{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:S6SNGRPHNZ37T3OOG34DBG74SB","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":"29e0d256f39473e93857aab1e85bc0456ed5b5c0ec0185ec40abc7dc72334bb0","cross_cats_sorted":["math.FA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-17T15:09:54Z","title_canon_sha256":"64c75ad7d60cf289b3e051680848096e6e3e0303893b961645c890d70bfffc4b"},"schema_version":"1.0","source":{"id":"1110.3692","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3692","created_at":"2026-05-18T03:28:20Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3692v2","created_at":"2026-05-18T03:28:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3692","created_at":"2026-05-18T03:28:20Z"},{"alias_kind":"pith_short_12","alias_value":"S6SNGRPHNZ37","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"S6SNGRPHNZ37T3OO","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"S6SNGRPH","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:8e58f7d1b27576f7aa56e9e58ab6db218e7fbc4d5d9e558eb19588f4a72651c9","target":"graph","created_at":"2026-05-18T03:28:20Z","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 prove a variant of the Titchmarsh convolution theorem for simply connected supersolvable Lie groups, namely we show that the convolution algebras of compactly supported continuous functions and compactly supported finite measures on such groups do not contain zero divisors. This can be also viewed as a topological version of the zero divisor conjecture of Kaplansky.","authors_text":"{\\L}ukasz Garncarek","cross_cats":["math.FA","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-17T15:09:54Z","title":"The problem of zero divisors in convolution algebras of supersolvable Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3692","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":"sha256:83cfa396335caaff7e3388f5229a8954b3223f3cd2127f3fe1508caac21e4e5a","target":"record","created_at":"2026-05-18T03:28:20Z","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":"29e0d256f39473e93857aab1e85bc0456ed5b5c0ec0185ec40abc7dc72334bb0","cross_cats_sorted":["math.FA","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-10-17T15:09:54Z","title_canon_sha256":"64c75ad7d60cf289b3e051680848096e6e3e0303893b961645c890d70bfffc4b"},"schema_version":"1.0","source":{"id":"1110.3692","kind":"arxiv","version":2}},"canonical_sha256":"97a4d345e76e77f9edce36f8309bfc904607220568cb637cae5171fb9e2d244e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97a4d345e76e77f9edce36f8309bfc904607220568cb637cae5171fb9e2d244e","first_computed_at":"2026-05-18T03:28:20.018523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:20.018523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6FU3poWs9/7cZG37HcaBlvUeQGrEutUyXNhKvL161nodhhgCZoMJ059Cqf9smiSX+5BUD+ZXj1qQw0l4QodGDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:20.019030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3692","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83cfa396335caaff7e3388f5229a8954b3223f3cd2127f3fe1508caac21e4e5a","sha256:8e58f7d1b27576f7aa56e9e58ab6db218e7fbc4d5d9e558eb19588f4a72651c9"],"state_sha256":"fcf6647a2aa448afa91a9c2d02c412405583a3d39aeb917e2ba8b548b973df93"}