{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KPF6IE5APJWGGR5NUBBDLLHB5J","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":"8be4d528a5b90f1d4aaad2250c4f8c633a68f9aa2f25745dd4dc901f06f72bab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-11T08:11:07Z","title_canon_sha256":"7eff7f1632321b10decb502a1d0f677d210c60e6838eee0a3f9e68fb8716eb72"},"schema_version":"1.0","source":{"id":"1808.03771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03771","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03771v1","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03771","created_at":"2026-05-17T23:47:30Z"},{"alias_kind":"pith_short_12","alias_value":"KPF6IE5APJWG","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KPF6IE5APJWGGR5N","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KPF6IE5A","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:dc895d634c1f2421d1f23793716c36b3dddecc678542af4607af4a4882f009b8","target":"graph","created_at":"2026-05-17T23:47:30Z","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 article considers a limit system by passing to the limit in the following Cahn--Hilliard type phase field system related to tumor growth as $\\beta\\searrow0$:\n  \\begin{equation*}\n  \\begin{cases}\n  \\alpha\\partial_{t} \\mu_{\\beta} + \\partial_{t} \\varphi_{\\beta}-\\Delta\\mu_{\\beta} = p(\\sigma_{\\beta} - \\mu_{\\beta}) & \\mbox{in}\\ \\Omega\\times(0, T),\n  \\\\[1mm]\n  \\mu_{\\beta} = \\beta\\partial_{t} \\varphi_{\\beta} + (-\\Delta+1)\\varphi_{\\beta} + \\xi_{\\beta} + \\pi(\\varphi_{\\beta}),\\ \\xi_{\\beta} \\in B(\\varphi_{\\beta})\n  & \\mbox{in}\\ \\Omega\\times(0, T),\n  \\\\[1mm]\n  \\partial_{t} \\sigma_{\\beta} -\\Delta\\sigma_","authors_text":"Shunsuke Kurima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-11T08:11:07Z","title":"Asymptotic analysis for Cahn--Hilliard type phase field systems related to tumor growth in general domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03771","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":"sha256:74b15867d250131b00990792efeb6a4a248db80ab2bc71f8e3c1f270dd7669fe","target":"record","created_at":"2026-05-17T23:47:30Z","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":"8be4d528a5b90f1d4aaad2250c4f8c633a68f9aa2f25745dd4dc901f06f72bab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-11T08:11:07Z","title_canon_sha256":"7eff7f1632321b10decb502a1d0f677d210c60e6838eee0a3f9e68fb8716eb72"},"schema_version":"1.0","source":{"id":"1808.03771","kind":"arxiv","version":1}},"canonical_sha256":"53cbe413a07a6c6347ada04235ace1ea781c8c9decab60eca6f1538fa7fb2b20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53cbe413a07a6c6347ada04235ace1ea781c8c9decab60eca6f1538fa7fb2b20","first_computed_at":"2026-05-17T23:47:30.574030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:30.574030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WBrWGr1xg4gFRbyXKGE3rCQbp8FRTVl4aTw9lfdjhQTWrwuQ8daw6gwwP/BDMgxCHnyr5XTAzSQm8fVUDtk2Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:30.574495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74b15867d250131b00990792efeb6a4a248db80ab2bc71f8e3c1f270dd7669fe","sha256:dc895d634c1f2421d1f23793716c36b3dddecc678542af4607af4a4882f009b8"],"state_sha256":"402f3dd1aa6a5cd3b08a7c9b4c4f8cef058331849b6e46ade6d744d0db4cdc70"}