{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XK4EQTSTL4E7BVUOXTOKBTZOHV","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":"33f48f49b393ca0c7f10d6a8ce706a6fd89494135fb9158386ed24b7f805982b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-31T13:47:21Z","title_canon_sha256":"659e02cc07e6dd8f2f95b459e3d33d52608b91e429b3e12de3ec94e09a93c203"},"schema_version":"1.0","source":{"id":"1108.6227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.6227","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"1108.6227v1","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.6227","created_at":"2026-05-18T04:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"XK4EQTSTL4E7","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"XK4EQTSTL4E7BVUO","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"XK4EQTST","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:f8cbb487f1853a6fe0f8f7fdb801dcec5238abdf032d0c7b1c1d289662b2d38d","target":"graph","created_at":"2026-05-18T04:14:26Z","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 second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic cylinder. Under natural assumptions on the coefficients and the inhomogeneity we can also prove convergence to an equilibrium or asymptotic almost periodicity.","authors_text":"Robin Nittka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-31T13:47:21Z","title":"Inhomogeneous Parabolic Neumann Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6227","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":"sha256:3aedecf71fb7228e12cbded83c8e93024dfc75e9bd05b75f5b8f91d7925dba19","target":"record","created_at":"2026-05-18T04:14:26Z","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":"33f48f49b393ca0c7f10d6a8ce706a6fd89494135fb9158386ed24b7f805982b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-08-31T13:47:21Z","title_canon_sha256":"659e02cc07e6dd8f2f95b459e3d33d52608b91e429b3e12de3ec94e09a93c203"},"schema_version":"1.0","source":{"id":"1108.6227","kind":"arxiv","version":1}},"canonical_sha256":"bab8484e535f09f0d68ebcdca0cf2e3d4fc27c5cc4209fe80265122d8a7583dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bab8484e535f09f0d68ebcdca0cf2e3d4fc27c5cc4209fe80265122d8a7583dd","first_computed_at":"2026-05-18T04:14:26.772756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:26.772756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PW3faMDIM47pSVtgsVm10BkMCq7z9jDWMKA2eWwsIJ/UDHF1fo225E9n5uck30ge9r6l+RHKHFdShCs5VL6aBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:26.773466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.6227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3aedecf71fb7228e12cbded83c8e93024dfc75e9bd05b75f5b8f91d7925dba19","sha256:f8cbb487f1853a6fe0f8f7fdb801dcec5238abdf032d0c7b1c1d289662b2d38d"],"state_sha256":"57379082b50bc24d37d7ed0c830614aab64f7c76d445264ad3e6845fa177a239"}