{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M3BPA2W7KP6XDU2U3WWPUYVK55","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":"29c21f4cb4841fb22cad486a9f3f0086c6357b25a0faa9e5aa80a48d28652812","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-28T13:32:28Z","title_canon_sha256":"02c3e5b34e5d6598a78cf4732c9ee2008b0421d2735e062983bc817302a7e7fe"},"schema_version":"1.0","source":{"id":"1411.7862","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.7862","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.7862v1","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7862","created_at":"2026-05-18T02:32:37Z"},{"alias_kind":"pith_short_12","alias_value":"M3BPA2W7KP6X","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M3BPA2W7KP6XDU2U","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M3BPA2W7","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:1cc9c57013cb1aa559c080534e7ef35f53caaa9be014ba970d7991e7eee195e4","target":"graph","created_at":"2026-05-18T02:32:37Z","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 study elliptic equations on bounded domain of Euclidean spaces in the variable H\\\"{o}lder spaces. Interior a priori Schauder estimates are given as well as global ones. Moreover, the existence and the uniqueness of solutions to the Dirichlet boundary value problem is proved.","authors_text":"Piotr Micha{\\l} Bies, Przemys{\\l}aw G\\'orka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-28T13:32:28Z","title":"Schauder theory in variable H\\\"older spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7862","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":"sha256:9f7d2f95de173183b1af89bbee657a59185ece89a6b303175bf38c6d254d8944","target":"record","created_at":"2026-05-18T02:32:37Z","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":"29c21f4cb4841fb22cad486a9f3f0086c6357b25a0faa9e5aa80a48d28652812","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-28T13:32:28Z","title_canon_sha256":"02c3e5b34e5d6598a78cf4732c9ee2008b0421d2735e062983bc817302a7e7fe"},"schema_version":"1.0","source":{"id":"1411.7862","kind":"arxiv","version":1}},"canonical_sha256":"66c2f06adf53fd71d354ddacfa62aaef4bccc4435fafb4481aabc1efe99489d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66c2f06adf53fd71d354ddacfa62aaef4bccc4435fafb4481aabc1efe99489d4","first_computed_at":"2026-05-18T02:32:37.083402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:37.083402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n3Qbom/UA9SW3BhW0H+sSYtYF0vY4FjBkYi+6e8ILDIssNo+Zmr0SMqqdXwKuw8pR/T37ujGGN6YgkDdc5E1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:37.083758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.7862","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f7d2f95de173183b1af89bbee657a59185ece89a6b303175bf38c6d254d8944","sha256:1cc9c57013cb1aa559c080534e7ef35f53caaa9be014ba970d7991e7eee195e4"],"state_sha256":"1c400f05e1831303dfe5f6f120e4d5652a755d37fef1172bef7312564ed229bb"}