{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EV5MRC2RM2UU6IFKC3VVB6BOB5","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":"63e7ffbcde85f0f7360246fe8e5e09a5b340a1f8325bcbaddd9b2c01aa584e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-06T07:53:30Z","title_canon_sha256":"8661811f5d87189a435aaa52f128a9558aa8f8bf3d06a1985723b05f20e2ea0d"},"schema_version":"1.0","source":{"id":"1905.01863","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01863","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01863v1","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01863","created_at":"2026-05-17T23:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"EV5MRC2RM2UU","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EV5MRC2RM2UU6IFK","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EV5MRC2R","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:6fe8c8fb382a48ab9be29a15c8c9de67683f8ff665ed449f7a3dc7d10f82e10a","target":"graph","created_at":"2026-05-17T23:46:57Z","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 consider the heat equation on a bounded domain subject to an inhomogeneous forcing in terms of a rate-independent (hysteresis) operator and a control variable. The aim of the paper is to establish a functional analytical setting which allows to prove weak differentiability properties of the control-to-state mapping. Using results of [BK] and [B] on the weak differentiability of scalar rate-independent operators, we prove Bouligand and Newton differentiability in suitable Bochner spaces of the control-to-state mapping in a parabolic problem.","authors_text":"Klemens Fellner, Martin Brokate, Matthias Lang-Batsching","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-06T07:53:30Z","title":"Weak differentiability of the control-to-state mapping in a parabolic equation with hysteresis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01863","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":"sha256:1467c96b28e450d5704771aaaac2838e491933e80ad75588c81706849b496c6e","target":"record","created_at":"2026-05-17T23:46:57Z","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":"63e7ffbcde85f0f7360246fe8e5e09a5b340a1f8325bcbaddd9b2c01aa584e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-06T07:53:30Z","title_canon_sha256":"8661811f5d87189a435aaa52f128a9558aa8f8bf3d06a1985723b05f20e2ea0d"},"schema_version":"1.0","source":{"id":"1905.01863","kind":"arxiv","version":1}},"canonical_sha256":"257ac88b5166a94f20aa16eb50f82e0f45a4d124553dd7d52995eb5e6c3d4d8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"257ac88b5166a94f20aa16eb50f82e0f45a4d124553dd7d52995eb5e6c3d4d8c","first_computed_at":"2026-05-17T23:46:57.195668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:57.195668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rVX9a0J4b+pp+6rYvbHj7hBxUCWLtl26f3qh2IU3X6fRZcWUh/aGEKtUMFvd2KHe1SdPfjt54dBgrD01FRA8Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:57.196372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01863","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1467c96b28e450d5704771aaaac2838e491933e80ad75588c81706849b496c6e","sha256:6fe8c8fb382a48ab9be29a15c8c9de67683f8ff665ed449f7a3dc7d10f82e10a"],"state_sha256":"0986a2df99bb64f97e7e26a9924f00a28a105513bc99edef853b5c2cb2b659df"}