{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:F6AC3YNN2557I63BXCWIC7T657","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":"555ed459711cc75e6970675581eff39d3dc7fcd87fe08b1c8281542aac79010b","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-08-20T14:54:29Z","title_canon_sha256":"cf8b197d4f0b9c780fc09ab64db3d6d7623535b572787d66b329b0841edb1d24"},"schema_version":"1.0","source":{"id":"1008.3520","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3520","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3520v2","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3520","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"pith_short_12","alias_value":"F6AC3YNN2557","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"F6AC3YNN2557I63B","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"F6AC3YNN","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:92d74ab2654bcb4741f96d994a373e192e31ccb3f5b15f91cedde59c3561a0d5","target":"graph","created_at":"2026-05-18T04:34:08Z","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":"Given an elliptic differential operator L of second order with smooth coefficients in a bounded domain with smooth boundary. We show that if the coefficients are H\\\"older-continuous up to the boundary and the boundary is $C^{2,\\alpha}$-smooth that on the space of all $C^{2,\\alpha}$-smooth (up to the boundary) functions u fulfilling both u=0 and Lu=0 (on the boundary) the operator L is dissipative and closable to an generator of a strong continuous operator semigroup in the space of continuous functions with zero boundary condition. Moreover we show that if the coefficients of the second order ","authors_text":"Benedict Baur","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-08-20T14:54:29Z","title":"Core property of smooth contractive embeddable functions for an elliptic operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3520","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:ab69ac4a87fb245869eaf88184ce4e76a3ef1d8388d88f0006c00cc44bd591ab","target":"record","created_at":"2026-05-18T04:34:08Z","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":"555ed459711cc75e6970675581eff39d3dc7fcd87fe08b1c8281542aac79010b","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-08-20T14:54:29Z","title_canon_sha256":"cf8b197d4f0b9c780fc09ab64db3d6d7623535b572787d66b329b0841edb1d24"},"schema_version":"1.0","source":{"id":"1008.3520","kind":"arxiv","version":2}},"canonical_sha256":"2f802de1add77bf47b61b8ac817e7eeff632f747ff27f50465113093c718e8f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f802de1add77bf47b61b8ac817e7eeff632f747ff27f50465113093c718e8f5","first_computed_at":"2026-05-18T04:34:08.732140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:08.732140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ijtxurgi65CqWRYVa6x83hMJbaCQByILdcNubge0KNNNrAAxcwA2AQYCfwnwQBOioMYbAvQiYnzgkybN0PVLCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:08.732660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3520","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab69ac4a87fb245869eaf88184ce4e76a3ef1d8388d88f0006c00cc44bd591ab","sha256:92d74ab2654bcb4741f96d994a373e192e31ccb3f5b15f91cedde59c3561a0d5"],"state_sha256":"b94ae37767108860c2fa01d3ea53d6b2dc6ff8fff9e591528676250d7d6b4d8c"}