{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XWJLAQIFAPKLQCEGAEPHI37LRA","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":"467700a26ce6697b36c7646326346f251fc5d5b2e890de4649d2b70d0bc4bfcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-07T01:23:13Z","title_canon_sha256":"e03d00cfb424dcb5a2eb575ea554e69070ce52be6baf11897b52d1c9c94d3024"},"schema_version":"1.0","source":{"id":"1206.1382","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1382","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1382v3","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1382","created_at":"2026-05-18T03:25:35Z"},{"alias_kind":"pith_short_12","alias_value":"XWJLAQIFAPKL","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XWJLAQIFAPKLQCEG","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XWJLAQIF","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:6b961990e0ccb6ff9f86eed9de510e9152373cad5808f579bb37a8896a3a802d","target":"graph","created_at":"2026-05-18T03:25:35Z","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":"In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Furthermore, we extend the result to some other p.c.f. fractals with Dihedral-3 symmetry.","authors_text":"Hua Qiu, Robert S. Strichartz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-07T01:23:13Z","title":"Mean value properties of harmonic functions on Sierpinski gasket type fractals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1382","kind":"arxiv","version":3},"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":"sha256:7e6ae2eba0eb2bf1579a48cc5bae9fa84a40121357af9bfc27e5336e2eb43611","target":"record","created_at":"2026-05-18T03:25:35Z","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":"467700a26ce6697b36c7646326346f251fc5d5b2e890de4649d2b70d0bc4bfcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-07T01:23:13Z","title_canon_sha256":"e03d00cfb424dcb5a2eb575ea554e69070ce52be6baf11897b52d1c9c94d3024"},"schema_version":"1.0","source":{"id":"1206.1382","kind":"arxiv","version":3}},"canonical_sha256":"bd92b0410503d4b80886011e746feb881a33543d69bece6196a126b9272d3a34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd92b0410503d4b80886011e746feb881a33543d69bece6196a126b9272d3a34","first_computed_at":"2026-05-18T03:25:35.100044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:35.100044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tvM5Z4PUmT0A64r1IM3PSSeuyk8rH8DsQRD4g7xbxhHLR3KVlk6JrFUOylX4jx1ZNvQRrUcIwz2huVP9kUfRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:35.100477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1382","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e6ae2eba0eb2bf1579a48cc5bae9fa84a40121357af9bfc27e5336e2eb43611","sha256:6b961990e0ccb6ff9f86eed9de510e9152373cad5808f579bb37a8896a3a802d"],"state_sha256":"a3316a0395c158be36cf1a34a1edfa863a59242429080cd31f0356220d96d0c9"}