{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:3L5X2QWGKBAB6V4VOBUJO4FEWV","short_pith_number":"pith:3L5X2QWG","schema_version":"1.0","canonical_sha256":"dafb7d42c650401f579570689770a4b55c808920819340efa3d9e1b91a1c77da","source":{"kind":"arxiv","id":"1905.13541","version":1},"attestation_state":"computed","paper":{"title":"The general linear equation on open connected sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Jens Schwaiger, Paolo Leonetti","submitted_at":"2019-05-31T12:12:49Z","abstract_excerpt":"Fix non-zero reals $\\alpha_1,\\ldots,\\alpha_n$ with $n\\ge 2$ and let $K$ be a non-empty open connected set in a topological vector space such that $\\sum_{i\\le n}\\alpha_iK\\subseteq K$ (which holds, in particular, if $K$ is an open convex cone and $\\alpha_1,\\ldots,\\alpha_n>0$). Let also $Y$ be a vector space over $\\mathbb{F}:=\\mathbb{Q}(\\alpha_1,\\ldots,\\alpha_n)$. We show, among others, that a function $f: K\\to Y$ satisfies the general linear equation $$ \\textstyle \\forall x_1,\\ldots,x_n \\in K,\\,\\,\\,\\,\\, f\\left(\\sum_{i\\le n}\\alpha_i x_i\\right)=\\sum_{i\\le n}\\alpha_i f(x_i) $$ if and only if there "},"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":"1905.13541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-05-31T12:12:49Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"5d07361e3fe90c67edae63b2ca25433f05249d18e2fced72b81e418ab85bdb91","abstract_canon_sha256":"3c5ebd3c29730fa4dc84841b5e3f18cf1fab8b2bd822e87d479f6dc4a71cd636"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:34.629202Z","signature_b64":"1Giqabu4f6QZ//BfybK5QYEtDFNAqzL1SG1TPkObwEEvJngkiG21Qz/+nmVmwCqBNrZysihc6E00Ic0hqcCzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dafb7d42c650401f579570689770a4b55c808920819340efa3d9e1b91a1c77da","last_reissued_at":"2026-05-17T23:44:34.628608Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:34.628608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The general linear equation on open connected sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Jens Schwaiger, Paolo Leonetti","submitted_at":"2019-05-31T12:12:49Z","abstract_excerpt":"Fix non-zero reals $\\alpha_1,\\ldots,\\alpha_n$ with $n\\ge 2$ and let $K$ be a non-empty open connected set in a topological vector space such that $\\sum_{i\\le n}\\alpha_iK\\subseteq K$ (which holds, in particular, if $K$ is an open convex cone and $\\alpha_1,\\ldots,\\alpha_n>0$). Let also $Y$ be a vector space over $\\mathbb{F}:=\\mathbb{Q}(\\alpha_1,\\ldots,\\alpha_n)$. We show, among others, that a function $f: K\\to Y$ satisfies the general linear equation $$ \\textstyle \\forall x_1,\\ldots,x_n \\in K,\\,\\,\\,\\,\\, f\\left(\\sum_{i\\le n}\\alpha_i x_i\\right)=\\sum_{i\\le n}\\alpha_i f(x_i) $$ if and only if there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13541","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":"1905.13541","created_at":"2026-05-17T23:44:34.628705+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.13541v1","created_at":"2026-05-17T23:44:34.628705+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.13541","created_at":"2026-05-17T23:44:34.628705+00:00"},{"alias_kind":"pith_short_12","alias_value":"3L5X2QWGKBAB","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"3L5X2QWGKBAB6V4V","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"3L5X2QWG","created_at":"2026-05-18T12:33:07.085635+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/3L5X2QWGKBAB6V4VOBUJO4FEWV","json":"https://pith.science/pith/3L5X2QWGKBAB6V4VOBUJO4FEWV.json","graph_json":"https://pith.science/api/pith-number/3L5X2QWGKBAB6V4VOBUJO4FEWV/graph.json","events_json":"https://pith.science/api/pith-number/3L5X2QWGKBAB6V4VOBUJO4FEWV/events.json","paper":"https://pith.science/paper/3L5X2QWG"},"agent_actions":{"view_html":"https://pith.science/pith/3L5X2QWGKBAB6V4VOBUJO4FEWV","download_json":"https://pith.science/pith/3L5X2QWGKBAB6V4VOBUJO4FEWV.json","view_paper":"https://pith.science/paper/3L5X2QWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.13541&json=true","fetch_graph":"https://pith.science/api/pith-number/3L5X2QWGKBAB6V4VOBUJO4FEWV/graph.json","fetch_events":"https://pith.science/api/pith-number/3L5X2QWGKBAB6V4VOBUJO4FEWV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3L5X2QWGKBAB6V4VOBUJO4FEWV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3L5X2QWGKBAB6V4VOBUJO4FEWV/action/storage_attestation","attest_author":"https://pith.science/pith/3L5X2QWGKBAB6V4VOBUJO4FEWV/action/author_attestation","sign_citation":"https://pith.science/pith/3L5X2QWGKBAB6V4VOBUJO4FEWV/action/citation_signature","submit_replication":"https://pith.science/pith/3L5X2QWGKBAB6V4VOBUJO4FEWV/action/replication_record"}},"created_at":"2026-05-17T23:44:34.628705+00:00","updated_at":"2026-05-17T23:44:34.628705+00:00"}