{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DTPOEYMEPFCEBJ4IS55MZPDWY2","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":"a39307eff02edc39981c5d989a5a07a14faed29a62b73c7faf1330dc66f43248","cross_cats_sorted":["math.GR","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-10-25T17:04:57Z","title_canon_sha256":"00c2b7ecc2990465f721329fc4dab29f528ac6b192b35c400f3c067ab806fc6d"},"schema_version":"1.0","source":{"id":"1010.5189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5189","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5189v1","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5189","created_at":"2026-05-18T04:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"DTPOEYMEPFCE","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DTPOEYMEPFCEBJ4I","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DTPOEYME","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:5d0cfae35dbbc396ed77926b3eb2dcec97e70922e802daf21453995a1596aa51","target":"graph","created_at":"2026-05-18T04:38:16Z","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 describe the structure of the automorphism groups of algebras Morita equivalent to the first Weyl algebra $ A_1 $. In particular, we give a geometric presentation for these groups in terms of amalgamated products, using the Bass-Serre theory of groups acting on graphs. A key r\\^ole in our approach is played by a transitive action of the automorphism group of the free algebra $ \\c < x, y > $ on the Calogero-Moser varieties $ \\CC_n $ defined in \\cite{BW}. Our results generalize well-known theorems of Dixmier and Makar-Limanov on automorphisms of $ A_1 $, answering an old question of Stafford ","authors_text":"Alimjon Eshmatov, Farkhod Eshmatov, Yuri Berest","cross_cats":["math.GR","math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-10-25T17:04:57Z","title":"Trees, Amalgams and Calogero-Moser Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5189","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":"sha256:9c9f74ca154cfd3fd11d153f3593055e9f5cec4b26331bbd6ee94ff7a0760972","target":"record","created_at":"2026-05-18T04:38:16Z","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":"a39307eff02edc39981c5d989a5a07a14faed29a62b73c7faf1330dc66f43248","cross_cats_sorted":["math.GR","math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2010-10-25T17:04:57Z","title_canon_sha256":"00c2b7ecc2990465f721329fc4dab29f528ac6b192b35c400f3c067ab806fc6d"},"schema_version":"1.0","source":{"id":"1010.5189","kind":"arxiv","version":1}},"canonical_sha256":"1cdee26184794440a788977accbc76c690c59d4a4a1681eec90b35053d2f5bc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cdee26184794440a788977accbc76c690c59d4a4a1681eec90b35053d2f5bc0","first_computed_at":"2026-05-18T04:38:16.586706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:16.586706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"udQHwmjalCUJCrnx1C6Gt07aUVgI9c2uqKLgc8ZlOkbvxj206EveMb77s1/pZ7HSPN7gk3+OsBhsbPFifdj6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:16.587213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c9f74ca154cfd3fd11d153f3593055e9f5cec4b26331bbd6ee94ff7a0760972","sha256:5d0cfae35dbbc396ed77926b3eb2dcec97e70922e802daf21453995a1596aa51"],"state_sha256":"6d809cfb7c06fbd514855f6fd7fa5ca3f30bc1dc283bcc1e68fd1d36f6319c25"}