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Let $\\mathbb{H}=H^{n-1}_{\\operatorname{prim}}(X_G, \\mathbb{C})$ be the middle dimensional primitive cohomology of $X_G$. We explicitly construct a BV algebra $\\mathbf{B\\"},"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":"1310.6710","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-24T18:58:37Z","cross_cats_sorted":["math-ph","math.AT","math.MP"],"title_canon_sha256":"d405a94b5ffac4b4c6aa341005c669cfcd5ef0f3098efe3ff2cea2bc9855c303","abstract_canon_sha256":"d41a9ffffe0381e77fe404d6a5d9fc7ab52be3dba0db1707a5cf4ae99929362d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.494126Z","signature_b64":"/fpfT3mF89srct/XOEq+CCAdRjFCjwOihltlhMoGHATCToiC6RZLek57CBQhiJHLmMGPEFiPKwWi27f57+fsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c95ce8e9701945ad499c7436c2f3582e1a793106703a1ef7c33c29bdc41a4367","last_reissued_at":"2026-05-18T01:11:55.493789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.493789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Enhanced homotopy theory for period integrals of smooth projective hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AT","math.MP"],"primary_cat":"math.AG","authors_text":"Jae-Suk Park, Jeehoon Park","submitted_at":"2013-10-24T18:58:37Z","abstract_excerpt":"The goal of this paper is to reveal hidden structures on the singular cohomology and the Griffiths period integral of a smooth projective hypersurface in terms of BV(Batalin-Vilkovisky) algebras and homotopy Lie theory (so called, $L_\\infty$-homotopy theory).\n  Let $X_G$ be a smooth projective hypersurface in the complex projective space $\\mathbf{P}^n$ defined by a homogeneous polynomial $G(\\underline x)$ of degree $d \\geq 1$. Let $\\mathbb{H}=H^{n-1}_{\\operatorname{prim}}(X_G, \\mathbb{C})$ be the middle dimensional primitive cohomology of $X_G$. 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