{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YWVXJDW7RLUC6KP4N325ZY74DN","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":"2c725caef2c91bad83d48836a5906cd693e47dc9c3525c8cfd1b233e46c9e6d5","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-01-25T18:09:48Z","title_canon_sha256":"44dca75bdfd04431d9642c6b1b5afa5c72f757d1b162f29120faad7b9d5a1530"},"schema_version":"1.0","source":{"id":"2401.14363","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.14363","created_at":"2026-07-05T08:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"2401.14363v2","created_at":"2026-07-05T08:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.14363","created_at":"2026-07-05T08:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"YWVXJDW7RLUC","created_at":"2026-07-05T08:32:35Z"},{"alias_kind":"pith_short_16","alias_value":"YWVXJDW7RLUC6KP4","created_at":"2026-07-05T08:32:35Z"},{"alias_kind":"pith_short_8","alias_value":"YWVXJDW7","created_at":"2026-07-05T08:32:35Z"}],"graph_snapshots":[{"event_id":"sha256:2a61ad31aa583fb75823c8c5a8648be001ab0d08b9d16e3b03ea166bbe60961b","target":"graph","created_at":"2026-07-05T08:32:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.14363/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a structure theorem for stable functions on amenable groups, which extends the arithmetic regularity lemma for stable subsets of finite groups. Given a group $G$, a function $f\\colon G\\to [-1,1]$ is called stable if the binary function $f(x\\cdot y)$ is stable in the sense of continuous logic. Roughly speaking, our main result says that if $G$ is amenable, then any stable function on $G$ is almost constant on all translates of a unitary Bohr neighborhood in $G$ of bounded complexity. The proof uses ingredients from topological dynamics and continuous model theory. We also prove several","authors_text":"Anand Pillay, Gabriel Conant","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-01-25T18:09:48Z","title":"An analytic version of stable arithmetic regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.14363","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":"sha256:59bd07aa44baf18f45680c90e04a01dd488272b21a5ea54e925ef39c5ea18e7b","target":"record","created_at":"2026-07-05T08:32:35Z","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":"2c725caef2c91bad83d48836a5906cd693e47dc9c3525c8cfd1b233e46c9e6d5","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-01-25T18:09:48Z","title_canon_sha256":"44dca75bdfd04431d9642c6b1b5afa5c72f757d1b162f29120faad7b9d5a1530"},"schema_version":"1.0","source":{"id":"2401.14363","kind":"arxiv","version":2}},"canonical_sha256":"c5ab748edf8ae82f29fc6ef5dce3fc1b6da0487e5bfd5235f43ac6b4cb228858","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5ab748edf8ae82f29fc6ef5dce3fc1b6da0487e5bfd5235f43ac6b4cb228858","first_computed_at":"2026-07-05T08:32:35.241390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:32:35.241390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bkGemGLK9LieMDiGPH/AWXDJeZplMO1mTnl2s405u8Pvhv3luTfwm9XeT8hrb+Lv5aBtX3LnnmFRi8bRz+gXDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:32:35.241916Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.14363","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59bd07aa44baf18f45680c90e04a01dd488272b21a5ea54e925ef39c5ea18e7b","sha256:2a61ad31aa583fb75823c8c5a8648be001ab0d08b9d16e3b03ea166bbe60961b"],"state_sha256":"c7e0863f1b1ca4d703ba0c514bbcb1f8389073c1bcd15fe9d5911349811afe53"}