{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RR5XGRSVNBKRKLT4YFDMZWLQ4P","short_pith_number":"pith:RR5XGRSV","canonical_record":{"source":{"id":"1202.0571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-02T22:03:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a672fef09c7f7f4dca06de4c5dcfc3dd557e3eef88a790a9cbd76154b83ce48d","abstract_canon_sha256":"6f68200179884b92ba1f704af478b7731506dbbe50d6572a6e52af1a9d5bf1f4"},"schema_version":"1.0"},"canonical_sha256":"8c7b7346556855152e7cc146ccd970e3fadad2573b582d85f5cf22138060851c","source":{"kind":"arxiv","id":"1202.0571","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0571","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0571v2","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0571","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"RR5XGRSVNBKR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RR5XGRSVNBKRKLT4","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RR5XGRSV","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RR5XGRSVNBKRKLT4YFDMZWLQ4P","target":"record","payload":{"canonical_record":{"source":{"id":"1202.0571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-02T22:03:28Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a672fef09c7f7f4dca06de4c5dcfc3dd557e3eef88a790a9cbd76154b83ce48d","abstract_canon_sha256":"6f68200179884b92ba1f704af478b7731506dbbe50d6572a6e52af1a9d5bf1f4"},"schema_version":"1.0"},"canonical_sha256":"8c7b7346556855152e7cc146ccd970e3fadad2573b582d85f5cf22138060851c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:26.730679Z","signature_b64":"RL6jurdD8ojdkupJhVf9DtWrCWxQx6LHrZrmXD8Z8zAJxi+lu4H+1gIsFw+ps8EOMy3zw6dGwV3IOEzpVavJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8c7b7346556855152e7cc146ccd970e3fadad2573b582d85f5cf22138060851c","last_reissued_at":"2026-05-18T04:02:26.730249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:26.730249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.0571","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lrhI7Gsw0E/fvsAXRvHGIqXB9OFFFM9yyW7V+OkEaOVfHIUlFxHu9KqMXyotVKv0CufsaP3gDs1X/rEJtHyGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:24:41.110193Z"},"content_sha256":"bc8dda162636e3b26eacd206f826cbf957ee54ac122610b61f3b8a95faf8bdca","schema_version":"1.0","event_id":"sha256:bc8dda162636e3b26eacd206f826cbf957ee54ac122610b61f3b8a95faf8bdca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RR5XGRSVNBKRKLT4YFDMZWLQ4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measure free factors of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Juan Alonso","submitted_at":"2012-02-02T22:03:28Z","abstract_excerpt":"Measure free factors are a generalization of the notion of free factors of a group, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by D. Gaboriau."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0571","kind":"arxiv","version":2},"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":"2026-05-18T04:02:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JsxXVq0GVfKItWlaTf3t1MYOlC80pAEO0kXOgerzABvwbJZH0tEfKj+crh/Y9x9fnw1Tk5WEaCCmuYJ3TzcFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T20:24:41.110545Z"},"content_sha256":"8ec03fa94613cb32aba33e85077631390d4d073c15ab4cd223f63a5a286d8278","schema_version":"1.0","event_id":"sha256:8ec03fa94613cb32aba33e85077631390d4d073c15ab4cd223f63a5a286d8278"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RR5XGRSVNBKRKLT4YFDMZWLQ4P/bundle.json","state_url":"https://pith.science/pith/RR5XGRSVNBKRKLT4YFDMZWLQ4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RR5XGRSVNBKRKLT4YFDMZWLQ4P/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":"2026-06-20T20:24:41Z","links":{"resolver":"https://pith.science/pith/RR5XGRSVNBKRKLT4YFDMZWLQ4P","bundle":"https://pith.science/pith/RR5XGRSVNBKRKLT4YFDMZWLQ4P/bundle.json","state":"https://pith.science/pith/RR5XGRSVNBKRKLT4YFDMZWLQ4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RR5XGRSVNBKRKLT4YFDMZWLQ4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RR5XGRSVNBKRKLT4YFDMZWLQ4P","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":"6f68200179884b92ba1f704af478b7731506dbbe50d6572a6e52af1a9d5bf1f4","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-02T22:03:28Z","title_canon_sha256":"a672fef09c7f7f4dca06de4c5dcfc3dd557e3eef88a790a9cbd76154b83ce48d"},"schema_version":"1.0","source":{"id":"1202.0571","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0571","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0571v2","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0571","created_at":"2026-05-18T04:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"RR5XGRSVNBKR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RR5XGRSVNBKRKLT4","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RR5XGRSV","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:8ec03fa94613cb32aba33e85077631390d4d073c15ab4cd223f63a5a286d8278","target":"graph","created_at":"2026-05-18T04:02:26Z","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":"Measure free factors are a generalization of the notion of free factors of a group, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by D. Gaboriau.","authors_text":"Juan Alonso","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-02T22:03:28Z","title":"Measure free factors of free groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0571","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:bc8dda162636e3b26eacd206f826cbf957ee54ac122610b61f3b8a95faf8bdca","target":"record","created_at":"2026-05-18T04:02:26Z","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":"6f68200179884b92ba1f704af478b7731506dbbe50d6572a6e52af1a9d5bf1f4","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-02-02T22:03:28Z","title_canon_sha256":"a672fef09c7f7f4dca06de4c5dcfc3dd557e3eef88a790a9cbd76154b83ce48d"},"schema_version":"1.0","source":{"id":"1202.0571","kind":"arxiv","version":2}},"canonical_sha256":"8c7b7346556855152e7cc146ccd970e3fadad2573b582d85f5cf22138060851c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c7b7346556855152e7cc146ccd970e3fadad2573b582d85f5cf22138060851c","first_computed_at":"2026-05-18T04:02:26.730249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:26.730249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RL6jurdD8ojdkupJhVf9DtWrCWxQx6LHrZrmXD8Z8zAJxi+lu4H+1gIsFw+ps8EOMy3zw6dGwV3IOEzpVavJCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:26.730679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0571","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc8dda162636e3b26eacd206f826cbf957ee54ac122610b61f3b8a95faf8bdca","sha256:8ec03fa94613cb32aba33e85077631390d4d073c15ab4cd223f63a5a286d8278"],"state_sha256":"35f65a82f9acb950e4fec2dd914797895f0dc1390cef7b9ea110a675bbb477b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lLwTCyAFpbhB9/7mz0MSvmmaNwWIG3FJ2h9tHpNHgNX4N1g/XWGs9H70KhS24uSVNRvNx0zS4k8IjMEXMPAPBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T20:24:41.112343Z","bundle_sha256":"9848f2d92ab5431f7bc17cdad735119b58045e5225af2a9935a0018af244d6ce"}}