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Then the pullback $f^*\\mathsf m$ of $\\mathsf m$ under $f$ is a metric of curvature $1$ with conical singularities of conical angles $4\\pi$ at the critical points of $f$. We study the $\\zeta$-regularized determinant of the Laplace operator on $X$ corresponding to the metric $f^*\\mathsf m$ as a functional on the moduli space of the pairs $("},"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":"1612.08660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-27T15:40:17Z","cross_cats_sorted":["math.DG","math.SP"],"title_canon_sha256":"f0be653a4f72db9ddba3780d5e56f170bfadbb2808f9d512f9a14463da571171","abstract_canon_sha256":"3c9b04278b623ec8f4cb5bedc02ce1dcb9a2482eb09d03d53cd08bb76420523a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:42.053167Z","signature_b64":"zyfoID88Lm/wJmVlKVLn85ugPduCfWjO/bjXUEXvk6SZZWA07BU4Vv0WvwWQRk2QFJ8N/I2NJ4++YkQn4DDeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61631e2234fd2672bb46b1e585e0773543e41392cca30252a0fea38db3da91dd","last_reissued_at":"2026-05-18T00:34:42.052512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:42.052512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metrics of constant positive curvature with conical singularities, Hurwitz spaces, and ${\\rm det}\\, \\Delta$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.AP","authors_text":"Alexey Kokotov, Victor Kalvin","submitted_at":"2016-12-27T15:40:17Z","abstract_excerpt":"Let $f: X\\to {\\Bbb C}P^1$ be a meromorphic function of degree $N$ with simple poles and simple critical points on a compact Riemann surface $X$ of genus $g$ and let $\\mathsf m$ be the standard round metric of curvature $1$ on the Riemann sphere ${\\Bbb C}P^1$. Then the pullback $f^*\\mathsf m$ of $\\mathsf m$ under $f$ is a metric of curvature $1$ with conical singularities of conical angles $4\\pi$ at the critical points of $f$. We study the $\\zeta$-regularized determinant of the Laplace operator on $X$ corresponding to the metric $f^*\\mathsf m$ as a functional on the moduli space of the pairs $("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08660","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":"1612.08660","created_at":"2026-05-18T00:34:42.052625+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08660v1","created_at":"2026-05-18T00:34:42.052625+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08660","created_at":"2026-05-18T00:34:42.052625+00:00"},{"alias_kind":"pith_short_12","alias_value":"MFRR4IRU7UTH","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MFRR4IRU7UTHFO2G","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MFRR4IRU","created_at":"2026-05-18T12:30:32.724797+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/MFRR4IRU7UTHFO2GWHSYLYDXGV","json":"https://pith.science/pith/MFRR4IRU7UTHFO2GWHSYLYDXGV.json","graph_json":"https://pith.science/api/pith-number/MFRR4IRU7UTHFO2GWHSYLYDXGV/graph.json","events_json":"https://pith.science/api/pith-number/MFRR4IRU7UTHFO2GWHSYLYDXGV/events.json","paper":"https://pith.science/paper/MFRR4IRU"},"agent_actions":{"view_html":"https://pith.science/pith/MFRR4IRU7UTHFO2GWHSYLYDXGV","download_json":"https://pith.science/pith/MFRR4IRU7UTHFO2GWHSYLYDXGV.json","view_paper":"https://pith.science/paper/MFRR4IRU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08660&json=true","fetch_graph":"https://pith.science/api/pith-number/MFRR4IRU7UTHFO2GWHSYLYDXGV/graph.json","fetch_events":"https://pith.science/api/pith-number/MFRR4IRU7UTHFO2GWHSYLYDXGV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MFRR4IRU7UTHFO2GWHSYLYDXGV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MFRR4IRU7UTHFO2GWHSYLYDXGV/action/storage_attestation","attest_author":"https://pith.science/pith/MFRR4IRU7UTHFO2GWHSYLYDXGV/action/author_attestation","sign_citation":"https://pith.science/pith/MFRR4IRU7UTHFO2GWHSYLYDXGV/action/citation_signature","submit_replication":"https://pith.science/pith/MFRR4IRU7UTHFO2GWHSYLYDXGV/action/replication_record"}},"created_at":"2026-05-18T00:34:42.052625+00:00","updated_at":"2026-05-18T00:34:42.052625+00:00"}