{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VDP4OU67MSG5DK5HVMDM5XV3ND","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":"663522c262c82db1c3182023d52257dd73667e153f9fa383c121bbb11979677c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T06:53:45Z","title_canon_sha256":"a4f10d5518fc2c848b6361974c601ce59940f33b9cffa68759d092683a08351b"},"schema_version":"1.0","source":{"id":"1612.06990","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06990","created_at":"2026-05-18T00:06:42Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06990v4","created_at":"2026-05-18T00:06:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06990","created_at":"2026-05-18T00:06:42Z"},{"alias_kind":"pith_short_12","alias_value":"VDP4OU67MSG5","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VDP4OU67MSG5DK5H","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VDP4OU67","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:56c8b0c7b7c94f49324d78f8d125915580eca382b0744bea02fa0e6c0a869358","target":"graph","created_at":"2026-05-18T00:06:42Z","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":"For an open set $V\\subset\\mathbb{C}^n$, denote by $\\mathscr{M}_{\\alpha}(V)$ the family of $\\alpha$-analytic functions that obey a boundary maximum modulus principle. We prove that, on a bounded domain $\\Omega\\subset \\mathbb{C}^n$, with continuous boundary (that in each variable separately allows a solution to the Dirichlet problem), a function $f \\in \\mathscr{M}_{\\alpha}(\\Omega\\setminus f^{-1}(0))$ automatically satisfies $f\\in \\mathscr{M}_{\\alpha}(\\Omega)$, if it is $C^{\\alpha_j-1}$-smooth, in the $z_j$ variable, $\\alpha\\in \\mathbb{Z}^n_+$, up to the boundary. For a submanifold $U\\subset \\mat","authors_text":"Abtin Daghighi, Frank Wikstr\\\"om","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T06:53:45Z","title":"Level sets of certain classes of $\\alpha$-analytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06990","kind":"arxiv","version":4},"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":"sha256:5803001ed3aa43af64bc76aad5864fe2177e6ad5e5162b875a9e5a054bd694ac","target":"record","created_at":"2026-05-18T00:06:42Z","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":"663522c262c82db1c3182023d52257dd73667e153f9fa383c121bbb11979677c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T06:53:45Z","title_canon_sha256":"a4f10d5518fc2c848b6361974c601ce59940f33b9cffa68759d092683a08351b"},"schema_version":"1.0","source":{"id":"1612.06990","kind":"arxiv","version":4}},"canonical_sha256":"a8dfc753df648dd1aba7ab06cedebb68e595e352092efaaadbe76cae1c6fdc98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8dfc753df648dd1aba7ab06cedebb68e595e352092efaaadbe76cae1c6fdc98","first_computed_at":"2026-05-18T00:06:42.142560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:42.142560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T6Sr9HQHQouMGtQYpcSI+Z3xFMrmpNEyIHqj/27YWHdm2HKQK7bu3OvEvRzroBCHnbUlkyk51L3tVvxUKIdQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:42.143081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06990","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5803001ed3aa43af64bc76aad5864fe2177e6ad5e5162b875a9e5a054bd694ac","sha256:56c8b0c7b7c94f49324d78f8d125915580eca382b0744bea02fa0e6c0a869358"],"state_sha256":"e47ace15380bae5974e751f62a32ebc6f74b8a8d2cd560ab65cd8e36d977a766"}