and prove that when inserted on codimension-one surfaces they factorize the spacetime into two halves. The factorization channels are further constrained by symmetries in the bulk. As a corollary, we solve such critical impurities in the 2d minimal models and establish the factorization phenomena previously observed for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06203","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/2504.06203/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":"2504.06203","created_at":"2026-07-05T10:46:17.077116+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.06203v1","created_at":"2026-07-05T10:46:17.077116+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.06203","created_at":"2026-07-05T10:46:17.077116+00:00"},{"alias_kind":"pith_short_12","alias_value":"4VC56FQVNNPH","created_at":"2026-07-05T10:46:17.077116+00:00"},{"alias_kind":"pith_short_16","alias_value":"4VC56FQVNNPHAYSJ","created_at":"2026-07-05T10:46:17.077116+00:00"},{"alias_kind":"pith_short_8","alias_value":"4VC56FQV","created_at":"2026-07-05T10:46:17.077116+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.16482","citing_title":"When Symmetries Twist: Anomaly Inflow on Monodromy Defects","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2605.22628","citing_title":"Ising surface defects can get dirty","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15187","citing_title":"Extraordinary Surface Criticalities for Interacting Fermions","ref_index":18,"is_internal_anchor":false},{"citing_arxiv_id":"2605.16482","citing_title":"When Symmetries Twist: Anomaly Inflow on Monodromy Defects","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2602.13627","citing_title":"Higher Connection in Open String Field Theory","ref_index":130,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13975","citing_title":"Protected operators in non-local defect CFTs from AdS","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2605.13961","citing_title":"A Twist on Scattering from Defect Anomalies","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2604.15187","citing_title":"Extraordinary Surface Criticalities for Interacting Fermions","ref_index":18,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC","json":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC.json","graph_json":"https://pith.science/api/pith-number/4VC56FQVNNPHAYSJPBXRMMAPKC/graph.json","events_json":"https://pith.science/api/pith-number/4VC56FQVNNPHAYSJPBXRMMAPKC/events.json","paper":"https://pith.science/paper/4VC56FQV"},"agent_actions":{"view_html":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC","download_json":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC.json","view_paper":"https://pith.science/paper/4VC56FQV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.06203&json=true","fetch_graph":"https://pith.science/api/pith-number/4VC56FQVNNPHAYSJPBXRMMAPKC/graph.json","fetch_events":"https://pith.science/api/pith-number/4VC56FQVNNPHAYSJPBXRMMAPKC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC/action/storage_attestation","attest_author":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC/action/author_attestation","sign_citation":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC/action/citation_signature","submit_replication":"https://pith.science/pith/4VC56FQVNNPHAYSJPBXRMMAPKC/action/replication_record"}},"created_at":"2026-07-05T10:46:17.077116+00:00","updated_at":"2026-07-05T10:46:17.077116+00:00"}