{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z3TPPBQKHMT4OXZFJBOKF5KEAY","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":"2898a87d50639a0c6b73e9702841e53d68f4e8cd2e6d7bac49024e2a16aef34e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-02-22T19:33:12Z","title_canon_sha256":"1fc95b8a4b18b5ea5a00e81dfcc5bd00a1dd37203362fb497a96c5ad6df0c01d"},"schema_version":"1.0","source":{"id":"1102.4589","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4589","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4589v3","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4589","created_at":"2026-05-18T01:22:29Z"},{"alias_kind":"pith_short_12","alias_value":"Z3TPPBQKHMT4","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z3TPPBQKHMT4OXZF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z3TPPBQK","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:b28234ea2682fb27cbc13a3d5919f91f34ae579d9a1c7d070af07f124e839143","target":"graph","created_at":"2026-05-18T01:22:29Z","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":"Generalized Baumslag-Solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups. Forester proved (in \"On uniqueness of JSJ decompositions of finitely generated groups\", Comment. Math. Helv. 78 (2003) pp 740-751) that in most cases the defining graphs are cyclic JSJ decompositions, in the sense of Rips and Sela. Here we extend Forester's results to graphs of groups with vertex groups that can be either infinite cyclic or quadratically hanging surface groups.","authors_text":"Juan Alonso","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-02-22T19:33:12Z","title":"JSJ decompositions of Quadratic Baumslag-Solitar groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4589","kind":"arxiv","version":3},"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:c17ec2fb84a3e8618b8774fbcda09837c2755ef698ca2175bb123d625b3dfb98","target":"record","created_at":"2026-05-18T01:22:29Z","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":"2898a87d50639a0c6b73e9702841e53d68f4e8cd2e6d7bac49024e2a16aef34e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-02-22T19:33:12Z","title_canon_sha256":"1fc95b8a4b18b5ea5a00e81dfcc5bd00a1dd37203362fb497a96c5ad6df0c01d"},"schema_version":"1.0","source":{"id":"1102.4589","kind":"arxiv","version":3}},"canonical_sha256":"cee6f7860a3b27c75f25485ca2f5440632948f0011e38c93da2c28f6f6a6da84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cee6f7860a3b27c75f25485ca2f5440632948f0011e38c93da2c28f6f6a6da84","first_computed_at":"2026-05-18T01:22:29.104131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:29.104131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6rmNn5UmxKVZkf1UuZP74pVvPpp26xAAO48FTV79s9Ab8qIO8TqtFUP809uIU56JFRm75aPMr12MYsImZnWcAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:29.104581Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4589","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c17ec2fb84a3e8618b8774fbcda09837c2755ef698ca2175bb123d625b3dfb98","sha256:b28234ea2682fb27cbc13a3d5919f91f34ae579d9a1c7d070af07f124e839143"],"state_sha256":"9dc9b3d54a3495191d6ef2b46e7a98716cc991bbc64fb4f0a89ba4964969cb0a"}