{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZSRDZLFNCFXB4LRRAELPDAVY2W","short_pith_number":"pith:ZSRDZLFN","canonical_record":{"source":{"id":"1205.5090","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T04:30:36Z","cross_cats_sorted":[],"title_canon_sha256":"5509a74b5de1025fc8211a3214f9dc91059fc449807319aaafaf4c29c30c9d27","abstract_canon_sha256":"49b57f2804e893c898fb06b9a967cec463b08ba334e74d0e505f83477412105d"},"schema_version":"1.0"},"canonical_sha256":"cca23cacad116e1e2e310116f182b8d5a16fad4abf705bf6e3235429d5a0532a","source":{"kind":"arxiv","id":"1205.5090","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5090","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5090v4","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5090","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZSRDZLFNCFXB","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZSRDZLFNCFXB4LRR","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZSRDZLFN","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZSRDZLFNCFXB4LRRAELPDAVY2W","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5090","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T04:30:36Z","cross_cats_sorted":[],"title_canon_sha256":"5509a74b5de1025fc8211a3214f9dc91059fc449807319aaafaf4c29c30c9d27","abstract_canon_sha256":"49b57f2804e893c898fb06b9a967cec463b08ba334e74d0e505f83477412105d"},"schema_version":"1.0"},"canonical_sha256":"cca23cacad116e1e2e310116f182b8d5a16fad4abf705bf6e3235429d5a0532a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:25.277814Z","signature_b64":"lLEwoEVRVn6UdWlnVAF+F4Aoajy1WIdsk5o9OhSPvEA0xqW3qfyXZD1hf5FR5XbtmBL4p/glfTT498mfIYM0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cca23cacad116e1e2e310116f182b8d5a16fad4abf705bf6e3235429d5a0532a","last_reissued_at":"2026-05-18T02:29:25.277285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:25.277285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5090","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mFdESbUx1StnJNQ3tCj0l98hzBPAKAoTBN+nfN/oKJU418eSH40kgLQcaltcY1yL6r04BmFg+oQy5ABUa/cRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:57:26.151777Z"},"content_sha256":"272cf4d6bd786e860d4e00354e1731499732752c328c060e15bb3fa41b898934","schema_version":"1.0","event_id":"sha256:272cf4d6bd786e860d4e00354e1731499732752c328c060e15bb3fa41b898934"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZSRDZLFNCFXB4LRRAELPDAVY2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite entropy actions of free groups, rigidity of stabilizers, and a Howe-Moore type phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Brandon Seward","submitted_at":"2012-05-23T04:30:36Z","abstract_excerpt":"We study a notion of entropy for probability measure preserving actions of finitely generated free groups, called f-invariant entropy, introduced by Lewis Bowen. In the degenerate case, the f-invariant entropy is negative infinity. In this paper we investigate the qualitative consequences of having finite f-invariant entropy. We find three main properties of such actions. First, the stabilizers occurring in factors of such actions are highly restricted. Specifically, the stabilizer of almost every point must be either trivial or of finite index. Second, such actions are very chaotic in the sen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5090","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tFstYRiVPNQVqFyeutj1Spr1a+NnwFFIPPkT/+4zKScdtTn/JduBo1b2EXDHjo/H2bbnX57sJzmmB3LlilpgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:57:26.152507Z"},"content_sha256":"34e2dc61b549f67c9fd9691c312060842482e0a9827a89fe5ae6c5c773415fca","schema_version":"1.0","event_id":"sha256:34e2dc61b549f67c9fd9691c312060842482e0a9827a89fe5ae6c5c773415fca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZSRDZLFNCFXB4LRRAELPDAVY2W/bundle.json","state_url":"https://pith.science/pith/ZSRDZLFNCFXB4LRRAELPDAVY2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZSRDZLFNCFXB4LRRAELPDAVY2W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T20:57:26Z","links":{"resolver":"https://pith.science/pith/ZSRDZLFNCFXB4LRRAELPDAVY2W","bundle":"https://pith.science/pith/ZSRDZLFNCFXB4LRRAELPDAVY2W/bundle.json","state":"https://pith.science/pith/ZSRDZLFNCFXB4LRRAELPDAVY2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZSRDZLFNCFXB4LRRAELPDAVY2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZSRDZLFNCFXB4LRRAELPDAVY2W","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":"49b57f2804e893c898fb06b9a967cec463b08ba334e74d0e505f83477412105d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T04:30:36Z","title_canon_sha256":"5509a74b5de1025fc8211a3214f9dc91059fc449807319aaafaf4c29c30c9d27"},"schema_version":"1.0","source":{"id":"1205.5090","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5090","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5090v4","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5090","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZSRDZLFNCFXB","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZSRDZLFNCFXB4LRR","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZSRDZLFN","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:34e2dc61b549f67c9fd9691c312060842482e0a9827a89fe5ae6c5c773415fca","target":"graph","created_at":"2026-05-18T02:29:25Z","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 study a notion of entropy for probability measure preserving actions of finitely generated free groups, called f-invariant entropy, introduced by Lewis Bowen. In the degenerate case, the f-invariant entropy is negative infinity. In this paper we investigate the qualitative consequences of having finite f-invariant entropy. We find three main properties of such actions. First, the stabilizers occurring in factors of such actions are highly restricted. Specifically, the stabilizer of almost every point must be either trivial or of finite index. Second, such actions are very chaotic in the sen","authors_text":"Brandon Seward","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T04:30:36Z","title":"Finite entropy actions of free groups, rigidity of stabilizers, and a Howe-Moore type phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5090","kind":"arxiv","version":4},"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":"sha256:272cf4d6bd786e860d4e00354e1731499732752c328c060e15bb3fa41b898934","target":"record","created_at":"2026-05-18T02:29:25Z","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":"49b57f2804e893c898fb06b9a967cec463b08ba334e74d0e505f83477412105d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-23T04:30:36Z","title_canon_sha256":"5509a74b5de1025fc8211a3214f9dc91059fc449807319aaafaf4c29c30c9d27"},"schema_version":"1.0","source":{"id":"1205.5090","kind":"arxiv","version":4}},"canonical_sha256":"cca23cacad116e1e2e310116f182b8d5a16fad4abf705bf6e3235429d5a0532a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cca23cacad116e1e2e310116f182b8d5a16fad4abf705bf6e3235429d5a0532a","first_computed_at":"2026-05-18T02:29:25.277285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:25.277285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lLEwoEVRVn6UdWlnVAF+F4Aoajy1WIdsk5o9OhSPvEA0xqW3qfyXZD1hf5FR5XbtmBL4p/glfTT498mfIYM0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:25.277814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5090","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:272cf4d6bd786e860d4e00354e1731499732752c328c060e15bb3fa41b898934","sha256:34e2dc61b549f67c9fd9691c312060842482e0a9827a89fe5ae6c5c773415fca"],"state_sha256":"9769a4858dbf14fa61a47e1c06356249d676a74eb2eb805b40b14e4f51fc4cd7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0mT4SCrPbpyFg3jdG0y34cqjPmB6buasn/b/Dz1y4EPRvXkp8MNeInEaBge21sh3tioSu+MO0yFHO1u0BLrnBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:57:26.156568Z","bundle_sha256":"1d16597476ea48cda6583c9b85fd3a716b81759160c085a31fb3eed86e4103a4"}}