{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GGIJW33WKB4SP7BP7RF44GTC4B","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":"eebfa87cf9b06750ffb0d3013148382ba6f9e8d298f84904ca8debe912bc04bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-09T01:55:56Z","title_canon_sha256":"d8b2ce4e937390b4900d7d2fc05554973572973d26595ea1de8f7399c285172a"},"schema_version":"1.0","source":{"id":"1706.02810","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02810","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02810v1","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02810","created_at":"2026-05-18T00:42:40Z"},{"alias_kind":"pith_short_12","alias_value":"GGIJW33WKB4S","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GGIJW33WKB4SP7BP","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GGIJW33W","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:4599dc72158ca0d7969b145ae24a5861e95c1e680049145943a660503a609137","target":"graph","created_at":"2026-05-18T00:42:40Z","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":"Starting from the Colombeau's full generalized functions, the sharp topologies and the notion of generalized points, we introduce a new kind differential calculus (for functions between totally disconnected spaces). We study generalized pointvalues, Colombeau's differential algebra, holomorphic and analytic functions. We show that the Embedding Theorem and the Open Mapping Theorem hold in this framework. Moreover, we study some applications in differential equations.","authors_text":"Antonio R. G. Garcia, Severino H. da Silva, Wagner Cortes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-09T01:55:56Z","title":"A Discontinuous Differential Calculus in the Framework Colombeau's Full Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02810","kind":"arxiv","version":1},"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:a49c4efc41e506513dc4c6b6d14e9c86994a1930aa6e90b365b36cdc23c9a0fc","target":"record","created_at":"2026-05-18T00:42:40Z","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":"eebfa87cf9b06750ffb0d3013148382ba6f9e8d298f84904ca8debe912bc04bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-09T01:55:56Z","title_canon_sha256":"d8b2ce4e937390b4900d7d2fc05554973572973d26595ea1de8f7399c285172a"},"schema_version":"1.0","source":{"id":"1706.02810","kind":"arxiv","version":1}},"canonical_sha256":"31909b6f76507927fc2ffc4bce1a62e0796aa1387e20b059ae3f33692dad1a11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31909b6f76507927fc2ffc4bce1a62e0796aa1387e20b059ae3f33692dad1a11","first_computed_at":"2026-05-18T00:42:40.848718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:40.848718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vHP9yCLKCW8OcHALF/4r/5Pb1V/YIYfH9drI+jNMD5hZX3mT+NXzpCzmcIrRd5gTGY9M3uUsHy8u9cv+8C9MBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:40.849379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02810","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a49c4efc41e506513dc4c6b6d14e9c86994a1930aa6e90b365b36cdc23c9a0fc","sha256:4599dc72158ca0d7969b145ae24a5861e95c1e680049145943a660503a609137"],"state_sha256":"fe44c1c43937361a36982e979820a739d1c1911f540c6f21d0f7a52658f2187c"}