{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SOILXNM626PXLKIPUMEIOSNGBL","short_pith_number":"pith:SOILXNM6","schema_version":"1.0","canonical_sha256":"9390bbb59ed79f75a90fa3088749a60acae72f4e554cd0d0c2e232694ee22316","source":{"kind":"arxiv","id":"2503.10505","version":2},"attestation_state":"computed","paper":{"title":"Negative resolution to the $C^*$-algebraic Tarski problem","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.GR","math.LO"],"primary_cat":"math.OA","authors_text":"Christopher Schafhauser, Srivatsav Kunnawalkam Elayavalli","submitted_at":"2025-03-13T16:08:40Z","abstract_excerpt":"We compute the $K_1$-group of ultraproducts of unital, simple $C^*$-algebras with unique trace and strict comparison. As an application, we prove that the reduced free group $C^*$-algebras $C^*_r(F_m)$ and $C^*_r(F_n)$ are elementarily equivalent (i.e., have isomorphic ultrapowers) if and only if $m = n$. This settles in the negative the $C^*$-algebraic analogue of Tarski's 1945 problem for groups."},"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":"2503.10505","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OA","submitted_at":"2025-03-13T16:08:40Z","cross_cats_sorted":["math.GR","math.LO"],"title_canon_sha256":"6836727d7d686dcc6656aeb93aec9a2522a024abde0678d28029fbd1b39a0af2","abstract_canon_sha256":"69a475f69fa51d19e7df5ae2e9920e693b3776651a6250b7c911f77d25626131"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:50:32.571632Z","signature_b64":"zhh7y7/2Ki4pgzEC9CK9TjKQv74MtSitxD7j6jgwcrlZjgnieqMJjCh4uubWvHCjDOUwtTPtM4cm5PHywmlbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9390bbb59ed79f75a90fa3088749a60acae72f4e554cd0d0c2e232694ee22316","last_reissued_at":"2026-07-05T10:50:32.571034Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:50:32.571034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Negative resolution to the $C^*$-algebraic Tarski problem","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.GR","math.LO"],"primary_cat":"math.OA","authors_text":"Christopher Schafhauser, Srivatsav Kunnawalkam Elayavalli","submitted_at":"2025-03-13T16:08:40Z","abstract_excerpt":"We compute the $K_1$-group of ultraproducts of unital, simple $C^*$-algebras with unique trace and strict comparison. As an application, we prove that the reduced free group $C^*$-algebras $C^*_r(F_m)$ and $C^*_r(F_n)$ are elementarily equivalent (i.e., have isomorphic ultrapowers) if and only if $m = n$. This settles in the negative the $C^*$-algebraic analogue of Tarski's 1945 problem for groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.10505","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.10505/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":"2503.10505","created_at":"2026-07-05T10:50:32.571104+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.10505v2","created_at":"2026-07-05T10:50:32.571104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.10505","created_at":"2026-07-05T10:50:32.571104+00:00"},{"alias_kind":"pith_short_12","alias_value":"SOILXNM626PX","created_at":"2026-07-05T10:50:32.571104+00:00"},{"alias_kind":"pith_short_16","alias_value":"SOILXNM626PXLKIP","created_at":"2026-07-05T10:50:32.571104+00:00"},{"alias_kind":"pith_short_8","alias_value":"SOILXNM6","created_at":"2026-07-05T10:50:32.571104+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":5,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2505.18569","citing_title":"Strict comparison for twisted group C*-algebras","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2506.10902","citing_title":"Nuclear C*-algebras: 99 problems","ref_index":264,"is_internal_anchor":false},{"citing_arxiv_id":"2601.19758","citing_title":"Pureness and stable rank one for reduced twisted group $\\mathrm{C}^\\ast$-algebras of certain group extensions","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12737","citing_title":"Selfless inclusions arising from commensurator groups of hyperbolic groups","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2604.06982","citing_title":"Selfless reduced amalgamated free products and HNN extensions","ref_index":7,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL","json":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL.json","graph_json":"https://pith.science/api/pith-number/SOILXNM626PXLKIPUMEIOSNGBL/graph.json","events_json":"https://pith.science/api/pith-number/SOILXNM626PXLKIPUMEIOSNGBL/events.json","paper":"https://pith.science/paper/SOILXNM6"},"agent_actions":{"view_html":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL","download_json":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL.json","view_paper":"https://pith.science/paper/SOILXNM6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.10505&json=true","fetch_graph":"https://pith.science/api/pith-number/SOILXNM626PXLKIPUMEIOSNGBL/graph.json","fetch_events":"https://pith.science/api/pith-number/SOILXNM626PXLKIPUMEIOSNGBL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL/action/storage_attestation","attest_author":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL/action/author_attestation","sign_citation":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL/action/citation_signature","submit_replication":"https://pith.science/pith/SOILXNM626PXLKIPUMEIOSNGBL/action/replication_record"}},"created_at":"2026-07-05T10:50:32.571104+00:00","updated_at":"2026-07-05T10:50:32.571104+00:00"}