{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OLRGK62DKZNBVTDEZ6PGPNAXBV","short_pith_number":"pith:OLRGK62D","canonical_record":{"source":{"id":"1504.08137","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-30T09:28:59Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b15d1ad5063b8c94492ca427b01b77208a60842625dc31c577513bd34db1c920","abstract_canon_sha256":"fa3234243fd5f28786cf04a6867d4da484971c4edbec260e65cee57935a25996"},"schema_version":"1.0"},"canonical_sha256":"72e2657b43565a1acc64cf9e67b4170d67043eb3e0df318e921eb13005128d29","source":{"kind":"arxiv","id":"1504.08137","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08137","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08137v3","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08137","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"pith_short_12","alias_value":"OLRGK62DKZNB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OLRGK62DKZNBVTDE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OLRGK62D","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OLRGK62DKZNBVTDEZ6PGPNAXBV","target":"record","payload":{"canonical_record":{"source":{"id":"1504.08137","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-30T09:28:59Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b15d1ad5063b8c94492ca427b01b77208a60842625dc31c577513bd34db1c920","abstract_canon_sha256":"fa3234243fd5f28786cf04a6867d4da484971c4edbec260e65cee57935a25996"},"schema_version":"1.0"},"canonical_sha256":"72e2657b43565a1acc64cf9e67b4170d67043eb3e0df318e921eb13005128d29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:21.274454Z","signature_b64":"hPY+FP4nkI0ph9hNtyexyMRj/rEqJY6yaD1ufoct6Hhpx6yKWwIDbu6hraU/LTzRFj0GPPMpe5jK4MKG3DjcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72e2657b43565a1acc64cf9e67b4170d67043eb3e0df318e921eb13005128d29","last_reissued_at":"2026-05-18T01:08:21.273759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:21.273759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.08137","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ej5PC3YDVpJrUCv3WCMkJUQs4DSEj6eBN9vR2RZI/TVVevlr1HSMbAjRVbwDE6RD1CBn058GvyMYfoAzJhEyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:37:46.210789Z"},"content_sha256":"93e17b427791e2b6abdb98b251e3558ca468810981011cdf52857f3b6f334d2f","schema_version":"1.0","event_id":"sha256:93e17b427791e2b6abdb98b251e3558ca468810981011cdf52857f3b6f334d2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OLRGK62DKZNBVTDEZ6PGPNAXBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive sofic entropy implies finite stabilizer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Tom Meyerovitch","submitted_at":"2015-04-30T09:28:59Z","abstract_excerpt":"We prove that for a measure preserving action of a sofic group with positive sofic entropy, the set of points with finite stabilizer have positive measure. This extends results of Weiss and Seward for amenable groups and free groups, respectively. It follows that the action of a sofic group on its subgroups by inner automorphisms has zero topological sofic entropy, and a faithful action with completely positive sofic entropy must be free."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08137","kind":"arxiv","version":3},"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":"2026-05-18T01:08:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJKLDG92VbASbfZp+hLhOuMFnz+M/2v31J2NVLD01av4X53CiFaJwfinmdq6moIHlVqutCQCcPppxdmgFVS1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:37:46.211122Z"},"content_sha256":"cf76db46edd1221cf106274aeb9b30d8aba41d2ab9bec8ee6c48dacfc863f2b8","schema_version":"1.0","event_id":"sha256:cf76db46edd1221cf106274aeb9b30d8aba41d2ab9bec8ee6c48dacfc863f2b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLRGK62DKZNBVTDEZ6PGPNAXBV/bundle.json","state_url":"https://pith.science/pith/OLRGK62DKZNBVTDEZ6PGPNAXBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLRGK62DKZNBVTDEZ6PGPNAXBV/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":"2026-06-24T08:37:46Z","links":{"resolver":"https://pith.science/pith/OLRGK62DKZNBVTDEZ6PGPNAXBV","bundle":"https://pith.science/pith/OLRGK62DKZNBVTDEZ6PGPNAXBV/bundle.json","state":"https://pith.science/pith/OLRGK62DKZNBVTDEZ6PGPNAXBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLRGK62DKZNBVTDEZ6PGPNAXBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OLRGK62DKZNBVTDEZ6PGPNAXBV","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":"fa3234243fd5f28786cf04a6867d4da484971c4edbec260e65cee57935a25996","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-30T09:28:59Z","title_canon_sha256":"b15d1ad5063b8c94492ca427b01b77208a60842625dc31c577513bd34db1c920"},"schema_version":"1.0","source":{"id":"1504.08137","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08137","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08137v3","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08137","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"pith_short_12","alias_value":"OLRGK62DKZNB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OLRGK62DKZNBVTDE","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OLRGK62D","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:cf76db46edd1221cf106274aeb9b30d8aba41d2ab9bec8ee6c48dacfc863f2b8","target":"graph","created_at":"2026-05-18T01:08:21Z","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 prove that for a measure preserving action of a sofic group with positive sofic entropy, the set of points with finite stabilizer have positive measure. This extends results of Weiss and Seward for amenable groups and free groups, respectively. It follows that the action of a sofic group on its subgroups by inner automorphisms has zero topological sofic entropy, and a faithful action with completely positive sofic entropy must be free.","authors_text":"Tom Meyerovitch","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-30T09:28:59Z","title":"Positive sofic entropy implies finite stabilizer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08137","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":"sha256:93e17b427791e2b6abdb98b251e3558ca468810981011cdf52857f3b6f334d2f","target":"record","created_at":"2026-05-18T01:08:21Z","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":"fa3234243fd5f28786cf04a6867d4da484971c4edbec260e65cee57935a25996","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-30T09:28:59Z","title_canon_sha256":"b15d1ad5063b8c94492ca427b01b77208a60842625dc31c577513bd34db1c920"},"schema_version":"1.0","source":{"id":"1504.08137","kind":"arxiv","version":3}},"canonical_sha256":"72e2657b43565a1acc64cf9e67b4170d67043eb3e0df318e921eb13005128d29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72e2657b43565a1acc64cf9e67b4170d67043eb3e0df318e921eb13005128d29","first_computed_at":"2026-05-18T01:08:21.273759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:21.273759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hPY+FP4nkI0ph9hNtyexyMRj/rEqJY6yaD1ufoct6Hhpx6yKWwIDbu6hraU/LTzRFj0GPPMpe5jK4MKG3DjcCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:21.274454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.08137","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93e17b427791e2b6abdb98b251e3558ca468810981011cdf52857f3b6f334d2f","sha256:cf76db46edd1221cf106274aeb9b30d8aba41d2ab9bec8ee6c48dacfc863f2b8"],"state_sha256":"c5c62b9578b2f576a194da9a63fbeb6fe1127aa38588ebee7466d15f27940875"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3EPltqGz6b6Pr5aLHpUizho7oiJKzNI5pAHGft2OpI7fVnKV3/DMqLa2kNK3eaTonA+HBJhuTzGsR7TEvyMDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:37:46.213268Z","bundle_sha256":"7cf18b9a1ae6c2e00fa7bed5ffe69dfd37659a360266756d5eab4a65a71b69ac"}}