{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OO34HGVD2OBYFQOVPTKV2IMYDG","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":"fbd6f164ebb8c9ea79c77248569bb29b309a759fcdfb1374133cd47a5a6cb24e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T11:31:32Z","title_canon_sha256":"b5b21e86c785006e84024590e77697219be623be01cfbaa9d63c67e0bd18270a"},"schema_version":"1.0","source":{"id":"1311.4702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.4702","created_at":"2026-05-18T02:51:33Z"},{"alias_kind":"arxiv_version","alias_value":"1311.4702v2","created_at":"2026-05-18T02:51:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4702","created_at":"2026-05-18T02:51:33Z"},{"alias_kind":"pith_short_12","alias_value":"OO34HGVD2OBY","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OO34HGVD2OBYFQOV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OO34HGVD","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:4f0395cbabeef1910e83ae0ede3f5e52c83f64d038162a9f069d361777ba8aff","target":"graph","created_at":"2026-05-18T02:51:33Z","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":"Extending earlier results on the existence of bounded imaginary powers for cone differential operators on weighted $L^p$-spaces $\\mathcal{H}^{0,\\gamma}_p(\\mathbb{B})$ over a manifold with conical singularities, we show how the same assumptions also yield the existence of bounded imaginary powers on higher order Mellin-Sobolev spaces $\\mathcal{H}^{s,\\gamma}_p(\\mathbb{B})$, $s\\geq0$. As an application we then consider the Cahn-Hilliard equation on a manifold with (possibly warped) conical singularities. Relying on our work for the case of straight cones, we first establish $R$-sectoriality (and ","authors_text":"Elmar Schrohe, Nikolaos Roidos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T11:31:32Z","title":"Bounded imaginary powers of cone differential operators on higher order Mellin-Sobolev spaces and applications to the Cahn-Hilliard equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4702","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":"sha256:65d876fee58b96f7ae50a21b8d7203b21f7418cefbca3a4114b8e1b8b2a7f5cd","target":"record","created_at":"2026-05-18T02:51:33Z","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":"fbd6f164ebb8c9ea79c77248569bb29b309a759fcdfb1374133cd47a5a6cb24e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-19T11:31:32Z","title_canon_sha256":"b5b21e86c785006e84024590e77697219be623be01cfbaa9d63c67e0bd18270a"},"schema_version":"1.0","source":{"id":"1311.4702","kind":"arxiv","version":2}},"canonical_sha256":"73b7c39aa3d38382c1d57cd55d2198199ddc63b879e63878b751b55a6087fa85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73b7c39aa3d38382c1d57cd55d2198199ddc63b879e63878b751b55a6087fa85","first_computed_at":"2026-05-18T02:51:33.821666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:33.821666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gCCZ8pk9grtg+wy8T0BOTZ7SL25ILqh3e4A2bY5iOVJrfk0CHM7A7nJe1EG1jkrX5V/pLHF+NNA1yZQDO+aXDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:33.822236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.4702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65d876fee58b96f7ae50a21b8d7203b21f7418cefbca3a4114b8e1b8b2a7f5cd","sha256:4f0395cbabeef1910e83ae0ede3f5e52c83f64d038162a9f069d361777ba8aff"],"state_sha256":"58ac2c776a0b553759bcc6927ac1575d2f3bddf048a86273a1786e7dd4a2955f"}