{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B67MD7PYVCLAZB7RDANX6ALFCB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0c78aa1ca752ff1aeaeba1c4ea7f4cd9c99739a6847f2dc0397fea39282a1266","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-19T14:51:16Z","title_canon_sha256":"a8447ed37f3d7cee6466c6715712e4de0126ad1c6ec47747fc2201cce3ce6aa1"},"schema_version":"1.0","source":{"id":"1408.4356","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4356","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4356v3","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4356","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"B67MD7PYVCLA","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B67MD7PYVCLAZB7R","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B67MD7PY","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:8e8e4d2580e5e888d059a69d555caecaab41ec1a7318abdc7167ef1c5f0252c7","target":"graph","created_at":"2026-05-17T23:50:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We provide a sufficient condition for a linear differential operator with constant coefficients $P(D)$ to be surjective on $C^\\infty(X)$ and $\\mathscr{D}'(X)$, respectively, where $X\\subseteq\\mathbb{R}^d$ is open. Moreover, for certain differential operators this sufficient condition is also necessary and thus a characterization of surjectivity for such differential operators on $C^\\infty(X)$, resp. on $\\mathscr{D}'(X)$, is derived. Additionally, we obtain for certain surjective differential operators $P(D)$ on $C^\\infty(X)$, resp. $\\mathscr{D}'(X)$, that the spaces of zero solutions $C_P^\\inf","authors_text":"Thomas Kalmes","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-19T14:51:16Z","title":"Surjectivity of differential operators and linear topological invariants for spaces of zero solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4356","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:35ed7e8031ea67493f8e4f8cbc4040ba3469dcce440a7f221f489ba718feb016","target":"record","created_at":"2026-05-17T23:50:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0c78aa1ca752ff1aeaeba1c4ea7f4cd9c99739a6847f2dc0397fea39282a1266","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-19T14:51:16Z","title_canon_sha256":"a8447ed37f3d7cee6466c6715712e4de0126ad1c6ec47747fc2201cce3ce6aa1"},"schema_version":"1.0","source":{"id":"1408.4356","kind":"arxiv","version":3}},"canonical_sha256":"0fbec1fdf8a8960c87f1181b7f016510635081634bb66c4869aeca46082749f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fbec1fdf8a8960c87f1181b7f016510635081634bb66c4869aeca46082749f1","first_computed_at":"2026-05-17T23:50:29.057381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:29.057381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7yzKcoqhAVGTr+ZK6BO/qnIShobFHN3ZEGOKABYsmej9KtGxfRyMZ0N0payWih+nqzsaEqUggphvr1+5FHtMDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:29.057931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4356","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35ed7e8031ea67493f8e4f8cbc4040ba3469dcce440a7f221f489ba718feb016","sha256:8e8e4d2580e5e888d059a69d555caecaab41ec1a7318abdc7167ef1c5f0252c7"],"state_sha256":"3a0209e66aa4f99ac2fa540b799819b67c3d6173221d96b5b30d9535fd0bd5bc"}