{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZYPIBRUNFMYKMDQFTW4I5NHZNQ","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":"5825f2187505605eeaeca3caf437b767552dce3d65d39ca61450f3d3ac8d501a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-10T05:43:34Z","title_canon_sha256":"533a59ed55b7be21fc9b8d6e2c4982e39ec3a502e5d269c6d6b5a0c415990666"},"schema_version":"1.0","source":{"id":"1710.03408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03408","created_at":"2026-05-18T00:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03408v1","created_at":"2026-05-18T00:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03408","created_at":"2026-05-18T00:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"ZYPIBRUNFMYK","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZYPIBRUNFMYKMDQF","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZYPIBRUN","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:40f9163d39d67000df32ff6538b3168b66562dbf951b6ae75e5209fc1c2ccf65","target":"graph","created_at":"2026-05-18T00:16:30Z","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":"This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\\Omega\\subset\\mathbb{R}^N$ ($N\\in{\\mathbb N}$), written as\n  \\[\n  \\frac{\\partial u}{\\partial t} + (-\\Delta+1)\\beta(u)\n  = g \\quad \\mbox{in}\\ \\Omega\\times(0, T),\n  \\] which represents the porous media, the fast diffusion equations, etc., where $\\beta$ is a single-valued maximal monotone function on $\\mathbb{R}$, and $T>0$. Existence and uniqueness for (P) were directly proved under a gr","authors_text":"Shunsuke Kurima, Takeshi Fukao, Tomomi Yokota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-10T05:43:34Z","title":"Nonlinear diffusion equations as asymptotic limits of Cahn--Hilliard systems on unbounded domains via Cauchy's criterion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03408","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:c167183d8d2126957288853bae29219b9b4725414d82dbb83093698cbe13c4a5","target":"record","created_at":"2026-05-18T00:16:30Z","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":"5825f2187505605eeaeca3caf437b767552dce3d65d39ca61450f3d3ac8d501a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-10T05:43:34Z","title_canon_sha256":"533a59ed55b7be21fc9b8d6e2c4982e39ec3a502e5d269c6d6b5a0c415990666"},"schema_version":"1.0","source":{"id":"1710.03408","kind":"arxiv","version":1}},"canonical_sha256":"ce1e80c68d2b30a60e059db88eb4f96c1cf71d92c39ad8e5300ea8f010d5be9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce1e80c68d2b30a60e059db88eb4f96c1cf71d92c39ad8e5300ea8f010d5be9f","first_computed_at":"2026-05-18T00:16:30.965657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:30.965657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AbjFCznXBBH7sA/SBqEZ65gaVbMkXi9f4fz9q1topucfTRV+hCxinVDdRkAXeez20vn9SWyKIHvGpJguUJjuBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:30.966192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c167183d8d2126957288853bae29219b9b4725414d82dbb83093698cbe13c4a5","sha256:40f9163d39d67000df32ff6538b3168b66562dbf951b6ae75e5209fc1c2ccf65"],"state_sha256":"22f8e3eeb25b5615b8103f8abb10d9ba3ab3ff6633f95ca556c5e73326281975"}