{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:JYM42OJUPI4LLRVRBALNCS7KMD","short_pith_number":"pith:JYM42OJU","schema_version":"1.0","canonical_sha256":"4e19cd39347a38b5c6b10816d14bea60ddc66fe98143311c3527aa81fce9dba5","source":{"kind":"arxiv","id":"2502.14970","version":3},"attestation_state":"computed","paper":{"title":"The Diophantine problem in Thompson's group F","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alex Levine, Luna Elliott","submitted_at":"2025-02-20T19:06:30Z","abstract_excerpt":"We show that the Diophantine problem in Thompson's group F is undecidable. Our proof uses the facts that F has finite commutator width and rank 2 abelianisation, then uses similar arguments used by B\\\"uchi and Senger and Ciobanu and Garreta to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable."},"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":"2502.14970","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-02-20T19:06:30Z","cross_cats_sorted":[],"title_canon_sha256":"7fd5fa31104afda8bfeb238b349b142e13fee55351c4508e4821911e9b1d5964","abstract_canon_sha256":"bc33dd71ee0f056c646e509a645c59063f1bafc90f44256c4a7201297404eed1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:45.036599Z","signature_b64":"I09RcVd1cUkcbQXGh0XguveTPcWlgNfeccsZcpOF2rqT66NWRuFfXzPLYDhD3qpOeb0+igzGSWqwYtdgTAsPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e19cd39347a38b5c6b10816d14bea60ddc66fe98143311c3527aa81fce9dba5","last_reissued_at":"2026-06-23T01:12:45.035959Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:45.035959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Diophantine problem in Thompson's group F","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alex Levine, Luna Elliott","submitted_at":"2025-02-20T19:06:30Z","abstract_excerpt":"We show that the Diophantine problem in Thompson's group F is undecidable. Our proof uses the facts that F has finite commutator width and rank 2 abelianisation, then uses similar arguments used by B\\\"uchi and Senger and Ciobanu and Garreta to show the Diophantine problem in free groups and monoids with abelianisation constraints is undecidable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.14970","kind":"arxiv","version":3},"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/2502.14970/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":"2502.14970","created_at":"2026-06-23T01:12:45.036033+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.14970v3","created_at":"2026-06-23T01:12:45.036033+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.14970","created_at":"2026-06-23T01:12:45.036033+00:00"},{"alias_kind":"pith_short_12","alias_value":"JYM42OJUPI4L","created_at":"2026-06-23T01:12:45.036033+00:00"},{"alias_kind":"pith_short_16","alias_value":"JYM42OJUPI4LLRVR","created_at":"2026-06-23T01:12:45.036033+00:00"},{"alias_kind":"pith_short_8","alias_value":"JYM42OJU","created_at":"2026-06-23T01:12:45.036033+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/JYM42OJUPI4LLRVRBALNCS7KMD","json":"https://pith.science/pith/JYM42OJUPI4LLRVRBALNCS7KMD.json","graph_json":"https://pith.science/api/pith-number/JYM42OJUPI4LLRVRBALNCS7KMD/graph.json","events_json":"https://pith.science/api/pith-number/JYM42OJUPI4LLRVRBALNCS7KMD/events.json","paper":"https://pith.science/paper/JYM42OJU"},"agent_actions":{"view_html":"https://pith.science/pith/JYM42OJUPI4LLRVRBALNCS7KMD","download_json":"https://pith.science/pith/JYM42OJUPI4LLRVRBALNCS7KMD.json","view_paper":"https://pith.science/paper/JYM42OJU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.14970&json=true","fetch_graph":"https://pith.science/api/pith-number/JYM42OJUPI4LLRVRBALNCS7KMD/graph.json","fetch_events":"https://pith.science/api/pith-number/JYM42OJUPI4LLRVRBALNCS7KMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JYM42OJUPI4LLRVRBALNCS7KMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JYM42OJUPI4LLRVRBALNCS7KMD/action/storage_attestation","attest_author":"https://pith.science/pith/JYM42OJUPI4LLRVRBALNCS7KMD/action/author_attestation","sign_citation":"https://pith.science/pith/JYM42OJUPI4LLRVRBALNCS7KMD/action/citation_signature","submit_replication":"https://pith.science/pith/JYM42OJUPI4LLRVRBALNCS7KMD/action/replication_record"}},"created_at":"2026-06-23T01:12:45.036033+00:00","updated_at":"2026-06-23T01:12:45.036033+00:00"}