{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:P3BRCGHEZTTO7AN32KRBDCCT43","short_pith_number":"pith:P3BRCGHE","schema_version":"1.0","canonical_sha256":"7ec31118e4cce6ef81bbd2a2118853e6e131ae611a72dbcd47dfe123dab72435","source":{"kind":"arxiv","id":"1806.05267","version":1},"attestation_state":"computed","paper":{"title":"A group with at least subexponential hyperlinear profile","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","quant-ph"],"primary_cat":"math.GR","authors_text":"William Slofstra","submitted_at":"2018-06-13T21:15:43Z","abstract_excerpt":"The hyperlinear profile of a group measures the growth rate of the dimension of unitary approximations to the group. We construct a finitely-presented group whose hyperlinear profile is at least subexponential, i.e. at least $\\exp(1/\\epsilon^{k})$ for some $0 < k < 1$. We use this group to give an example of a two-player non-local game requiring subexponential Hilbert space dimension to play near-perfectly."},"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":"1806.05267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-06-13T21:15:43Z","cross_cats_sorted":["math.OA","quant-ph"],"title_canon_sha256":"12dd6af29f45e69f4f870c2c932790e770438850d7f3e978294a71a941dcf9e9","abstract_canon_sha256":"7d6741b61dd8b2757d141cf4994e36c4531d4a21b2f23e477b0c14c7fe189b5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:16.592351Z","signature_b64":"x1oX51wHhEcZXJPJGl4W5hUab9UT3w6mbFEnodQcKIIs2KSUmjF1H8b6291bJRfCLQ4YPuqENysdUFlqnx03Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ec31118e4cce6ef81bbd2a2118853e6e131ae611a72dbcd47dfe123dab72435","last_reissued_at":"2026-05-18T00:13:16.591671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:16.591671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A group with at least subexponential hyperlinear profile","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","quant-ph"],"primary_cat":"math.GR","authors_text":"William Slofstra","submitted_at":"2018-06-13T21:15:43Z","abstract_excerpt":"The hyperlinear profile of a group measures the growth rate of the dimension of unitary approximations to the group. We construct a finitely-presented group whose hyperlinear profile is at least subexponential, i.e. at least $\\exp(1/\\epsilon^{k})$ for some $0 < k < 1$. We use this group to give an example of a two-player non-local game requiring subexponential Hilbert space dimension to play near-perfectly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05267","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":"1806.05267","created_at":"2026-05-18T00:13:16.591769+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.05267v1","created_at":"2026-05-18T00:13:16.591769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05267","created_at":"2026-05-18T00:13:16.591769+00:00"},{"alias_kind":"pith_short_12","alias_value":"P3BRCGHEZTTO","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"P3BRCGHEZTTO7AN3","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"P3BRCGHE","created_at":"2026-05-18T12:32:43.782077+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/P3BRCGHEZTTO7AN32KRBDCCT43","json":"https://pith.science/pith/P3BRCGHEZTTO7AN32KRBDCCT43.json","graph_json":"https://pith.science/api/pith-number/P3BRCGHEZTTO7AN32KRBDCCT43/graph.json","events_json":"https://pith.science/api/pith-number/P3BRCGHEZTTO7AN32KRBDCCT43/events.json","paper":"https://pith.science/paper/P3BRCGHE"},"agent_actions":{"view_html":"https://pith.science/pith/P3BRCGHEZTTO7AN32KRBDCCT43","download_json":"https://pith.science/pith/P3BRCGHEZTTO7AN32KRBDCCT43.json","view_paper":"https://pith.science/paper/P3BRCGHE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.05267&json=true","fetch_graph":"https://pith.science/api/pith-number/P3BRCGHEZTTO7AN32KRBDCCT43/graph.json","fetch_events":"https://pith.science/api/pith-number/P3BRCGHEZTTO7AN32KRBDCCT43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P3BRCGHEZTTO7AN32KRBDCCT43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P3BRCGHEZTTO7AN32KRBDCCT43/action/storage_attestation","attest_author":"https://pith.science/pith/P3BRCGHEZTTO7AN32KRBDCCT43/action/author_attestation","sign_citation":"https://pith.science/pith/P3BRCGHEZTTO7AN32KRBDCCT43/action/citation_signature","submit_replication":"https://pith.science/pith/P3BRCGHEZTTO7AN32KRBDCCT43/action/replication_record"}},"created_at":"2026-05-18T00:13:16.591769+00:00","updated_at":"2026-05-18T00:13:16.591769+00:00"}