{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GU2QW4IC46WBYRA3FXIAOHWHJY","short_pith_number":"pith:GU2QW4IC","schema_version":"1.0","canonical_sha256":"35350b7102e7ac1c441b2dd0071ec74e06281db559bd8c7c1760bf6b9cdafac8","source":{"kind":"arxiv","id":"1311.3268","version":2},"attestation_state":"computed","paper":{"title":"On the Expansion of Group-Based Lifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Alexandra Kolla, Karthekeyan Chandrasekaran, Naman Agarwal, Vivek Madan","submitted_at":"2013-11-13T19:44:04Z","abstract_excerpt":"A $k$-lift of an $n$-vertex base graph $G$ is a graph $H$ on $n\\times k$ vertices, where each vertex $v$ of $G$ is replaced by $k$ vertices $v_1,\\cdots{},v_k$ and each edge $(u,v)$ in $G$ is replaced by a matching representing a bijection $\\pi_{uv}$ so that the edges of $H$ are of the form $(u_i,v_{\\pi_{uv}(i)})$. Lifts have been studied as a means to efficiently construct expanders. In this work, we study lifts obtained from groups and group actions. We derive the spectrum of such lifts via the representation theory principles of the underlying group. Our main results are:\n  (1) There is a co"},"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":"1311.3268","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-11-13T19:44:04Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ee9dcd7679a39364044fea049f3cde9d58df32355cb8a87c4274b9663b42ef4d","abstract_canon_sha256":"4d622f70313b2219366b472c937cc486bcfb9ac6b4d0146861e329069722d61c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:48.425611Z","signature_b64":"R0pQi6XiWd/rZJPePHMy7IcknGJ+U7af2VBVzae8EKMhli+zBW0wmtvWXgUZ1UKN/8i1ekBEmYUibIrMFwqYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35350b7102e7ac1c441b2dd0071ec74e06281db559bd8c7c1760bf6b9cdafac8","last_reissued_at":"2026-05-18T00:54:48.425105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:48.425105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Expansion of Group-Based Lifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Alexandra Kolla, Karthekeyan Chandrasekaran, Naman Agarwal, Vivek Madan","submitted_at":"2013-11-13T19:44:04Z","abstract_excerpt":"A $k$-lift of an $n$-vertex base graph $G$ is a graph $H$ on $n\\times k$ vertices, where each vertex $v$ of $G$ is replaced by $k$ vertices $v_1,\\cdots{},v_k$ and each edge $(u,v)$ in $G$ is replaced by a matching representing a bijection $\\pi_{uv}$ so that the edges of $H$ are of the form $(u_i,v_{\\pi_{uv}(i)})$. Lifts have been studied as a means to efficiently construct expanders. In this work, we study lifts obtained from groups and group actions. We derive the spectrum of such lifts via the representation theory principles of the underlying group. Our main results are:\n  (1) There is a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3268","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":"1311.3268","created_at":"2026-05-18T00:54:48.425175+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.3268v2","created_at":"2026-05-18T00:54:48.425175+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3268","created_at":"2026-05-18T00:54:48.425175+00:00"},{"alias_kind":"pith_short_12","alias_value":"GU2QW4IC46WB","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GU2QW4IC46WBYRA3","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GU2QW4IC","created_at":"2026-05-18T12:27:45.050594+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/GU2QW4IC46WBYRA3FXIAOHWHJY","json":"https://pith.science/pith/GU2QW4IC46WBYRA3FXIAOHWHJY.json","graph_json":"https://pith.science/api/pith-number/GU2QW4IC46WBYRA3FXIAOHWHJY/graph.json","events_json":"https://pith.science/api/pith-number/GU2QW4IC46WBYRA3FXIAOHWHJY/events.json","paper":"https://pith.science/paper/GU2QW4IC"},"agent_actions":{"view_html":"https://pith.science/pith/GU2QW4IC46WBYRA3FXIAOHWHJY","download_json":"https://pith.science/pith/GU2QW4IC46WBYRA3FXIAOHWHJY.json","view_paper":"https://pith.science/paper/GU2QW4IC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.3268&json=true","fetch_graph":"https://pith.science/api/pith-number/GU2QW4IC46WBYRA3FXIAOHWHJY/graph.json","fetch_events":"https://pith.science/api/pith-number/GU2QW4IC46WBYRA3FXIAOHWHJY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GU2QW4IC46WBYRA3FXIAOHWHJY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GU2QW4IC46WBYRA3FXIAOHWHJY/action/storage_attestation","attest_author":"https://pith.science/pith/GU2QW4IC46WBYRA3FXIAOHWHJY/action/author_attestation","sign_citation":"https://pith.science/pith/GU2QW4IC46WBYRA3FXIAOHWHJY/action/citation_signature","submit_replication":"https://pith.science/pith/GU2QW4IC46WBYRA3FXIAOHWHJY/action/replication_record"}},"created_at":"2026-05-18T00:54:48.425175+00:00","updated_at":"2026-05-18T00:54:48.425175+00:00"}