{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KNFQILEBYUAHRRMMDKF5F66MFJ","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":"cc010c214bf1e3ae2bb8260365e4b91667cc9b8891fb385dbefb338062b258ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-20T21:46:44Z","title_canon_sha256":"8a95f1688def5b38f09f213eb83a6b1d2f4b3de6b500aa8a40b1dbbf509e7a03"},"schema_version":"1.0","source":{"id":"2605.21761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.21761","created_at":"2026-05-22T01:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"2605.21761v1","created_at":"2026-05-22T01:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.21761","created_at":"2026-05-22T01:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"KNFQILEBYUAH","created_at":"2026-05-22T01:03:30Z"},{"alias_kind":"pith_short_16","alias_value":"KNFQILEBYUAHRRMM","created_at":"2026-05-22T01:03:30Z"},{"alias_kind":"pith_short_8","alias_value":"KNFQILEB","created_at":"2026-05-22T01:03:30Z"}],"graph_snapshots":[{"event_id":"sha256:53f59b2cfdcba33290a87d38819a1a34b4a6b7205474f47390fc19f6eab742b9","target":"graph","created_at":"2026-05-22T01:03:30Z","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/2605.21761/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that every $C^2$ minimal action of Thompson group $T$ on the circle is ergodic with respect to the Lebesgue measure. If such action is not minimal then the Lebesgue measure of the exceptional minimal set is zero.","authors_text":"Klaudiusz Czudek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-20T21:46:44Z","title":"Ergodicity of $C^2$ minimal actions of Thompson group $T$ on the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21761","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":"sha256:571785e7b5b4a8104bb4a8a1c9b1e8ade34334a90025c85366f670129e28e3c7","target":"record","created_at":"2026-05-22T01:03:30Z","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":"cc010c214bf1e3ae2bb8260365e4b91667cc9b8891fb385dbefb338062b258ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-20T21:46:44Z","title_canon_sha256":"8a95f1688def5b38f09f213eb83a6b1d2f4b3de6b500aa8a40b1dbbf509e7a03"},"schema_version":"1.0","source":{"id":"2605.21761","kind":"arxiv","version":1}},"canonical_sha256":"534b042c81c50078c58c1a8bd2fbcc2a5b0a30020a90b97c9ae69957b1fd08d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"534b042c81c50078c58c1a8bd2fbcc2a5b0a30020a90b97c9ae69957b1fd08d7","first_computed_at":"2026-05-22T01:03:30.843635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:30.843635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z5RO1TLh6/EK+30szVime9H4cV4ialOLGqGPh1/IyijCDtxltixcr6fnj93JdeRBsSRTw+qc5sM/tC/hZ5cLAQ==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:30.844294Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.21761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:571785e7b5b4a8104bb4a8a1c9b1e8ade34334a90025c85366f670129e28e3c7","sha256:53f59b2cfdcba33290a87d38819a1a34b4a6b7205474f47390fc19f6eab742b9"],"state_sha256":"6dbc114907feb75c2c7e29cdca71c0bb461d8f1474542bce3306b13f898365f2"}