{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7C2MQWDEERKSHILUKE5EFZQQTV","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":"c7b2a541e1ab59d9d7ea70aeaa5eb00d8bbad23f6fb5cb3e3a8e2c49faac0856","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-18T16:25:29Z","title_canon_sha256":"376eb24ba210b79d4faefb132c4368f45d66c5169233f25ad47411bd431f1d67"},"schema_version":"1.0","source":{"id":"1509.05688","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05688","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05688v1","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05688","created_at":"2026-05-18T01:32:42Z"},{"alias_kind":"pith_short_12","alias_value":"7C2MQWDEERKS","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7C2MQWDEERKSHILU","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7C2MQWDE","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:4076129f7fff1da86891c2b717e056c207123170972b233e6a17ce3ffe275633","target":"graph","created_at":"2026-05-18T01:32:42Z","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 give a necessary and sufficient condition for the fundamental group of a finite graph of groups with infinite cyclic edge groups to be acylindrically hyperbolic, from which it follows that a finitely generated group splitting over Z cannot be simple. We also give a necessary and sufficient condition (when the vertex groups are torsion free) for the fundamental group to be balanced, where a group is said to be balanced if $x^m$ conjugate to $x^n$ implies that $|m|=|n|$ for all infinite order elements $x$.","authors_text":"J.O. Button","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-18T16:25:29Z","title":"Balanced groups and graphs of groups with infinite cyclic edge groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05688","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":"sha256:4aa42a614c8de073bb9c7ad7d83454ae46bdcb522535f255675b47906fca9d6c","target":"record","created_at":"2026-05-18T01:32:42Z","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":"c7b2a541e1ab59d9d7ea70aeaa5eb00d8bbad23f6fb5cb3e3a8e2c49faac0856","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-18T16:25:29Z","title_canon_sha256":"376eb24ba210b79d4faefb132c4368f45d66c5169233f25ad47411bd431f1d67"},"schema_version":"1.0","source":{"id":"1509.05688","kind":"arxiv","version":1}},"canonical_sha256":"f8b4c85864245523a174513a42e6109d5cc9554e7acecf492430b697d1888e73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8b4c85864245523a174513a42e6109d5cc9554e7acecf492430b697d1888e73","first_computed_at":"2026-05-18T01:32:42.602135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:42.602135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1aMwMfP1hUKmFftrIyFkx4Z6VUovX6PycuXsF/Hzdn8RqPhH44g+sUtm9dXl6yI6TrvAQr/baKjKsIfmZY+oAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:42.602574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05688","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aa42a614c8de073bb9c7ad7d83454ae46bdcb522535f255675b47906fca9d6c","sha256:4076129f7fff1da86891c2b717e056c207123170972b233e6a17ce3ffe275633"],"state_sha256":"82ca5d79e9a9c10e804212e8c02972f262022065827e7463072a4580e9fc8195"}