{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JXVQ75VPIZQ4KPKYQ2GDQTV5AR","short_pith_number":"pith:JXVQ75VP","schema_version":"1.0","canonical_sha256":"4deb0ff6af4661c53d58868c384ebd046a0bfa4393362193d82dc04c0d34810d","source":{"kind":"arxiv","id":"1503.08021","version":1},"attestation_state":"computed","paper":{"title":"Gauss-Manin Connections for Boundary Singularities and Isochore Deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Konstantinos Kourliouros","submitted_at":"2015-03-27T10:58:53Z","abstract_excerpt":"We study here the relative cohomology and the Gauss-Manin connections associated to an isolated singularity of a function on a manifold with boundary, i.e. with a fixed hyperplane section. We prove several relative analogs of classical theorems obtained mainly by E. Brieskorn and B. Malgrange, concerning the properties of the Gauss-Manin connection as well as its relations with the Picard-Lefschetz monodromy and the asymptotics of integrals of holomorphic forms along the vanishing cycles. Finally, we give an application in isochore deformation theory, i.e. the deformation theory of boundary si"},"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":"1503.08021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-27T10:58:53Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"94af3e367bd7e93bc046034abdade95fab8fecdfe186a385e6d28cebcededa15","abstract_canon_sha256":"b123028a0f322ba17df038d7d7392155203e751d13f2bdfeace2590aa0e09e1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:11.721742Z","signature_b64":"4tQpGZD9Lb6q/XLFhSKqEIBE9ekgKy8Wf0l+iuCCtrqRlSEsKQND/XhPd8JD64Lk69/Dx95dEvz82uGeoPLEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4deb0ff6af4661c53d58868c384ebd046a0bfa4393362193d82dc04c0d34810d","last_reissued_at":"2026-05-18T02:20:11.721268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:11.721268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gauss-Manin Connections for Boundary Singularities and Isochore Deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Konstantinos Kourliouros","submitted_at":"2015-03-27T10:58:53Z","abstract_excerpt":"We study here the relative cohomology and the Gauss-Manin connections associated to an isolated singularity of a function on a manifold with boundary, i.e. with a fixed hyperplane section. We prove several relative analogs of classical theorems obtained mainly by E. Brieskorn and B. Malgrange, concerning the properties of the Gauss-Manin connection as well as its relations with the Picard-Lefschetz monodromy and the asymptotics of integrals of holomorphic forms along the vanishing cycles. Finally, we give an application in isochore deformation theory, i.e. the deformation theory of boundary si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08021","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":"1503.08021","created_at":"2026-05-18T02:20:11.721350+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.08021v1","created_at":"2026-05-18T02:20:11.721350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08021","created_at":"2026-05-18T02:20:11.721350+00:00"},{"alias_kind":"pith_short_12","alias_value":"JXVQ75VPIZQ4","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JXVQ75VPIZQ4KPKY","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JXVQ75VP","created_at":"2026-05-18T12:29:27.538025+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/JXVQ75VPIZQ4KPKYQ2GDQTV5AR","json":"https://pith.science/pith/JXVQ75VPIZQ4KPKYQ2GDQTV5AR.json","graph_json":"https://pith.science/api/pith-number/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/graph.json","events_json":"https://pith.science/api/pith-number/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/events.json","paper":"https://pith.science/paper/JXVQ75VP"},"agent_actions":{"view_html":"https://pith.science/pith/JXVQ75VPIZQ4KPKYQ2GDQTV5AR","download_json":"https://pith.science/pith/JXVQ75VPIZQ4KPKYQ2GDQTV5AR.json","view_paper":"https://pith.science/paper/JXVQ75VP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.08021&json=true","fetch_graph":"https://pith.science/api/pith-number/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/graph.json","fetch_events":"https://pith.science/api/pith-number/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/action/storage_attestation","attest_author":"https://pith.science/pith/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/action/author_attestation","sign_citation":"https://pith.science/pith/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/action/citation_signature","submit_replication":"https://pith.science/pith/JXVQ75VPIZQ4KPKYQ2GDQTV5AR/action/replication_record"}},"created_at":"2026-05-18T02:20:11.721350+00:00","updated_at":"2026-05-18T02:20:11.721350+00:00"}