{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:OVYCG2NSDXJF4E2QJCMZ7JLZIA","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":"681b18c232ce0a3ce42ea3626761b25618da24fa36e2d6c24ba21f8e3f187b60","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1995-09-08T14:44:20Z","title_canon_sha256":"414cb87956421c02fc8aba5385339ddcbd4bb9082968bee3951f8f170103bdef"},"schema_version":"1.0","source":{"id":"cond-mat/9509043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9509043","created_at":"2026-05-18T04:27:48Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9509043v1","created_at":"2026-05-18T04:27:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9509043","created_at":"2026-05-18T04:27:48Z"},{"alias_kind":"pith_short_12","alias_value":"OVYCG2NSDXJF","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"OVYCG2NSDXJF4E2Q","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"OVYCG2NS","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:780f5fa4d8d3b04fd2d8091d4b58056589058cdcc50c14f4eb37713b846ae9a0","target":"graph","created_at":"2026-05-18T04:27:48Z","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 report a new type of restoration of macroscopic isotropy (homogenization) in fractals with microscopic anisotropy. The phenomenon is observed in various physical setups, including diffusions, random walks, resistor networks, and Gaussian field theories. The mechanism is unique in that it is absent in spaces with translational invariance, while universal in that it is observed in a wide class of fractals.","authors_text":"Hiroshi Watanabe, Kumiko Hattori, Martin T. Barlow, Tetsuya Hattori","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat","submitted_at":"1995-09-08T14:44:20Z","title":"Restoration of isotropy on fractals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9509043","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":"sha256:331d9f2f0e14bfb2f623c54a92bff878a2fe76b36915e1862324907ab22607f3","target":"record","created_at":"2026-05-18T04:27:48Z","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":"681b18c232ce0a3ce42ea3626761b25618da24fa36e2d6c24ba21f8e3f187b60","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat","submitted_at":"1995-09-08T14:44:20Z","title_canon_sha256":"414cb87956421c02fc8aba5385339ddcbd4bb9082968bee3951f8f170103bdef"},"schema_version":"1.0","source":{"id":"cond-mat/9509043","kind":"arxiv","version":1}},"canonical_sha256":"75702369b21dd25e135048999fa5794014cd269b0a73a805a8a60657d2b339a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75702369b21dd25e135048999fa5794014cd269b0a73a805a8a60657d2b339a4","first_computed_at":"2026-05-18T04:27:48.097774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:48.097774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z0h3aWdsHFxYPcc37GctnJQc8X69OTJTXUH6/eNiAe4gXJR+sTDaoULP2fcXRJRuRPuvbSXRg4xq58miq7nYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:48.098219Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9509043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:331d9f2f0e14bfb2f623c54a92bff878a2fe76b36915e1862324907ab22607f3","sha256:780f5fa4d8d3b04fd2d8091d4b58056589058cdcc50c14f4eb37713b846ae9a0"],"state_sha256":"b257d9e577e98327530fd5fe6aa5ab813e1e82828282a927eb578eaadb921d31"}