{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:HXH3H3B2LB5RZ2JB7DOAIWKLQZ","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":"f93fbbfe787fe21a61a95e977a8df71e49d190ee877ea74eedfc2cc101c7a6ea","cross_cats_sorted":["cond-mat","gr-qc","quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2000-08-29T14:58:54Z","title_canon_sha256":"cbd72e34ff3efd1da3755e66fdd360a04d60cc8393f921b311449f7f55761ed6"},"schema_version":"1.0","source":{"id":"hep-th/0008222","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0008222","created_at":"2026-05-18T00:37:10Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0008222v3","created_at":"2026-05-18T00:37:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0008222","created_at":"2026-05-18T00:37:10Z"},{"alias_kind":"pith_short_12","alias_value":"HXH3H3B2LB5R","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"HXH3H3B2LB5RZ2JB","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"HXH3H3B2","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:47def853506a6d5861f23c6ccc76978e8e1af7c14e2df45bc6c261bde729c8ae","target":"graph","created_at":"2026-05-18T00:37:10Z","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":"The concept of fractal index is introduced in connection with the idea of universal class $h$ of particles or quasiparticles, termed fractons, which obey fractal statistics. We show the relation between fractons and conformal field theory(CFT)-quasiparticles taking into account the central charge $c[\\nu]$ and the particle-hole duality $\\nu\\longleftrightarrow\\frac{1}{\\nu}$, for integer-value $\\nu$ of the statistical parameter. The Hausdorff dimension $h$ which labelled the universal classes of particles and the conformal anomaly are therefore related. We also establish a connection between Roge","authors_text":"Wellington da Cruz","cross_cats":["cond-mat","gr-qc","quant-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2000-08-29T14:58:54Z","title":"Fractal statistics, fractal index and fractons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0008222","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:ddcba061abdc612e1a8632540dbb7bf35774b975052fc107b900e81829944c40","target":"record","created_at":"2026-05-18T00:37:10Z","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":"f93fbbfe787fe21a61a95e977a8df71e49d190ee877ea74eedfc2cc101c7a6ea","cross_cats_sorted":["cond-mat","gr-qc","quant-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2000-08-29T14:58:54Z","title_canon_sha256":"cbd72e34ff3efd1da3755e66fdd360a04d60cc8393f921b311449f7f55761ed6"},"schema_version":"1.0","source":{"id":"hep-th/0008222","kind":"arxiv","version":3}},"canonical_sha256":"3dcfb3ec3a587b1ce921f8dc04594b8668a5ff9117f5b6580ccdbd7bef5c2cf8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dcfb3ec3a587b1ce921f8dc04594b8668a5ff9117f5b6580ccdbd7bef5c2cf8","first_computed_at":"2026-05-18T00:37:10.714927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:10.714927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zTe5CS05Ln6AfkpDUXa002YxEtEsotBknus/NB/50j9QEufeiikIpnn1r2xh4obsPNDYj9/dqnKLvbtZ0lbLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:10.715876Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0008222","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddcba061abdc612e1a8632540dbb7bf35774b975052fc107b900e81829944c40","sha256:47def853506a6d5861f23c6ccc76978e8e1af7c14e2df45bc6c261bde729c8ae"],"state_sha256":"9c4528d9551ea6b18d5f5ddafaa4e473656a2705d576a062a97dbb2ad6a98357"}