{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JEBTW7B42ACLNBL5M6RMWSH6TN","short_pith_number":"pith:JEBTW7B4","schema_version":"1.0","canonical_sha256":"49033b7c3cd004b6857d67a2cb48fe9b69bf920b4849877e1958049538083ad8","source":{"kind":"arxiv","id":"1604.06905","version":4},"attestation_state":"computed","paper":{"title":"A functorial extension of the Magnus representation to the category of three-dimensional cobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gwenael Massuyeau, Juan Serrano de Rodrigo, Vincent Florens","submitted_at":"2016-04-23T13:42:23Z","abstract_excerpt":"Let $R$ be an integral domain and $G$ be a subgroup of its group of units. We consider the category $\\mathbf{\\mathsf{Cob}}_G$ of 3-dimensional cobordisms between oriented surfaces with connected boundary, equipped with a representation of their fundamental group in $G$. Under some mild conditions on $R$, we construct a monoidal functor from $\\mathbf{\\mathsf{Cob}}_G$ to the category $\\mathbf{\\mathsf{pLagr}}_R$ consisting of \"pointed Lagrangian relations\" between skew-Hermitian $R$-modules. We call it the \"Magnus functor\" since it contains the Magnus representation of mapping class groups as a s"},"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":"1604.06905","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-04-23T13:42:23Z","cross_cats_sorted":[],"title_canon_sha256":"4f4e7c3a1ac14a15acb4f6167575085bf4ef5f5d98975f620e09368d43164809","abstract_canon_sha256":"495def3cf3a27fe10569c369b66e6a909ca492bfef7aa4c65da1a4215482428b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:31.698670Z","signature_b64":"3Np2tRzQ6qVROcHTmqyF412Cl3Sr/Vp/sxJ47ZozeCEnQOiSiZ2Kd5xPzUoWQ5JWgCRRnpAYi9Y/8XTKd2bjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49033b7c3cd004b6857d67a2cb48fe9b69bf920b4849877e1958049538083ad8","last_reissued_at":"2026-05-18T00:27:31.697891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:31.697891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A functorial extension of the Magnus representation to the category of three-dimensional cobordisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gwenael Massuyeau, Juan Serrano de Rodrigo, Vincent Florens","submitted_at":"2016-04-23T13:42:23Z","abstract_excerpt":"Let $R$ be an integral domain and $G$ be a subgroup of its group of units. We consider the category $\\mathbf{\\mathsf{Cob}}_G$ of 3-dimensional cobordisms between oriented surfaces with connected boundary, equipped with a representation of their fundamental group in $G$. Under some mild conditions on $R$, we construct a monoidal functor from $\\mathbf{\\mathsf{Cob}}_G$ to the category $\\mathbf{\\mathsf{pLagr}}_R$ consisting of \"pointed Lagrangian relations\" between skew-Hermitian $R$-modules. We call it the \"Magnus functor\" since it contains the Magnus representation of mapping class groups as a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06905","kind":"arxiv","version":4},"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":"1604.06905","created_at":"2026-05-18T00:27:31.698023+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.06905v4","created_at":"2026-05-18T00:27:31.698023+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06905","created_at":"2026-05-18T00:27:31.698023+00:00"},{"alias_kind":"pith_short_12","alias_value":"JEBTW7B42ACL","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JEBTW7B42ACLNBL5","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JEBTW7B4","created_at":"2026-05-18T12:30:25.849896+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/JEBTW7B42ACLNBL5M6RMWSH6TN","json":"https://pith.science/pith/JEBTW7B42ACLNBL5M6RMWSH6TN.json","graph_json":"https://pith.science/api/pith-number/JEBTW7B42ACLNBL5M6RMWSH6TN/graph.json","events_json":"https://pith.science/api/pith-number/JEBTW7B42ACLNBL5M6RMWSH6TN/events.json","paper":"https://pith.science/paper/JEBTW7B4"},"agent_actions":{"view_html":"https://pith.science/pith/JEBTW7B42ACLNBL5M6RMWSH6TN","download_json":"https://pith.science/pith/JEBTW7B42ACLNBL5M6RMWSH6TN.json","view_paper":"https://pith.science/paper/JEBTW7B4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.06905&json=true","fetch_graph":"https://pith.science/api/pith-number/JEBTW7B42ACLNBL5M6RMWSH6TN/graph.json","fetch_events":"https://pith.science/api/pith-number/JEBTW7B42ACLNBL5M6RMWSH6TN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JEBTW7B42ACLNBL5M6RMWSH6TN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JEBTW7B42ACLNBL5M6RMWSH6TN/action/storage_attestation","attest_author":"https://pith.science/pith/JEBTW7B42ACLNBL5M6RMWSH6TN/action/author_attestation","sign_citation":"https://pith.science/pith/JEBTW7B42ACLNBL5M6RMWSH6TN/action/citation_signature","submit_replication":"https://pith.science/pith/JEBTW7B42ACLNBL5M6RMWSH6TN/action/replication_record"}},"created_at":"2026-05-18T00:27:31.698023+00:00","updated_at":"2026-05-18T00:27:31.698023+00:00"}