{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YNUG7DAQKMQQ66JYQF45CSQGYH","short_pith_number":"pith:YNUG7DAQ","canonical_record":{"source":{"id":"1304.1856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-06T05:02:10Z","cross_cats_sorted":[],"title_canon_sha256":"a592f489fafb0274dfb8ead046f8ea5f27387bbaaefc0c058d4c7b5ad4553669","abstract_canon_sha256":"2bfce16b9e7bae8b617eb50835b23b9030e0ad67d8f9bdb123b87deb16b3d398"},"schema_version":"1.0"},"canonical_sha256":"c3686f8c1053210f79388179d14a06c1e8c9cd8066a8b6b2088ffe5f793bebd3","source":{"kind":"arxiv","id":"1304.1856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1856","created_at":"2026-05-18T03:28:44Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1856v1","created_at":"2026-05-18T03:28:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1856","created_at":"2026-05-18T03:28:44Z"},{"alias_kind":"pith_short_12","alias_value":"YNUG7DAQKMQQ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YNUG7DAQKMQQ66JY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YNUG7DAQ","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YNUG7DAQKMQQ66JYQF45CSQGYH","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-06T05:02:10Z","cross_cats_sorted":[],"title_canon_sha256":"a592f489fafb0274dfb8ead046f8ea5f27387bbaaefc0c058d4c7b5ad4553669","abstract_canon_sha256":"2bfce16b9e7bae8b617eb50835b23b9030e0ad67d8f9bdb123b87deb16b3d398"},"schema_version":"1.0"},"canonical_sha256":"c3686f8c1053210f79388179d14a06c1e8c9cd8066a8b6b2088ffe5f793bebd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:44.959227Z","signature_b64":"B9ZqNfQC1TRNSnJXa71FRMKEO3W3gQ8kA4nYoPuoVTdgC5vor+qiTaxwY/SIijjpfeskpttys2fhQSuscaTsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3686f8c1053210f79388179d14a06c1e8c9cd8066a8b6b2088ffe5f793bebd3","last_reissued_at":"2026-05-18T03:28:44.958595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:44.958595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1856","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sN1KULEf5xYPRpLaG9XyD1r5Dc1AhaCYrg7rAsvniMeTA/mhWbAc5ONzHWlhT7V+l0YkCSl2OYnqb6HivMRgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:44:49.901059Z"},"content_sha256":"855a3790e753ec128c4c8928166db4c0f3126363bcd9f8ff6e3d0e9885052214","schema_version":"1.0","event_id":"sha256:855a3790e753ec128c4c8928166db4c0f3126363bcd9f8ff6e3d0e9885052214"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YNUG7DAQKMQQ66JYQF45CSQGYH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The existence of free non-cyclic subgroups in weakly locally finite division rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bui Xuan Hai, Nguyen Kim Ngoc","submitted_at":"2013-04-06T05:02:10Z","abstract_excerpt":"In this paper we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains free non-cyclic subgroups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1856","kind":"arxiv","version":1},"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":"2026-05-18T03:28:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6tdFmj5l3eKjpqmLKf4eGDM0mDpv0gw3pjm5u3cRc1YTdXt7/aNPkpL5+vlW6/wHQa6WZf1JqwW0AW4JwlGHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:44:49.901423Z"},"content_sha256":"cf33f9e9487752eca66e6c4c72465acfaa7d6f79f149ef4715285bd1364bcb8c","schema_version":"1.0","event_id":"sha256:cf33f9e9487752eca66e6c4c72465acfaa7d6f79f149ef4715285bd1364bcb8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YNUG7DAQKMQQ66JYQF45CSQGYH/bundle.json","state_url":"https://pith.science/pith/YNUG7DAQKMQQ66JYQF45CSQGYH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YNUG7DAQKMQQ66JYQF45CSQGYH/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":"2026-06-12T08:44:49Z","links":{"resolver":"https://pith.science/pith/YNUG7DAQKMQQ66JYQF45CSQGYH","bundle":"https://pith.science/pith/YNUG7DAQKMQQ66JYQF45CSQGYH/bundle.json","state":"https://pith.science/pith/YNUG7DAQKMQQ66JYQF45CSQGYH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YNUG7DAQKMQQ66JYQF45CSQGYH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YNUG7DAQKMQQ66JYQF45CSQGYH","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":"2bfce16b9e7bae8b617eb50835b23b9030e0ad67d8f9bdb123b87deb16b3d398","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-06T05:02:10Z","title_canon_sha256":"a592f489fafb0274dfb8ead046f8ea5f27387bbaaefc0c058d4c7b5ad4553669"},"schema_version":"1.0","source":{"id":"1304.1856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1856","created_at":"2026-05-18T03:28:44Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1856v1","created_at":"2026-05-18T03:28:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1856","created_at":"2026-05-18T03:28:44Z"},{"alias_kind":"pith_short_12","alias_value":"YNUG7DAQKMQQ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YNUG7DAQKMQQ66JY","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YNUG7DAQ","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:cf33f9e9487752eca66e6c4c72465acfaa7d6f79f149ef4715285bd1364bcb8c","target":"graph","created_at":"2026-05-18T03:28:44Z","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":"In this paper we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains free non-cyclic subgroups.","authors_text":"Bui Xuan Hai, Nguyen Kim Ngoc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-06T05:02:10Z","title":"The existence of free non-cyclic subgroups in weakly locally finite division rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1856","kind":"arxiv","version":1},"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":"sha256:855a3790e753ec128c4c8928166db4c0f3126363bcd9f8ff6e3d0e9885052214","target":"record","created_at":"2026-05-18T03:28:44Z","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":"2bfce16b9e7bae8b617eb50835b23b9030e0ad67d8f9bdb123b87deb16b3d398","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-04-06T05:02:10Z","title_canon_sha256":"a592f489fafb0274dfb8ead046f8ea5f27387bbaaefc0c058d4c7b5ad4553669"},"schema_version":"1.0","source":{"id":"1304.1856","kind":"arxiv","version":1}},"canonical_sha256":"c3686f8c1053210f79388179d14a06c1e8c9cd8066a8b6b2088ffe5f793bebd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3686f8c1053210f79388179d14a06c1e8c9cd8066a8b6b2088ffe5f793bebd3","first_computed_at":"2026-05-18T03:28:44.958595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:44.958595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B9ZqNfQC1TRNSnJXa71FRMKEO3W3gQ8kA4nYoPuoVTdgC5vor+qiTaxwY/SIijjpfeskpttys2fhQSuscaTsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:44.959227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:855a3790e753ec128c4c8928166db4c0f3126363bcd9f8ff6e3d0e9885052214","sha256:cf33f9e9487752eca66e6c4c72465acfaa7d6f79f149ef4715285bd1364bcb8c"],"state_sha256":"854e8c5f95ad4f4b1b6939c634e72d5ef1175f866b8b2f068b85a14c1b21ee5d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L48A2qkvUtFd8cbqcBS6HF1qwN1wnJckwtAknv5aObOQ5Q0Lcn1Gw6WuIjY4IYaCcwwI4nqqdljvpRghm5YYAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:44:49.903926Z","bundle_sha256":"52139a351e85889312d596cb1bbe0d6ac5680c156fad6cdaa822da5532595fe3"}}