{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:5DI2M45YZB4H23X5MEA63RY543","short_pith_number":"pith:5DI2M45Y","schema_version":"1.0","canonical_sha256":"e8d1a673b8c8787d6efd6101edc71de6c7431c9b6ae6b37dc6fbd330c3ce6dcd","source":{"kind":"arxiv","id":"math/0306011","version":4},"attestation_state":"computed","paper":{"title":"An Uncountable Family of Non Orbit Equivalent Actions of $\\Bbb F_n$","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Damien Gaboriau, Sorin Popa","submitted_at":"2003-05-31T18:22:40Z","abstract_excerpt":"For each $2 \\leq n \\leq \\infty$, we construct an uncountable family of free ergodic measure preserving actions $\\alpha_t$ of the free group $\\Bbb F_n$ on the standard probability space $(X, \\mu)$ such that any two are non orbit equivalent (in fact, not even stably orbit equivalent). These actions are all ``rigid'' (in the sense of [Po01]), with the II$_1$ factors $L^\\infty(X, \\mu)\\rtimes_{\\alpha_t} \\Bbb F_n$ mutually non stably isomorphic (even non-stably isomorphic) and in the class $\\Cal H\\Cal T_{_{s}}.$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0306011","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2003-05-31T18:22:40Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"ae0f2cadf6361ce3dab3ad568c4d5bb51196313d6f4c5033a34831277e834ff7","abstract_canon_sha256":"f2a51916538e4524d74b11e9a8f6503c890dde2643fc194dfe36742d462bc5c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:21.185602Z","signature_b64":"00D1IeCGUNb1z1GMkNaX+WFPQ5HNPC+VpxpsHXKG/GxQd4TS0iIJ66nsf4kNj5Ovw8BcHiwC2dh8ukblMyiMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8d1a673b8c8787d6efd6101edc71de6c7431c9b6ae6b37dc6fbd330c3ce6dcd","last_reissued_at":"2026-07-04T14:37:21.185224Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:21.185224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Uncountable Family of Non Orbit Equivalent Actions of $\\Bbb F_n$","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Damien Gaboriau, Sorin Popa","submitted_at":"2003-05-31T18:22:40Z","abstract_excerpt":"For each $2 \\leq n \\leq \\infty$, we construct an uncountable family of free ergodic measure preserving actions $\\alpha_t$ of the free group $\\Bbb F_n$ on the standard probability space $(X, \\mu)$ such that any two are non orbit equivalent (in fact, not even stably orbit equivalent). These actions are all ``rigid'' (in the sense of [Po01]), with the II$_1$ factors $L^\\infty(X, \\mu)\\rtimes_{\\alpha_t} \\Bbb F_n$ mutually non stably isomorphic (even non-stably isomorphic) and in the class $\\Cal H\\Cal T_{_{s}}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306011","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0306011/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0306011","created_at":"2026-07-04T14:37:21.185281+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0306011v4","created_at":"2026-07-04T14:37:21.185281+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0306011","created_at":"2026-07-04T14:37:21.185281+00:00"},{"alias_kind":"pith_short_12","alias_value":"5DI2M45YZB4H","created_at":"2026-07-04T14:37:21.185281+00:00"},{"alias_kind":"pith_short_16","alias_value":"5DI2M45YZB4H23X5","created_at":"2026-07-04T14:37:21.185281+00:00"},{"alias_kind":"pith_short_8","alias_value":"5DI2M45Y","created_at":"2026-07-04T14:37:21.185281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543","json":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543.json","graph_json":"https://pith.science/api/pith-number/5DI2M45YZB4H23X5MEA63RY543/graph.json","events_json":"https://pith.science/api/pith-number/5DI2M45YZB4H23X5MEA63RY543/events.json","paper":"https://pith.science/paper/5DI2M45Y"},"agent_actions":{"view_html":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543","download_json":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543.json","view_paper":"https://pith.science/paper/5DI2M45Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0306011&json=true","fetch_graph":"https://pith.science/api/pith-number/5DI2M45YZB4H23X5MEA63RY543/graph.json","fetch_events":"https://pith.science/api/pith-number/5DI2M45YZB4H23X5MEA63RY543/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543/action/storage_attestation","attest_author":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543/action/author_attestation","sign_citation":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543/action/citation_signature","submit_replication":"https://pith.science/pith/5DI2M45YZB4H23X5MEA63RY543/action/replication_record"}},"created_at":"2026-07-04T14:37:21.185281+00:00","updated_at":"2026-07-04T14:37:21.185281+00:00"}