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The ideal $\\mathcal{I}_{(a_{n})} $ of all precompact subsets of $(G, \\tau_{(a_{n}) } )$ defines a coarse structure on $G$ with base of entourages $\\{(x, y): x-y \\in P \\}$, $P\\in\\mathcal{I}_{(a_{n})}. $ We prove that $asdim \\ \\ (G, \\mathcal{I}_{(a_{n}) }) =\\infty $ for every non-trivial $T$-sequence $(a_{n})$ on "},"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":"1902.02320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2019-02-06T18:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"1c7cefb3f63c40873e795e45c3b0c688d453492f4e7d8c1facbf7fb8aad54fbf","abstract_canon_sha256":"4d9a9d3b772f90af8f909277ed27a94a3e8f9a170022135459349f096993c805"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:37.339110Z","signature_b64":"OLLagGVyGAErndX0gzSxp1ZhZtQfBh/6McIIAkhCaT6P+y5YJxk4Ut2E1gGLSU5N7IGDgORSwDmJJnohpTcJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cd85ea2d7916ffc689cab1f2a85f636ac171f610b5a01bf72412b2e398cc9e5","last_reissued_at":"2026-05-17T23:54:37.338584Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:37.338584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coarse structures on groups defined by $T$-sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"D. Dikranjan, I. Protasov","submitted_at":"2019-02-06T18:30:59Z","abstract_excerpt":"A sequence $(a_{n}) $ in an Abelian group is called a $T$-sequence if there exists a Hausdorff group topology on $G$ in which $(a_{n}) $ converges to $0$. For a $T$-sequence $(a_{n}) $, $\\tau_{(a_{n}) } $ denotes the strongest group topology on $G$ in which $(a_{n}) $ converges to $0$. The ideal $\\mathcal{I}_{(a_{n})} $ of all precompact subsets of $(G, \\tau_{(a_{n}) } )$ defines a coarse structure on $G$ with base of entourages $\\{(x, y): x-y \\in P \\}$, $P\\in\\mathcal{I}_{(a_{n})}. $ We prove that $asdim \\ \\ (G, \\mathcal{I}_{(a_{n}) }) =\\infty $ for every non-trivial $T$-sequence $(a_{n})$ on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02320","kind":"arxiv","version":1},"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":"1902.02320","created_at":"2026-05-17T23:54:37.338636+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.02320v1","created_at":"2026-05-17T23:54:37.338636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02320","created_at":"2026-05-17T23:54:37.338636+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTMF5IWXSFX7","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTMF5IWXSFX7Y2E4","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTMF5IWX","created_at":"2026-05-18T12:33:21.387695+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/LTMF5IWXSFX7Y2E4VMPSVBPWG2","json":"https://pith.science/pith/LTMF5IWXSFX7Y2E4VMPSVBPWG2.json","graph_json":"https://pith.science/api/pith-number/LTMF5IWXSFX7Y2E4VMPSVBPWG2/graph.json","events_json":"https://pith.science/api/pith-number/LTMF5IWXSFX7Y2E4VMPSVBPWG2/events.json","paper":"https://pith.science/paper/LTMF5IWX"},"agent_actions":{"view_html":"https://pith.science/pith/LTMF5IWXSFX7Y2E4VMPSVBPWG2","download_json":"https://pith.science/pith/LTMF5IWXSFX7Y2E4VMPSVBPWG2.json","view_paper":"https://pith.science/paper/LTMF5IWX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.02320&json=true","fetch_graph":"https://pith.science/api/pith-number/LTMF5IWXSFX7Y2E4VMPSVBPWG2/graph.json","fetch_events":"https://pith.science/api/pith-number/LTMF5IWXSFX7Y2E4VMPSVBPWG2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTMF5IWXSFX7Y2E4VMPSVBPWG2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTMF5IWXSFX7Y2E4VMPSVBPWG2/action/storage_attestation","attest_author":"https://pith.science/pith/LTMF5IWXSFX7Y2E4VMPSVBPWG2/action/author_attestation","sign_citation":"https://pith.science/pith/LTMF5IWXSFX7Y2E4VMPSVBPWG2/action/citation_signature","submit_replication":"https://pith.science/pith/LTMF5IWXSFX7Y2E4VMPSVBPWG2/action/replication_record"}},"created_at":"2026-05-17T23:54:37.338636+00:00","updated_at":"2026-05-17T23:54:37.338636+00:00"}