{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5S77HODDMEMQNFEL6EOI2GIPSS","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":"095c7d7e01e28eb1e0545691a25216f3f906b2d52315e2a2ff7be263c5e07cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-15T14:50:32Z","title_canon_sha256":"c85b0b36c3cf6e81ecd8a59216e390f103f2242076ac21bd344e14b342b73735"},"schema_version":"1.0","source":{"id":"1004.2643","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2643","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2643v3","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2643","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"5S77HODDMEMQ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5S77HODDMEMQNFEL","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5S77HODD","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:55b1cd3adc11f1a605988afe268509a9276cd1ef5674d8a543484a1e36cb64f9","target":"graph","created_at":"2026-05-18T01:31:12Z","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":"The main goal of this paper is to characterize arbitrary nonlinear (non-multilinear) mappings $f:X_{1}\\times...\\times X_{n}\\rightarrow Y$ between Banach spaces that satisfy a quite natural Pietsch Domination-type theorem around a given point $(a_{1},...,a_{n})\\in$ $X_{1}\\times...\\times X_{n}$. As a consequence of our approach a notion of weighted summability arises naturally, which may be an interesting topic for further investigation.","authors_text":"Daniel Pellegrino, Joedson Santos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-15T14:50:32Z","title":"On summability of nonlinear mappings: a new approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2643","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:e76262e1ac9d9355c892ec19ad6b113b74bfff96170aea48dfc4c8c7345e3637","target":"record","created_at":"2026-05-18T01:31:12Z","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":"095c7d7e01e28eb1e0545691a25216f3f906b2d52315e2a2ff7be263c5e07cb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-04-15T14:50:32Z","title_canon_sha256":"c85b0b36c3cf6e81ecd8a59216e390f103f2242076ac21bd344e14b342b73735"},"schema_version":"1.0","source":{"id":"1004.2643","kind":"arxiv","version":3}},"canonical_sha256":"ecbff3b863611906948bf11c8d190f94835fe9eb7eaa1f6b74ddef7fc09fdd16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecbff3b863611906948bf11c8d190f94835fe9eb7eaa1f6b74ddef7fc09fdd16","first_computed_at":"2026-05-18T01:31:12.204823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:12.204823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EFnMJbDGnDtlo2LNDe7NzXt19bnT4+KD41ILiLT/XWVUMXiys5B1FytRe2okPdE/uXPlt75uaG0ohUJaMVwYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:12.205343Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2643","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e76262e1ac9d9355c892ec19ad6b113b74bfff96170aea48dfc4c8c7345e3637","sha256:55b1cd3adc11f1a605988afe268509a9276cd1ef5674d8a543484a1e36cb64f9"],"state_sha256":"adec5f927b24f0c9c5cb68eaf8de5949f95cdcd01881b644a8f12fa8886f2862"}