{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OMU2HPVFVZXRNMY2ZRXBILFJAN","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":"a28278deee865fdb44ac533a64396378e703632c4b30947024cf076798ab3208","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-17T21:18:47Z","title_canon_sha256":"cca1332432214528698066a0cd3b7a40d73a27e9bc62768549aa783a2573412e"},"schema_version":"1.0","source":{"id":"2606.19606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.19606","created_at":"2026-06-19T16:12:30Z"},{"alias_kind":"arxiv_version","alias_value":"2606.19606v1","created_at":"2026-06-19T16:12:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19606","created_at":"2026-06-19T16:12:30Z"},{"alias_kind":"pith_short_12","alias_value":"OMU2HPVFVZXR","created_at":"2026-06-19T16:12:30Z"},{"alias_kind":"pith_short_16","alias_value":"OMU2HPVFVZXRNMY2","created_at":"2026-06-19T16:12:30Z"},{"alias_kind":"pith_short_8","alias_value":"OMU2HPVF","created_at":"2026-06-19T16:12:30Z"}],"graph_snapshots":[{"event_id":"sha256:7b953ca1daca87f7be8e50318b17c07e9b910d7f32662c7cf70d6ff14783891a","target":"graph","created_at":"2026-06-19T16:12:30Z","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/2606.19606/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be the fundamental group of a compact surface, a finitely generated free group, or more generally a finitely generated right-angled Artin group. We prove that the von Neumann dimension function of $\\mathrm{Out}(G)$ is valued in a discrete subgroup of $\\mathbb Q$. This is accomplished by establishing the Strong Atiyah Conjecture for a torsion-free subgroup of $\\mathrm{Out}(G)$ of finite index. We also prove that for every field $\\mathbb K$, there exists a torsion-free subgroup $H \\leqslant \\mathrm{Out}(G)$ of finite index such that $\\mathbb K[H]$ embeds into a division ring, and hence s","authors_text":"Andrew Ng, Sam P. Fisher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-17T21:18:47Z","title":"Outer automorphism groups and the Atiyah Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19606","kind":"arxiv","version":1},"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":"sha256:35a31ea5922ce1ec41f3b836af40f4db79e6302925f3aa47496ba158c6f0421b","target":"record","created_at":"2026-06-19T16:12:30Z","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":"a28278deee865fdb44ac533a64396378e703632c4b30947024cf076798ab3208","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-06-17T21:18:47Z","title_canon_sha256":"cca1332432214528698066a0cd3b7a40d73a27e9bc62768549aa783a2573412e"},"schema_version":"1.0","source":{"id":"2606.19606","kind":"arxiv","version":1}},"canonical_sha256":"7329a3bea5ae6f16b31acc6e142ca903455c17031cfc8d273c5a2a8f67746e9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7329a3bea5ae6f16b31acc6e142ca903455c17031cfc8d273c5a2a8f67746e9a","first_computed_at":"2026-06-19T16:12:30.033052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:30.033052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k8+hgCZJs+BbpNdmMA9syuh9qW0y3o2KCxwmsQx74oRm6t4ub6hyE3IOmC0f4H4hle1h8B2/XO4D853FGETeCQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:30.033412Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.19606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35a31ea5922ce1ec41f3b836af40f4db79e6302925f3aa47496ba158c6f0421b","sha256:7b953ca1daca87f7be8e50318b17c07e9b910d7f32662c7cf70d6ff14783891a"],"state_sha256":"1f24f845fb44015412d3dd2552bae24c5299cf1f710f6122cbc6107c9da05b00"}