{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:KRQU6GLZSATBZPYVKFNHGUNNHK","short_pith_number":"pith:KRQU6GLZ","schema_version":"1.0","canonical_sha256":"54614f197990261cbf15515a7351ad3aaa9700db8660a1e4ee2f9863024eb595","source":{"kind":"arxiv","id":"2607.06698","version":1},"attestation_state":"computed","paper":{"title":"Infinity-harmonic functions and inverse mean curvature flow clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Kai Xu","submitted_at":"2026-07-07T18:15:29Z","abstract_excerpt":"An $\\infty$-harmonic function is a viscosity solution of $\\nabla^2 u(\\nabla u,\\nabla u)=0$, or equivalently, an absolute minimizer of $\\|\\nabla u\\|_{L^\\infty}$. We prove a variety of new structural and regularity results in two dimensions, including:\n  1. $\\infty$-harmonic functions in domains of $\\mathbb{R}^2$ are $C^{1,1/3}$.\n  2. Critical points are isolated, and at each critical point, the solution has a unique quasiradial blow-up.\n  3. Entire solutions with polynomial growth have unique quasiradial blow-downs, and are determined by their Fourier modes at infinity.\n  These results are cons"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.06698","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-07T18:15:29Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"25c3b351f26deea208eb92d7904bc72b1159d78dac9d7dfb86f026de34e2eb32","abstract_canon_sha256":"0f250854d8d8d1024b3845d72ba559dbaf2b44c533e7e2db8e27a7ae331d531b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T00:19:23.771272Z","signature_b64":"g0qKCkz2qiXm8Mj3YQpbpbLZVh4UolLvP3CGvZXuLf0SY1K3NxuBuK5TQI8QWvYQ3MpUJtA9ip0u1fhbUBMbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54614f197990261cbf15515a7351ad3aaa9700db8660a1e4ee2f9863024eb595","last_reissued_at":"2026-07-09T00:19:23.770834Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T00:19:23.770834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinity-harmonic functions and inverse mean curvature flow clusters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Kai Xu","submitted_at":"2026-07-07T18:15:29Z","abstract_excerpt":"An $\\infty$-harmonic function is a viscosity solution of $\\nabla^2 u(\\nabla u,\\nabla u)=0$, or equivalently, an absolute minimizer of $\\|\\nabla u\\|_{L^\\infty}$. We prove a variety of new structural and regularity results in two dimensions, including:\n  1. $\\infty$-harmonic functions in domains of $\\mathbb{R}^2$ are $C^{1,1/3}$.\n  2. Critical points are isolated, and at each critical point, the solution has a unique quasiradial blow-up.\n  3. Entire solutions with polynomial growth have unique quasiradial blow-downs, and are determined by their Fourier modes at infinity.\n  These results are cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06698","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06698/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.06698","created_at":"2026-07-09T00:19:23.770897+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.06698v1","created_at":"2026-07-09T00:19:23.770897+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06698","created_at":"2026-07-09T00:19:23.770897+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRQU6GLZSATB","created_at":"2026-07-09T00:19:23.770897+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRQU6GLZSATBZPYV","created_at":"2026-07-09T00:19:23.770897+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRQU6GLZ","created_at":"2026-07-09T00:19:23.770897+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK","json":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK.json","graph_json":"https://pith.science/api/pith-number/KRQU6GLZSATBZPYVKFNHGUNNHK/graph.json","events_json":"https://pith.science/api/pith-number/KRQU6GLZSATBZPYVKFNHGUNNHK/events.json","paper":"https://pith.science/paper/KRQU6GLZ"},"agent_actions":{"view_html":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK","download_json":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK.json","view_paper":"https://pith.science/paper/KRQU6GLZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.06698&json=true","fetch_graph":"https://pith.science/api/pith-number/KRQU6GLZSATBZPYVKFNHGUNNHK/graph.json","fetch_events":"https://pith.science/api/pith-number/KRQU6GLZSATBZPYVKFNHGUNNHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK/action/storage_attestation","attest_author":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK/action/author_attestation","sign_citation":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK/action/citation_signature","submit_replication":"https://pith.science/pith/KRQU6GLZSATBZPYVKFNHGUNNHK/action/replication_record"}},"created_at":"2026-07-09T00:19:23.770897+00:00","updated_at":"2026-07-09T00:19:23.770897+00:00"}