{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ZT5ZX66TVVA32CJBC2WYQDS4PP","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":"ddb1b76e3fe9ddc138c30736894406663ae1a17fed00febba2ae939bcb213251","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-09T21:13:38Z","title_canon_sha256":"40f166e3f0f4c35b059c53aeb23543f50052c59e390f7f71e6237584177cd71b"},"schema_version":"1.0","source":{"id":"0812.1802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.1802","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"0812.1802v2","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.1802","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"ZT5ZX66TVVA3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZT5ZX66TVVA32CJB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZT5ZX66T","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:a1be536aa4b952606ef3bbcd5c77f65491e6964dfa96beaf565cca45a8e9660f","target":"graph","created_at":"2026-05-18T00:12:11Z","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 prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Consequently for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined.","authors_text":"Alexander Teplyaev, Martin T. Barlow, Richard F. Bass, Takashi Kumagai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-09T21:13:38Z","title":"Brownian motion on the Sierpinski carpet"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.1802","kind":"arxiv","version":2},"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:f79b0977a534c73ddb675f50576e88d2bf88d1fac5c2e2760721da2efc8ccfa3","target":"record","created_at":"2026-05-18T00:12:11Z","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":"ddb1b76e3fe9ddc138c30736894406663ae1a17fed00febba2ae939bcb213251","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-09T21:13:38Z","title_canon_sha256":"40f166e3f0f4c35b059c53aeb23543f50052c59e390f7f71e6237584177cd71b"},"schema_version":"1.0","source":{"id":"0812.1802","kind":"arxiv","version":2}},"canonical_sha256":"ccfb9bfbd3ad41bd092116ad880e5c7bd67c7bc04621bf45872159f9b48c542f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccfb9bfbd3ad41bd092116ad880e5c7bd67c7bc04621bf45872159f9b48c542f","first_computed_at":"2026-05-18T00:12:11.911359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:11.911359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cDQXhp+ph50TdqKAW0r1ZPo2DpW6IOIFZAyBdJNN+mdCTNsvhYIXqcpOCHcPf9Ns96feEeCb+egaXQNgSOXuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:11.912026Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.1802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f79b0977a534c73ddb675f50576e88d2bf88d1fac5c2e2760721da2efc8ccfa3","sha256:a1be536aa4b952606ef3bbcd5c77f65491e6964dfa96beaf565cca45a8e9660f"],"state_sha256":"3873657476c612d06dd72d6e5aa88df24d16d15ff1a06e752e089d3ebc43f002"}