{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IXVQYORE6MUJOOB4FD6FR6BDID","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":"8d0520fbb608519970a21b341c965e0e0d0d98901e497a03270d6c6a1981d93c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-20T15:59:24Z","title_canon_sha256":"feb2d5fd05863cc4699d5ce8c80f3cace924272e681cef8a75e350946621ee63"},"schema_version":"1.0","source":{"id":"1811.08554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.08554","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1811.08554v1","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.08554","created_at":"2026-05-18T00:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"IXVQYORE6MUJ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IXVQYORE6MUJOOB4","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IXVQYORE","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:42e0ee0685628844c2de34f0e112ed2c9986541bc096833b3747ff06078d1337","target":"graph","created_at":"2026-05-18T00:00:12Z","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":"In this paper, we study the existence of distributional solutions solving \\cref{main-3} on a bounded domain $\\Omega$ satisfying a uniform capacity density condition where the nonlinear structure $\\mathcal{A}(x,t,\\nabla u)$ is modelled after the standard parabolic $p$-Laplace operator. In this regard, we need to prove a priori estimates for the gradient of the solution below the natural exponent and a higher integrability result for very weak solutions at the initial boundary. The elliptic counterpart to these two estimates are fairly well developed over the past few decades, but no analogous t","authors_text":"Karthik Adimurthi, Sun-Sig Byun, Wontae Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-20T15:59:24Z","title":"Partial existence result for Homogeneous Quasilinear parabolic problems beyond the duality pairing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.08554","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:fe22b513e76dab4b87ff2fa3a2710b32c68e3940a98974613486df3e81cb478d","target":"record","created_at":"2026-05-18T00:00:12Z","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":"8d0520fbb608519970a21b341c965e0e0d0d98901e497a03270d6c6a1981d93c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-20T15:59:24Z","title_canon_sha256":"feb2d5fd05863cc4699d5ce8c80f3cace924272e681cef8a75e350946621ee63"},"schema_version":"1.0","source":{"id":"1811.08554","kind":"arxiv","version":1}},"canonical_sha256":"45eb0c3a24f32897383c28fc58f82340eff34e9898622f2b18c9b8c8d6b09c95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45eb0c3a24f32897383c28fc58f82340eff34e9898622f2b18c9b8c8d6b09c95","first_computed_at":"2026-05-18T00:00:12.240197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:12.240197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ErZ6emdSgdRREFKnuQ0ccbtkwpqULLK1FOC/tgFdE7md7H5yIlvQhQBXnZ+q3OBQ0OSqzt4vyW7drEpfYEbVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:12.240862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.08554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe22b513e76dab4b87ff2fa3a2710b32c68e3940a98974613486df3e81cb478d","sha256:42e0ee0685628844c2de34f0e112ed2c9986541bc096833b3747ff06078d1337"],"state_sha256":"04962e9982cd414f260bf631343f1dc7894cd33e60315211c879f9a8fc220b02"}