{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TVVKJL73FGQL7DAWRFATHG6J6B","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":"58e3a3a6fce977a7d0d86af73690592bbbd86889a51e3107fee876065e3fc379","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-06T17:01:45Z","title_canon_sha256":"ca91d604e83cdc41d5cc7787b528ea747d19234f075d35848ed0ded85f9c34c4"},"schema_version":"1.0","source":{"id":"2606.08257","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08257","created_at":"2026-06-09T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08257v1","created_at":"2026-06-09T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08257","created_at":"2026-06-09T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"TVVKJL73FGQL","created_at":"2026-06-09T01:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"TVVKJL73FGQL7DAW","created_at":"2026-06-09T01:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"TVVKJL73","created_at":"2026-06-09T01:05:31Z"}],"graph_snapshots":[{"event_id":"sha256:dc5d0413bbf1790283933ae6001e3ca05a8f7f9054dc703a28e182d1b8ceb601","target":"graph","created_at":"2026-06-09T01:05:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.08257/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It has been a long standing conjecture that the $ \\infty $-harmonic functions in the plane have a 1/3-H\\\"older continuous gradient. It \\emph{is} known that solutions are $ C^1 $ and that the gradient is locally $ \\alpha $-H\\\"older, but $ \\alpha $ comes without any positive lower bound. Aronsson's solution $ x^{4/3} - y^{4/3} $ shows that no better general regularity is possible.\n  In the plane there is also a connection between the $ \\infty $-Laplace equation and the one-dimensional heat equation, observed already by Aronsson himself. I shall show that this link can be accessed under a certain","authors_text":"Karl K. Brustad","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-06T17:01:45Z","title":"Infinity-harmonic functions in the plane: Regularity by injectivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08257","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:c213a6feb029d7ca9cb3a127a9a3d9ea90685c4d3651df7d4dda8c6a171b1154","target":"record","created_at":"2026-06-09T01:05:31Z","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":"58e3a3a6fce977a7d0d86af73690592bbbd86889a51e3107fee876065e3fc379","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-06-06T17:01:45Z","title_canon_sha256":"ca91d604e83cdc41d5cc7787b528ea747d19234f075d35848ed0ded85f9c34c4"},"schema_version":"1.0","source":{"id":"2606.08257","kind":"arxiv","version":1}},"canonical_sha256":"9d6aa4affb29a0bf8c168941339bc9f0718ae1210708c1d9a3483631d23dafd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d6aa4affb29a0bf8c168941339bc9f0718ae1210708c1d9a3483631d23dafd2","first_computed_at":"2026-06-09T01:05:31.541773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:31.541773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YgKXllTkshGfg3+Upf9CszsdTgmdxmWtwQqPqNcwF25FKhRmJHHc8s1vvUgu1Cf2v3BtCCHzWsti5yxbKm0EAw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:31.542190Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08257","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c213a6feb029d7ca9cb3a127a9a3d9ea90685c4d3651df7d4dda8c6a171b1154","sha256:dc5d0413bbf1790283933ae6001e3ca05a8f7f9054dc703a28e182d1b8ceb601"],"state_sha256":"a005afbb896fe42f9daaebfe0ab3e08f3b57af28a13816912f2924fe27dbb0d9"}