{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CUHMXFHTU2PJ7X6QH65NXIKT5N","short_pith_number":"pith:CUHMXFHT","canonical_record":{"source":{"id":"1112.1790","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-08T09:21:53Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"a1f6a10084b84b73e3deceb30df23dc6928d8405338696219e6db6b5fe69f5ff","abstract_canon_sha256":"05e79b4b17c525b8ad373be0cf4c8eaa2d9781901958555ae6ebaae2059ae5dc"},"schema_version":"1.0"},"canonical_sha256":"150ecb94f3a69e9fdfd03fbadba153eb45cbacd31ceb6334c4b5f49ae7abf22c","source":{"kind":"arxiv","id":"1112.1790","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1790","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1790v4","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1790","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"CUHMXFHTU2PJ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CUHMXFHTU2PJ7X6Q","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CUHMXFHT","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CUHMXFHTU2PJ7X6QH65NXIKT5N","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1790","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-08T09:21:53Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"a1f6a10084b84b73e3deceb30df23dc6928d8405338696219e6db6b5fe69f5ff","abstract_canon_sha256":"05e79b4b17c525b8ad373be0cf4c8eaa2d9781901958555ae6ebaae2059ae5dc"},"schema_version":"1.0"},"canonical_sha256":"150ecb94f3a69e9fdfd03fbadba153eb45cbacd31ceb6334c4b5f49ae7abf22c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.206061Z","signature_b64":"at/6/LLIfnmWk8a/vfDHL+oRBbXETJYgrUGKaucTStQvFYKe9iAgIvqO8sU53Vr6EHvQ5gqkDE+qcDrcPC/fAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"150ecb94f3a69e9fdfd03fbadba153eb45cbacd31ceb6334c4b5f49ae7abf22c","last_reissued_at":"2026-05-18T02:25:19.205666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.205666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1790","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":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LO27nLeRCDLxV58t4hbjIGJ7rcYevqYyw1KHoxGPseIjYYVjk+8mh/K1Y8IMoruniZEM0GVTFTtLXcjiJyclCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:41:41.260137Z"},"content_sha256":"d5d1cb31a4283105be84284beeeb458fcfea719837a4c5f11985ae535393b224","schema_version":"1.0","event_id":"sha256:d5d1cb31a4283105be84284beeeb458fcfea719837a4c5f11985ae535393b224"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CUHMXFHTU2PJ7X6QH65NXIKT5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finitely presented groups related to Kaplansky's Direct Finiteness Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Kate Juschenko, Ken Dykema, Timo Heister","submitted_at":"2011-12-08T09:21:53Z","abstract_excerpt":"We consider a family of finitely presented groups, called Universal Left Invertible Element (or ULIE) groups, that are universal for existence of one--sided invertible elements in a group ring K[G], where K is a field or a division ring. We show that for testing Kaplansky's Direct Finiteness Conjecture, it suffices to test it on ULIE groups, and we show that there is an infinite family of non-amenable ULIE groups. We consider the Invertibles Conjecture and we show that it is equivalent to a question about ULIE groups. We also show that for any group G, direct finiteness of K[ G x H ] for all f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1790","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":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1wpKMwo6W8Bc0dOzzeqf9FsRPEBOxGZIHYxejgJoqFhSWeGQQ6Z2XNx9bHDaVfBD9mSIWRdQ9c6W+ZCWVfpvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:41:41.260563Z"},"content_sha256":"688a24068383c3c0abe12e30610b29607e1a5c2b5337026e678eed81f69f34e3","schema_version":"1.0","event_id":"sha256:688a24068383c3c0abe12e30610b29607e1a5c2b5337026e678eed81f69f34e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUHMXFHTU2PJ7X6QH65NXIKT5N/bundle.json","state_url":"https://pith.science/pith/CUHMXFHTU2PJ7X6QH65NXIKT5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUHMXFHTU2PJ7X6QH65NXIKT5N/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":"2026-05-21T12:41:41Z","links":{"resolver":"https://pith.science/pith/CUHMXFHTU2PJ7X6QH65NXIKT5N","bundle":"https://pith.science/pith/CUHMXFHTU2PJ7X6QH65NXIKT5N/bundle.json","state":"https://pith.science/pith/CUHMXFHTU2PJ7X6QH65NXIKT5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUHMXFHTU2PJ7X6QH65NXIKT5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CUHMXFHTU2PJ7X6QH65NXIKT5N","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":"05e79b4b17c525b8ad373be0cf4c8eaa2d9781901958555ae6ebaae2059ae5dc","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-08T09:21:53Z","title_canon_sha256":"a1f6a10084b84b73e3deceb30df23dc6928d8405338696219e6db6b5fe69f5ff"},"schema_version":"1.0","source":{"id":"1112.1790","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1790","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1790v4","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1790","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"CUHMXFHTU2PJ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CUHMXFHTU2PJ7X6Q","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CUHMXFHT","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:688a24068383c3c0abe12e30610b29607e1a5c2b5337026e678eed81f69f34e3","target":"graph","created_at":"2026-05-18T02:25:19Z","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 consider a family of finitely presented groups, called Universal Left Invertible Element (or ULIE) groups, that are universal for existence of one--sided invertible elements in a group ring K[G], where K is a field or a division ring. We show that for testing Kaplansky's Direct Finiteness Conjecture, it suffices to test it on ULIE groups, and we show that there is an infinite family of non-amenable ULIE groups. We consider the Invertibles Conjecture and we show that it is equivalent to a question about ULIE groups. We also show that for any group G, direct finiteness of K[ G x H ] for all f","authors_text":"Kate Juschenko, Ken Dykema, Timo Heister","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-08T09:21:53Z","title":"Finitely presented groups related to Kaplansky's Direct Finiteness Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1790","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:d5d1cb31a4283105be84284beeeb458fcfea719837a4c5f11985ae535393b224","target":"record","created_at":"2026-05-18T02:25:19Z","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":"05e79b4b17c525b8ad373be0cf4c8eaa2d9781901958555ae6ebaae2059ae5dc","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-12-08T09:21:53Z","title_canon_sha256":"a1f6a10084b84b73e3deceb30df23dc6928d8405338696219e6db6b5fe69f5ff"},"schema_version":"1.0","source":{"id":"1112.1790","kind":"arxiv","version":4}},"canonical_sha256":"150ecb94f3a69e9fdfd03fbadba153eb45cbacd31ceb6334c4b5f49ae7abf22c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"150ecb94f3a69e9fdfd03fbadba153eb45cbacd31ceb6334c4b5f49ae7abf22c","first_computed_at":"2026-05-18T02:25:19.205666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:19.205666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"at/6/LLIfnmWk8a/vfDHL+oRBbXETJYgrUGKaucTStQvFYKe9iAgIvqO8sU53Vr6EHvQ5gqkDE+qcDrcPC/fAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:19.206061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1790","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5d1cb31a4283105be84284beeeb458fcfea719837a4c5f11985ae535393b224","sha256:688a24068383c3c0abe12e30610b29607e1a5c2b5337026e678eed81f69f34e3"],"state_sha256":"7e390bc8f240eca5c18fa24efc961eecea5b241c138c236a24d5ae9de1de2ec0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kwo+JEOlJiOizw5Xg0q4JCzm6pQvIG/2KP467O/0zfyK9MtukHyfDQk290zNo5geyIv62dDYWMBTW73n0ZXeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T12:41:41.262733Z","bundle_sha256":"f1c1ee86916cb314e01f605b1de957431b657a716402b05f7828fee9ee7a86b0"}}