{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CPLNKRSANCVKJAPLL5LRQUXKCV","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":"bfe2e54009465fee7d498ab691f3b5f0830f96ad3b54161a342785dd67a1570d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-31T14:08:14Z","title_canon_sha256":"218caf2c30aee74dc1a931a7fb703ed2c3301f411df0db4862839439193d272e"},"schema_version":"1.0","source":{"id":"1508.07836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07836","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07836v1","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07836","created_at":"2026-05-18T01:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"CPLNKRSANCVK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CPLNKRSANCVKJAPL","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CPLNKRSA","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:f9f16e2855ad822179b6d0896afcf1fc55aa4499c174578006b10e5afd3a00fd","target":"graph","created_at":"2026-05-18T01:34:31Z","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 define a homogeneous parabolic De Giorgi classes of order 2 which suits a mixed type class of evolution equations whose simplest example is $\\mu (x) \\frac{\\partial u}{\\partial t} - \\Delta u = 0$ where $\\mu$ can be positive, null and negative, so in particular elliptic-parabolic and forward-backward parabolic equations are included. For functions belonging to this class we prove local boundedness and show a Harnack inequality which, as by-products, gives H\\\"older-continuity, in particular in the interface $I$ where $\\mu$ change sign, and a maximum principle.","authors_text":"Fabio Paronetto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-31T14:08:14Z","title":"A Harnack's inequality for mixed type evolution equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07836","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":"sha256:827fb16ea9171ff43cc4a2ac6c667f584452fea3dfbd9d7ce756bf32942f70fc","target":"record","created_at":"2026-05-18T01:34:31Z","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":"bfe2e54009465fee7d498ab691f3b5f0830f96ad3b54161a342785dd67a1570d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-31T14:08:14Z","title_canon_sha256":"218caf2c30aee74dc1a931a7fb703ed2c3301f411df0db4862839439193d272e"},"schema_version":"1.0","source":{"id":"1508.07836","kind":"arxiv","version":1}},"canonical_sha256":"13d6d5464068aaa481eb5f571852ea154b98f1ca389b7247d63098f07aff2be8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13d6d5464068aaa481eb5f571852ea154b98f1ca389b7247d63098f07aff2be8","first_computed_at":"2026-05-18T01:34:31.359257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:31.359257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s7CbpF9+E7BFOOeclWRGfKwg1gyfaS/Il3lE77f/sOrE7UbEadu3684LchhccD76dIOYzMCUf/F+7gsWosvpCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:31.359661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:827fb16ea9171ff43cc4a2ac6c667f584452fea3dfbd9d7ce756bf32942f70fc","sha256:f9f16e2855ad822179b6d0896afcf1fc55aa4499c174578006b10e5afd3a00fd"],"state_sha256":"6f857f27aa15e0a7f3a5915c0cdc9ad9f7cd8697235ed0c3a1df370a637e4660"}