{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6WD3OLLQNSS5CR573ZYUB6BQ4Q","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":"ea4620c2d606d5708e6b7f10b50cf806e4a146c777bb67e02170d06849658393","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T17:23:13Z","title_canon_sha256":"99d62947ef891cd18f665314b8933a37e9152dc4801ce5cad9a026a47248452d"},"schema_version":"1.0","source":{"id":"1708.06329","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06329","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06329v1","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06329","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"6WD3OLLQNSS5","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6WD3OLLQNSS5CR57","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6WD3OLLQ","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:822716042051127b0c8567468613ef69b1cabfbb6a746150610d1c11d19438b7","target":"graph","created_at":"2026-05-18T00:37:42Z","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 introduce a notion of quasilinear parabolic equations over metric measure spaces. Under sharp structural conditions, we prove that local weak solutions are locally bounded and satisfy the parabolic Harnack inequality. Applications include the parabolic maximum principle and pointwise estimates for weak solutions.","authors_text":"Janna Lierl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T17:23:13Z","title":"Local behavior of solutions of quasilinear parabolic equations on metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06329","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":"sha256:29d65b09bff11cecaf8dca4128e168cc673d44e09f5b09f79d7f1ec3b85f8ef9","target":"record","created_at":"2026-05-18T00:37:42Z","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":"ea4620c2d606d5708e6b7f10b50cf806e4a146c777bb67e02170d06849658393","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-21T17:23:13Z","title_canon_sha256":"99d62947ef891cd18f665314b8933a37e9152dc4801ce5cad9a026a47248452d"},"schema_version":"1.0","source":{"id":"1708.06329","kind":"arxiv","version":1}},"canonical_sha256":"f587b72d706ca5d147bfde7140f830e40ccdaba6ac69c5938b2ef1360fa47a97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f587b72d706ca5d147bfde7140f830e40ccdaba6ac69c5938b2ef1360fa47a97","first_computed_at":"2026-05-18T00:37:42.579856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:42.579856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dVFd2kjJGbn1pdSkQPn5IdCgYb5Ow31DJJWF3SdyHaUk7Jgqlk9gaFozFhtDxIMboMkIfvzGln3u5wC5CLPDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:42.580569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06329","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29d65b09bff11cecaf8dca4128e168cc673d44e09f5b09f79d7f1ec3b85f8ef9","sha256:822716042051127b0c8567468613ef69b1cabfbb6a746150610d1c11d19438b7"],"state_sha256":"493cc9acec36fdd04de7556f1321204a8190fe0b60bcffef81407fe16004a3cd"}