{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:S2QU53FDRI422WMX6UXAVKDIFU","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":"489d9aae0a74b536f450f04ed09bc1deda8ab2c93c83faeecc1926b009530fd2","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AP","submitted_at":"2004-06-18T13:46:48Z","title_canon_sha256":"e5ff99bbe422074379e7f2393feea0b85f867a93c2e9982bd2adb7147c2f4f82"},"schema_version":"1.0","source":{"id":"math/0406368","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406368","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406368v1","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406368","created_at":"2026-05-18T03:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"S2QU53FDRI42","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"S2QU53FDRI422WMX","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"S2QU53FD","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:fe2d83239cdf7e9ab31073e8aa3bb839db21fcaa0d9a3e23d764ce2139283a7d","target":"graph","created_at":"2026-05-18T03:58:14Z","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 consider the Hele-Shaw flow that arises from injection of two-dimensional fluid into a point of a curved surface. The resulting fluid domains have and are more or less determined implicitly by a mean value property for harmonic functions. We improve on the results of Hedenmalm and Shimorin \\cite{HS} and obtain essentially the same conclusions while imposing a weaker curvature condition on the surface. Incidentally, the curvature condition is the same as the one that appears in a recent paper of Hedenmalm and Perdomo, where the problem of finding smooth area minimizing surfaces for a given c","authors_text":"Anders Olofsson, Haakan Hedenmalm","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2004-06-18T13:46:48Z","title":"Hele-Shaw flow on weakly hyperbolic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406368","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":"sha256:5ae19eef3f3c595b44c34057c13913a839e6607b4fd8c320fd1b25bb33737dd5","target":"record","created_at":"2026-05-18T03:58:14Z","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":"489d9aae0a74b536f450f04ed09bc1deda8ab2c93c83faeecc1926b009530fd2","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.AP","submitted_at":"2004-06-18T13:46:48Z","title_canon_sha256":"e5ff99bbe422074379e7f2393feea0b85f867a93c2e9982bd2adb7147c2f4f82"},"schema_version":"1.0","source":{"id":"math/0406368","kind":"arxiv","version":1}},"canonical_sha256":"96a14eeca38a39ad5997f52e0aa8682d0d845381aadfeb4fc83d77f02b299f54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96a14eeca38a39ad5997f52e0aa8682d0d845381aadfeb4fc83d77f02b299f54","first_computed_at":"2026-05-18T03:58:14.503898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:14.503898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NNfRtuYhafhr79Uud5WM09Eu7tzwI3oWm/rnKtOTM6WEfxIjW0YYnPh8SAbH8WiButkrC7Q6aITWZXi55pA5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:14.504341Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0406368","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ae19eef3f3c595b44c34057c13913a839e6607b4fd8c320fd1b25bb33737dd5","sha256:fe2d83239cdf7e9ab31073e8aa3bb839db21fcaa0d9a3e23d764ce2139283a7d"],"state_sha256":"cf6cfcc702adaaa789e90976eaff59169096e30821aa417dcbd89c9821728688"}