{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BISBWQAKMMIGKHJWVYZLMVBEYT","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":"bc8516098131997258aad4e639d2bb2bbb45b9330eed717939ff33cdab45ee13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-31T14:38:31Z","title_canon_sha256":"0f80f147992b635acc0da44db45da0a8c115cf583f1c5001a5ee1b4fd5d5a495"},"schema_version":"1.0","source":{"id":"1208.6510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6510","created_at":"2026-05-18T02:16:51Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6510v2","created_at":"2026-05-18T02:16:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6510","created_at":"2026-05-18T02:16:51Z"},{"alias_kind":"pith_short_12","alias_value":"BISBWQAKMMIG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BISBWQAKMMIGKHJW","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BISBWQAK","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:745558001371d7dfaf54553214ba13cb9e1937f6310ed44bd13bac83e65c3489","target":"graph","created_at":"2026-05-18T02:16:51Z","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 develop differential calculus of $C^{r,s}$-mappings on products of locally convex spaces and prove exponential laws for such mappings. As an application, we consider differential equations in Banach spaces depending on a parameter in a locally convex space. Under suitable assumptions, the associated flows are mappings of class $C^{r,s}$.","authors_text":"Alexander Schmeding, Hamza Alzaareer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-31T14:38:31Z","title":"Differentiable mappings on products with different degrees of differentiability in the two factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6510","kind":"arxiv","version":2},"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:a6771adab93946a213f499b868a6a7cab606ee947e75d522634cb0b8cd1f04a1","target":"record","created_at":"2026-05-18T02:16:51Z","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":"bc8516098131997258aad4e639d2bb2bbb45b9330eed717939ff33cdab45ee13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-31T14:38:31Z","title_canon_sha256":"0f80f147992b635acc0da44db45da0a8c115cf583f1c5001a5ee1b4fd5d5a495"},"schema_version":"1.0","source":{"id":"1208.6510","kind":"arxiv","version":2}},"canonical_sha256":"0a241b400a6310651d36ae32b65424c4deba4f064f16f2a4a220ad2187acaff8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a241b400a6310651d36ae32b65424c4deba4f064f16f2a4a220ad2187acaff8","first_computed_at":"2026-05-18T02:16:51.516501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:51.516501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RSOZaa+/lToLg9q66U8iWJLEn9kep50Y36zRdBM1z0UkhEoLWiDK+hjKZbk2TWm+rxInnXTfJI0piQFg0N7iBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:51.517213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6771adab93946a213f499b868a6a7cab606ee947e75d522634cb0b8cd1f04a1","sha256:745558001371d7dfaf54553214ba13cb9e1937f6310ed44bd13bac83e65c3489"],"state_sha256":"8ab652758dbd4c4342ecf80dad05e989a69839872eb98165f8d6bbad21275f37"}