{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7BEHFCHWTAJUEI5R4IZYCYZHO5","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":"8249cfd88f3c2d2ce99cfb09cbbc9df1632285a979504359f001c8d763ad0a89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-17T08:29:05Z","title_canon_sha256":"adc523f8735aba281771c10100627157d407e1397b2c3ca04695ea5c85e29560"},"schema_version":"1.0","source":{"id":"1807.06275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06275","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06275v1","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06275","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"7BEHFCHWTAJU","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7BEHFCHWTAJUEI5R","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7BEHFCHW","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:3859e76a8d832aac915950bd60d500cbe32b99997982cecb95f9a8546b876f99","target":"graph","created_at":"2026-05-18T00:10:33Z","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":"A finitely generated group $G$ acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag--Solitar group ($GBS$ group). We prove that a 1-knot group $G$ is $GBS$ group iff $G$ is a torus-knot group and describe all n-knot GBS groups for $n\\geqslant 3$.","authors_text":"Andrey Mamontov, Fedor Dudkin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-17T08:29:05Z","title":"On knot groups acting on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06275","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":"sha256:2693a6f1bf7d610e05268e799bf87b6938f94c1b15c2d30b2b9a1cba4adb00f6","target":"record","created_at":"2026-05-18T00:10:33Z","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":"8249cfd88f3c2d2ce99cfb09cbbc9df1632285a979504359f001c8d763ad0a89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-07-17T08:29:05Z","title_canon_sha256":"adc523f8735aba281771c10100627157d407e1397b2c3ca04695ea5c85e29560"},"schema_version":"1.0","source":{"id":"1807.06275","kind":"arxiv","version":1}},"canonical_sha256":"f8487288f698134223b1e2338163277744ddc7b352ee1df74f15249977c8310e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8487288f698134223b1e2338163277744ddc7b352ee1df74f15249977c8310e","first_computed_at":"2026-05-18T00:10:33.516368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:33.516368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hwvkALk0/L8kf9PJITY6SQQBaq0rbTlSJPUkvGDTCIEESPshdZFVWejJbyPK9wKnyAXkZBmOKDAupqw0FneuCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:33.516984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2693a6f1bf7d610e05268e799bf87b6938f94c1b15c2d30b2b9a1cba4adb00f6","sha256:3859e76a8d832aac915950bd60d500cbe32b99997982cecb95f9a8546b876f99"],"state_sha256":"1246cecf2c33cb822eb9ef240460f71e864076e13bee3ab566b225a791af4851"}