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If a topological group $G$ contains an injective convergent sequence then $G$ is box $\\omega$-resolvable. Every infinite totally bounded topological group $G$ is partially box $n$-resolvable for each natural number $n$, and $G$ is box $\\kappa$-resolvable for each infinite cardinal $\\kappa, \\kappa<|G|$."},"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":"1511.01046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-11-02T09:36:52Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"1d36c524c79d0511940f93f6bd38ab93eb3f64e4ff60372841153f27509602ef","abstract_canon_sha256":"a07c18c2d20e13ce4252908d997794458e633699062f3cd75eb4272728a2ba77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:55.358024Z","signature_b64":"DbTl8FirOjwpXG4Wng18phSXXvow5e+6PUVUNr/ZDuuSzAYnlvy3Fuep5JzsKfFA0pRaUF6hoAd7XnPlAApbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"051a62056c410d4b5c12d334462c4e60e9e5285afa72e030bc126838d1ca7fd6","last_reissued_at":"2026-05-18T01:27:55.357184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:55.357184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Box Resolvability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.GN","authors_text":"Igor Protasov","submitted_at":"2015-11-02T09:36:52Z","abstract_excerpt":"We say that a topological group $G$ is partially box $\\kappa$-resolvable if there exist a dense subset $B$ of $G$ and a subset $A $ of $G$, $|A|=\\kappa$ such that the subsets $\\{ aB: a\\in A\\}$ are pairwise disjoint. If $G=AB$ then $G$ is called box $\\kappa$-resolvable. We prove two theorems. If a topological group $G$ contains an injective convergent sequence then $G$ is box $\\omega$-resolvable. Every infinite totally bounded topological group $G$ is partially box $n$-resolvable for each natural number $n$, and $G$ is box $\\kappa$-resolvable for each infinite cardinal $\\kappa, \\kappa<|G|$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01046","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":"1511.01046","created_at":"2026-05-18T01:27:55.357335+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.01046v1","created_at":"2026-05-18T01:27:55.357335+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01046","created_at":"2026-05-18T01:27:55.357335+00:00"},{"alias_kind":"pith_short_12","alias_value":"AUNGEBLMIEGU","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AUNGEBLMIEGUWXAS","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AUNGEBLM","created_at":"2026-05-18T12:29:10.953037+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/AUNGEBLMIEGUWXAS2M2EMLCOMD","json":"https://pith.science/pith/AUNGEBLMIEGUWXAS2M2EMLCOMD.json","graph_json":"https://pith.science/api/pith-number/AUNGEBLMIEGUWXAS2M2EMLCOMD/graph.json","events_json":"https://pith.science/api/pith-number/AUNGEBLMIEGUWXAS2M2EMLCOMD/events.json","paper":"https://pith.science/paper/AUNGEBLM"},"agent_actions":{"view_html":"https://pith.science/pith/AUNGEBLMIEGUWXAS2M2EMLCOMD","download_json":"https://pith.science/pith/AUNGEBLMIEGUWXAS2M2EMLCOMD.json","view_paper":"https://pith.science/paper/AUNGEBLM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.01046&json=true","fetch_graph":"https://pith.science/api/pith-number/AUNGEBLMIEGUWXAS2M2EMLCOMD/graph.json","fetch_events":"https://pith.science/api/pith-number/AUNGEBLMIEGUWXAS2M2EMLCOMD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AUNGEBLMIEGUWXAS2M2EMLCOMD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AUNGEBLMIEGUWXAS2M2EMLCOMD/action/storage_attestation","attest_author":"https://pith.science/pith/AUNGEBLMIEGUWXAS2M2EMLCOMD/action/author_attestation","sign_citation":"https://pith.science/pith/AUNGEBLMIEGUWXAS2M2EMLCOMD/action/citation_signature","submit_replication":"https://pith.science/pith/AUNGEBLMIEGUWXAS2M2EMLCOMD/action/replication_record"}},"created_at":"2026-05-18T01:27:55.357335+00:00","updated_at":"2026-05-18T01:27:55.357335+00:00"}