{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:R6X2YCE4THZDXIGY7KRIVD6T4K","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":"3af7d9d032aa6c998fff3822496412fa852ee776fdb99c4605275b0bdc17ed86","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T15:15:57Z","title_canon_sha256":"2934368f1ac67b3e49e98e3c80dba5a25f3e2d41d50e6fb5afb1853f37f62378"},"schema_version":"1.0","source":{"id":"2606.20347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20347","created_at":"2026-06-19T16:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20347v1","created_at":"2026-06-19T16:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20347","created_at":"2026-06-19T16:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"R6X2YCE4THZD","created_at":"2026-06-19T16:13:09Z"},{"alias_kind":"pith_short_16","alias_value":"R6X2YCE4THZDXIGY","created_at":"2026-06-19T16:13:09Z"},{"alias_kind":"pith_short_8","alias_value":"R6X2YCE4","created_at":"2026-06-19T16:13:09Z"}],"graph_snapshots":[{"event_id":"sha256:c0d9da39e4a6f5a13efff7a6233735dc50024343bd731f3e0a8a6a4346a663b2","target":"graph","created_at":"2026-06-19T16:13:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.20347/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural networks learn features that reflect the hierarchical, multi-scale structure of natural data. Synthetic datasets used to evaluate interpretability methods typically lack this structure, limiting their value as realistic toy models. To close this gap, we introduce a family of synthetic datasets consisting of hierarchical functions defined on critical mean-field percolation clusters embedded in a high-dimensional data space. The percolation data consists of sparse, low-dimensional fractal clusters with a power-law size distribution. Latent variables modeling a taxonomic hierarchy generate","authors_text":"Aryeh Brill, Tom Ingebretsen Carlson","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T15:15:57Z","title":"Critical Percolation as a Synthetic Data Model for Interpretability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20347","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":"sha256:218a30174c61096b2217d59050309ed73782dc3d232f016eb306430d2fcc03c4","target":"record","created_at":"2026-06-19T16:13:09Z","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":"3af7d9d032aa6c998fff3822496412fa852ee776fdb99c4605275b0bdc17ed86","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T15:15:57Z","title_canon_sha256":"2934368f1ac67b3e49e98e3c80dba5a25f3e2d41d50e6fb5afb1853f37f62378"},"schema_version":"1.0","source":{"id":"2606.20347","kind":"arxiv","version":1}},"canonical_sha256":"8fafac089c99f23ba0d8faa28a8fd3e2935129ee39ef20962b9a4066993937cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fafac089c99f23ba0d8faa28a8fd3e2935129ee39ef20962b9a4066993937cd","first_computed_at":"2026-06-19T16:13:09.519757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:13:09.519757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SptaJwyDDORygTfkIigsfNnh7wRjFalgpxkI6LyVsTIG7FfG/UGtULPq5ZH+QppHylD0Ce91wU9Qldlf0UcjCQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:13:09.520106Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:218a30174c61096b2217d59050309ed73782dc3d232f016eb306430d2fcc03c4","sha256:c0d9da39e4a6f5a13efff7a6233735dc50024343bd731f3e0a8a6a4346a663b2"],"state_sha256":"ef48611f87d31e93bc2fdac649f02bedb9fdd1a1369c00a1e52781952d07e97b"}