{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:XA6MYC2DN3YCS3RPNFIC2GTI6S","short_pith_number":"pith:XA6MYC2D","schema_version":"1.0","canonical_sha256":"b83ccc0b436ef0296e2f69502d1a68f487656989cb7306481772517538461c8a","source":{"kind":"arxiv","id":"2501.19014","version":1},"attestation_state":"computed","paper":{"title":"Entanglement Entropy and Cauchy-Hadamard Renormalization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"hep-th","authors_text":"Benoit Estienne, Jiasheng Lin","submitted_at":"2025-01-31T10:26:32Z","abstract_excerpt":"This note presents a purely geometric construction of the so-called twist-field correlation functions in Conformal Field Theory (CFT), derived from conical singularities. This approach provides a purely mathematical interpretation of the seminal results in physics by Cardy and Calabrese on the entanglement entropy of quantum systems. Specifically, we begin by defining CFT partition functions on surfaces with conical singularities, using a ``Cauchy-Hadamard renormalization'' of the Polyakov anomaly integral. Next, we demonstrate that for a branched cover $f:\\Sigma_d\\to \\Sigma$ with $d$ sheets, "},"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":"2501.19014","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-01-31T10:26:32Z","cross_cats_sorted":["math-ph","math.DG","math.MP"],"title_canon_sha256":"4fd6121a993edd4d63b8f0bc095db1a575fad63227a5dca02aaf09454809ef49","abstract_canon_sha256":"11c57a3f9f65385dfcc8904483f049972cff11e8bfb40b7ccbb983146fc18caf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:55.035959Z","signature_b64":"BvRLxlwgeMf+iRDQjwA6CEFIbkotFfteFxeUDXtyd1OcfPYeGtDt7vhD0RjpJmC2bXdKNXxQy/MNlwQU5QhrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b83ccc0b436ef0296e2f69502d1a68f487656989cb7306481772517538461c8a","last_reissued_at":"2026-07-05T10:07:55.035453Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:55.035453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entanglement Entropy and Cauchy-Hadamard Renormalization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"hep-th","authors_text":"Benoit Estienne, Jiasheng Lin","submitted_at":"2025-01-31T10:26:32Z","abstract_excerpt":"This note presents a purely geometric construction of the so-called twist-field correlation functions in Conformal Field Theory (CFT), derived from conical singularities. This approach provides a purely mathematical interpretation of the seminal results in physics by Cardy and Calabrese on the entanglement entropy of quantum systems. Specifically, we begin by defining CFT partition functions on surfaces with conical singularities, using a ``Cauchy-Hadamard renormalization'' of the Polyakov anomaly integral. Next, we demonstrate that for a branched cover $f:\\Sigma_d\\to \\Sigma$ with $d$ sheets, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.19014","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/2501.19014/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":"2501.19014","created_at":"2026-07-05T10:07:55.035525+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.19014v1","created_at":"2026-07-05T10:07:55.035525+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.19014","created_at":"2026-07-05T10:07:55.035525+00:00"},{"alias_kind":"pith_short_12","alias_value":"XA6MYC2DN3YC","created_at":"2026-07-05T10:07:55.035525+00:00"},{"alias_kind":"pith_short_16","alias_value":"XA6MYC2DN3YCS3RP","created_at":"2026-07-05T10:07:55.035525+00:00"},{"alias_kind":"pith_short_8","alias_value":"XA6MYC2D","created_at":"2026-07-05T10:07:55.035525+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.21655","citing_title":"Constructive Quantum Field Theory on Curved Surfaces and Related Topics","ref_index":2002,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S","json":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S.json","graph_json":"https://pith.science/api/pith-number/XA6MYC2DN3YCS3RPNFIC2GTI6S/graph.json","events_json":"https://pith.science/api/pith-number/XA6MYC2DN3YCS3RPNFIC2GTI6S/events.json","paper":"https://pith.science/paper/XA6MYC2D"},"agent_actions":{"view_html":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S","download_json":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S.json","view_paper":"https://pith.science/paper/XA6MYC2D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.19014&json=true","fetch_graph":"https://pith.science/api/pith-number/XA6MYC2DN3YCS3RPNFIC2GTI6S/graph.json","fetch_events":"https://pith.science/api/pith-number/XA6MYC2DN3YCS3RPNFIC2GTI6S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S/action/storage_attestation","attest_author":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S/action/author_attestation","sign_citation":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S/action/citation_signature","submit_replication":"https://pith.science/pith/XA6MYC2DN3YCS3RPNFIC2GTI6S/action/replication_record"}},"created_at":"2026-07-05T10:07:55.035525+00:00","updated_at":"2026-07-05T10:07:55.035525+00:00"}