{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PCWDOV7Y2U2UMKNZJDA6I5CK2E","short_pith_number":"pith:PCWDOV7Y","schema_version":"1.0","canonical_sha256":"78ac3757f8d5354629b948c1e4744ad12416b7c8d362681bfde4ec3a6345477c","source":{"kind":"arxiv","id":"1610.06245","version":2},"attestation_state":"computed","paper":{"title":"Commensurability for certain right-angled Coxeter groups and geometric amalgams of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Anne Thomas, Emily Stark, Pallavi Dani","submitted_at":"2016-10-19T23:42:31Z","abstract_excerpt":"We give explicit necessary and sufficient conditions for the abstract commensurability of certain families of 1-ended, hyperbolic groups, namely right-angled Coxeter groups defined by generalized theta-graphs and cycles of generalized theta-graphs, and geometric amalgams of free groups whose JSJ graphs are trees of diameter at most 4. We also show that if a geometric amalgam of free groups has JSJ graph a tree, then it is commensurable to a right-angled Coxeter group, and give an example of a geometric amalgam of free groups which is not quasi-isometric (hence not commensurable) to any group w"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.06245","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-19T23:42:31Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"e67720c44bd64f0b8b0ece9d1744c8c8b409660be5e266964606fb54f0c0e695","abstract_canon_sha256":"be7ffa80e6711f489ae6be7896a557d4aae63a062f754eb8f9ebcf72777b0d64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:39.583979Z","signature_b64":"djaxRXU+CMTp3yBImakhuTrtuuAxXExRF9eUojkYEQogMusQ+4bJA8t3iverkaMNfBjE5J8ioISZShsEN1DvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78ac3757f8d5354629b948c1e4744ad12416b7c8d362681bfde4ec3a6345477c","last_reissued_at":"2026-05-18T00:33:39.583368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:39.583368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commensurability for certain right-angled Coxeter groups and geometric amalgams of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Anne Thomas, Emily Stark, Pallavi Dani","submitted_at":"2016-10-19T23:42:31Z","abstract_excerpt":"We give explicit necessary and sufficient conditions for the abstract commensurability of certain families of 1-ended, hyperbolic groups, namely right-angled Coxeter groups defined by generalized theta-graphs and cycles of generalized theta-graphs, and geometric amalgams of free groups whose JSJ graphs are trees of diameter at most 4. We also show that if a geometric amalgam of free groups has JSJ graph a tree, then it is commensurable to a right-angled Coxeter group, and give an example of a geometric amalgam of free groups which is not quasi-isometric (hence not commensurable) to any group w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06245","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1610.06245","created_at":"2026-05-18T00:33:39.583442+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06245v2","created_at":"2026-05-18T00:33:39.583442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06245","created_at":"2026-05-18T00:33:39.583442+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCWDOV7Y2U2U","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCWDOV7Y2U2UMKNZ","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCWDOV7Y","created_at":"2026-05-18T12:30:39.010887+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E","json":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E.json","graph_json":"https://pith.science/api/pith-number/PCWDOV7Y2U2UMKNZJDA6I5CK2E/graph.json","events_json":"https://pith.science/api/pith-number/PCWDOV7Y2U2UMKNZJDA6I5CK2E/events.json","paper":"https://pith.science/paper/PCWDOV7Y"},"agent_actions":{"view_html":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E","download_json":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E.json","view_paper":"https://pith.science/paper/PCWDOV7Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06245&json=true","fetch_graph":"https://pith.science/api/pith-number/PCWDOV7Y2U2UMKNZJDA6I5CK2E/graph.json","fetch_events":"https://pith.science/api/pith-number/PCWDOV7Y2U2UMKNZJDA6I5CK2E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E/action/storage_attestation","attest_author":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E/action/author_attestation","sign_citation":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E/action/citation_signature","submit_replication":"https://pith.science/pith/PCWDOV7Y2U2UMKNZJDA6I5CK2E/action/replication_record"}},"created_at":"2026-05-18T00:33:39.583442+00:00","updated_at":"2026-05-18T00:33:39.583442+00:00"}