{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:73RLRHMJNA7UQRKPOKSZDPUGAF","short_pith_number":"pith:73RLRHMJ","schema_version":"1.0","canonical_sha256":"fee2b89d89683f48454f72a591be8601524de7ecfaead5dcb385ccefa5da13d5","source":{"kind":"arxiv","id":"1809.10332","version":1},"attestation_state":"computed","paper":{"title":"Commensurability growths of algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Daniel Studenmund, Khalid Bou-Rabee, Tasho Kaletha","submitted_at":"2018-09-27T03:34:59Z","abstract_excerpt":"Fixing a subgroup $\\Gamma$ in a group $G$, the full commensurability growth function assigns to each $n$ the cardinality of the set of subgroups $\\Delta$ of $G$ with $[\\Gamma: \\Gamma \\cap \\Delta][\\Delta : \\Gamma \\cap \\Delta] \\leq n$. For pairs $\\Gamma \\leq G$, where $G$ is a Chevalley group scheme defined over $\\mathbb{Z}$ and $\\Gamma$ is an arithmetic lattice in $G$, we give precise estimates for the full commensurability growth, relating it to subgroup growth and a computable invariant that depends only on $G$."},"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":"1809.10332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-09-27T03:34:59Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"d3d85cd6bf7a5648e45fe3de9f2b2ca87c68c87e488d6f34c0c0197b90dbc6c8","abstract_canon_sha256":"c2f86dcb06da7ef1a45117d327459c9b86019d82aa34681a45a453bae66f1650"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:38.590760Z","signature_b64":"5MzrAC600vm0VJmbs+a47F2BRN5ZllHc25CElt5GSBYEb61CpIcg3Z2Hu7rdzrwRugZK7ygr2GSIAskqf2fiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fee2b89d89683f48454f72a591be8601524de7ecfaead5dcb385ccefa5da13d5","last_reissued_at":"2026-05-18T00:04:38.590398Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:38.590398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commensurability growths of algebraic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Daniel Studenmund, Khalid Bou-Rabee, Tasho Kaletha","submitted_at":"2018-09-27T03:34:59Z","abstract_excerpt":"Fixing a subgroup $\\Gamma$ in a group $G$, the full commensurability growth function assigns to each $n$ the cardinality of the set of subgroups $\\Delta$ of $G$ with $[\\Gamma: \\Gamma \\cap \\Delta][\\Delta : \\Gamma \\cap \\Delta] \\leq n$. For pairs $\\Gamma \\leq G$, where $G$ is a Chevalley group scheme defined over $\\mathbb{Z}$ and $\\Gamma$ is an arithmetic lattice in $G$, we give precise estimates for the full commensurability growth, relating it to subgroup growth and a computable invariant that depends only on $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10332","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":"1809.10332","created_at":"2026-05-18T00:04:38.590452+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.10332v1","created_at":"2026-05-18T00:04:38.590452+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10332","created_at":"2026-05-18T00:04:38.590452+00:00"},{"alias_kind":"pith_short_12","alias_value":"73RLRHMJNA7U","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"73RLRHMJNA7UQRKP","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"73RLRHMJ","created_at":"2026-05-18T12:32:11.075285+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/73RLRHMJNA7UQRKPOKSZDPUGAF","json":"https://pith.science/pith/73RLRHMJNA7UQRKPOKSZDPUGAF.json","graph_json":"https://pith.science/api/pith-number/73RLRHMJNA7UQRKPOKSZDPUGAF/graph.json","events_json":"https://pith.science/api/pith-number/73RLRHMJNA7UQRKPOKSZDPUGAF/events.json","paper":"https://pith.science/paper/73RLRHMJ"},"agent_actions":{"view_html":"https://pith.science/pith/73RLRHMJNA7UQRKPOKSZDPUGAF","download_json":"https://pith.science/pith/73RLRHMJNA7UQRKPOKSZDPUGAF.json","view_paper":"https://pith.science/paper/73RLRHMJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.10332&json=true","fetch_graph":"https://pith.science/api/pith-number/73RLRHMJNA7UQRKPOKSZDPUGAF/graph.json","fetch_events":"https://pith.science/api/pith-number/73RLRHMJNA7UQRKPOKSZDPUGAF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/73RLRHMJNA7UQRKPOKSZDPUGAF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/73RLRHMJNA7UQRKPOKSZDPUGAF/action/storage_attestation","attest_author":"https://pith.science/pith/73RLRHMJNA7UQRKPOKSZDPUGAF/action/author_attestation","sign_citation":"https://pith.science/pith/73RLRHMJNA7UQRKPOKSZDPUGAF/action/citation_signature","submit_replication":"https://pith.science/pith/73RLRHMJNA7UQRKPOKSZDPUGAF/action/replication_record"}},"created_at":"2026-05-18T00:04:38.590452+00:00","updated_at":"2026-05-18T00:04:38.590452+00:00"}