{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EUMM4VCNPRXHT4QB2TRSZ6K4KF","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":"fd1b5da974ebb6353c97ce823cfecfa2078b1c795c5aebb68807df7fc4246cdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-11T05:14:34Z","title_canon_sha256":"eae5ed862f86213b6bcde25945f982dddc8b986398f629fbfa4bd6f0b4842067"},"schema_version":"1.0","source":{"id":"1708.03434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03434","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03434v1","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03434","created_at":"2026-05-18T00:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"EUMM4VCNPRXH","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EUMM4VCNPRXHT4QB","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EUMM4VCN","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:38ca77f5edd8e7442e69fc829676547c6fc2e21e2fe417da013c377f5881ce6d","target":"graph","created_at":"2026-05-18T00:38:13Z","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":"Graham Theorem on the unit ball $B_{n}$ in $\\mathbb{C}^{n}$ states that every invariant harmonic function $u\\in C^{n}(\\overline{B}_{n})$ must be pluriharmonic in $B_{n}$. This rigidity phenomenon of Graham have been studied by many authors. In this paper, we prove that Graham theorem holds on classical bounded symmetric domains. Which include Type I domains, Type II domains, Type III domains III(n) with even $n$ and some special Type IV domains.","authors_text":"Ren-Yu Chen, Song-Ying Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-11T05:14:34Z","title":"Graham Theorem on Bounded Symmetric Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03434","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:b100ee57af5e193bd6eed2362c4c22bfdb556249bc57908ceebb5d80ccc2f641","target":"record","created_at":"2026-05-18T00:38:13Z","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":"fd1b5da974ebb6353c97ce823cfecfa2078b1c795c5aebb68807df7fc4246cdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-11T05:14:34Z","title_canon_sha256":"eae5ed862f86213b6bcde25945f982dddc8b986398f629fbfa4bd6f0b4842067"},"schema_version":"1.0","source":{"id":"1708.03434","kind":"arxiv","version":1}},"canonical_sha256":"2518ce544d7c6e79f201d4e32cf95c5156836e1a6429c5e3dc9027aa2a17dbd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2518ce544d7c6e79f201d4e32cf95c5156836e1a6429c5e3dc9027aa2a17dbd7","first_computed_at":"2026-05-18T00:38:13.133878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:13.133878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9OStLxlYNRl+pLMPQTJXP4A0bPpGeVV7lfVnsEkJ0CttuqkrIEk0UWD+J5fqxPwYtNgnuWeTcGMKj0cfGCVoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:13.134552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b100ee57af5e193bd6eed2362c4c22bfdb556249bc57908ceebb5d80ccc2f641","sha256:38ca77f5edd8e7442e69fc829676547c6fc2e21e2fe417da013c377f5881ce6d"],"state_sha256":"4cb6fbdef03ae87d70dfc04a0c621f12cd8338e0c25f8c31f49036fdf09f60bd"}