{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TU7F6SFMUZYRWCYLEPBLZSRNSC","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":"9af9e65ce3b31d1d7650dbf59a79eedd5f77ae46609feb109d7de1dfcd16a477","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-28T22:50:20Z","title_canon_sha256":"2fd1addc1d9f2d6ea31517bea6ef5288cd3aa9269d01640d821b6c201b24358b"},"schema_version":"1.0","source":{"id":"1507.07981","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07981","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07981v2","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07981","created_at":"2026-05-18T01:36:06Z"},{"alias_kind":"pith_short_12","alias_value":"TU7F6SFMUZYR","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TU7F6SFMUZYRWCYL","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TU7F6SFM","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:32a622c1f44cb5b28e91e3e12c1db6703a927705df322f9240057ecb71868958","target":"graph","created_at":"2026-05-18T01:36:06Z","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":"Rigid actions have zero Rokhlin entropy and nonpositive sofic entropy. Because rigidity is a stable orbit-equivalence invariant, this provides the first example of an essentially free, ergodic, probability-measure-preserving action of the free group that has nonpositive sofic entropy and any essentially free action stably-orbit-equivalent to it also has nonpositive sofic entropy.","authors_text":"Lewis Bowen","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-28T22:50:20Z","title":"Rigid actions have zero entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07981","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":"sha256:013a16c06fdb460ae3bf2a18c508c2d2c9729b5bd39c5f2f8f5db5753f1e20dd","target":"record","created_at":"2026-05-18T01:36:06Z","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":"9af9e65ce3b31d1d7650dbf59a79eedd5f77ae46609feb109d7de1dfcd16a477","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-28T22:50:20Z","title_canon_sha256":"2fd1addc1d9f2d6ea31517bea6ef5288cd3aa9269d01640d821b6c201b24358b"},"schema_version":"1.0","source":{"id":"1507.07981","kind":"arxiv","version":2}},"canonical_sha256":"9d3e5f48aca6711b0b0b23c2bcca2d90a23f9f197b49cc43813c998f7c678a2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d3e5f48aca6711b0b0b23c2bcca2d90a23f9f197b49cc43813c998f7c678a2b","first_computed_at":"2026-05-18T01:36:06.702802Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:06.702802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"koVlpGUR1OuvXHM0wBr01H4qvcgm/r5iuGj7Wr46VomC3lfOuGH3edjgiKDQMi64N7KkIy1EGbv2ageACl15Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:06.703225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07981","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:013a16c06fdb460ae3bf2a18c508c2d2c9729b5bd39c5f2f8f5db5753f1e20dd","sha256:32a622c1f44cb5b28e91e3e12c1db6703a927705df322f9240057ecb71868958"],"state_sha256":"7ec86a687807040994a4b242b1e0fe00cdc4a14ec409f06e8211d5fe1f0db026"}