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We give a complete classification of all separately continuous $k$--linear operators $D\\:\\Ga _c(E_1M)\\x\\dots\\x\\Ga_c(E_kM)\\to \\Ga (EM)$ defined on sections with compact supports, which commute with Lie derivatives, i\\.e\\. which satisfy $$ \\Cal L_X(D(s_1,\\dots ,s_k))=\\sum _{i=1}^kD(s_1,\\dots ,\\Cal L_Xs_i,\\dots,s_k), $$ for all vector f"},"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":"dg-ga/9409005","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"dg-ga","submitted_at":"1994-09-28T13:16:35Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"36548e6b546dc8bd8a5e1e90687443c808f12ff56b050be87a1bca798ba05a12","abstract_canon_sha256":"6c418c65b74131f9ec156964b45b847a9e7648e44b521b05f1c7a745a3a9d99e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:48.762971Z","signature_b64":"r1Ow/h1+pWEXkHaGLQF7S8SWBoASSz97Y3UutpJ0Kc8OGF0bh/vHI0BFRwM9loxgjO20oVN1psfgzkJu77nCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aebc6a914390d41213705b75c93ef8b05f94cc35a6565e40bbe0016e4f3a1aff","last_reissued_at":"2026-05-18T01:06:48.762506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:48.762506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On multilinear operators commuting with Lie derivatives","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"dg-ga","authors_text":"Andreas Cap, Jan Slovak","submitted_at":"1994-09-28T13:16:35Z","abstract_excerpt":"Let $E_1,\\dots ,E_k$ and $E$ be natural vector bundles defined over the category $\\Cal Mf_m^+$ of smooth oriented $m$--dimensional manifolds and orientation preserving local diffeomorphisms, with $m\\geq 2$. Let $M$ be an object of $\\Cal Mf_m^+$ which is connected. We give a complete classification of all separately continuous $k$--linear operators $D\\:\\Ga _c(E_1M)\\x\\dots\\x\\Ga_c(E_kM)\\to \\Ga (EM)$ defined on sections with compact supports, which commute with Lie derivatives, i\\.e\\. which satisfy $$ \\Cal L_X(D(s_1,\\dots ,s_k))=\\sum _{i=1}^kD(s_1,\\dots ,\\Cal L_Xs_i,\\dots,s_k), $$ for all vector f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"dg-ga/9409005","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":"dg-ga/9409005","created_at":"2026-05-18T01:06:48.762580+00:00"},{"alias_kind":"arxiv_version","alias_value":"dg-ga/9409005v1","created_at":"2026-05-18T01:06:48.762580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.dg-ga/9409005","created_at":"2026-05-18T01:06:48.762580+00:00"},{"alias_kind":"pith_short_12","alias_value":"V26GVEKDSDKB","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"V26GVEKDSDKBEE3Q","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"V26GVEKD","created_at":"2026-05-18T12:25:47.102015+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/V26GVEKDSDKBEE3QLN24SPXYWB","json":"https://pith.science/pith/V26GVEKDSDKBEE3QLN24SPXYWB.json","graph_json":"https://pith.science/api/pith-number/V26GVEKDSDKBEE3QLN24SPXYWB/graph.json","events_json":"https://pith.science/api/pith-number/V26GVEKDSDKBEE3QLN24SPXYWB/events.json","paper":"https://pith.science/paper/V26GVEKD"},"agent_actions":{"view_html":"https://pith.science/pith/V26GVEKDSDKBEE3QLN24SPXYWB","download_json":"https://pith.science/pith/V26GVEKDSDKBEE3QLN24SPXYWB.json","view_paper":"https://pith.science/paper/V26GVEKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=dg-ga/9409005&json=true","fetch_graph":"https://pith.science/api/pith-number/V26GVEKDSDKBEE3QLN24SPXYWB/graph.json","fetch_events":"https://pith.science/api/pith-number/V26GVEKDSDKBEE3QLN24SPXYWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V26GVEKDSDKBEE3QLN24SPXYWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V26GVEKDSDKBEE3QLN24SPXYWB/action/storage_attestation","attest_author":"https://pith.science/pith/V26GVEKDSDKBEE3QLN24SPXYWB/action/author_attestation","sign_citation":"https://pith.science/pith/V26GVEKDSDKBEE3QLN24SPXYWB/action/citation_signature","submit_replication":"https://pith.science/pith/V26GVEKDSDKBEE3QLN24SPXYWB/action/replication_record"}},"created_at":"2026-05-18T01:06:48.762580+00:00","updated_at":"2026-05-18T01:06:48.762580+00:00"}