{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WOKMDXJZ6UTJSJR77MFQALD4UC","short_pith_number":"pith:WOKMDXJZ","schema_version":"1.0","canonical_sha256":"b394c1dd39f52699263ffb0b002c7ca0a0a2ff86205629532103df3919c29948","source":{"kind":"arxiv","id":"1607.07734","version":1},"attestation_state":"computed","paper":{"title":"On groups and simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Alexander Lubotzky, Ron Rosenthal, Zur Luria","submitted_at":"2016-07-26T14:50:51Z","abstract_excerpt":"The theory of $k$-regular graphs is closely related to group theory. Every $k$-regular, bipartite graph is a Schreier graph with respect to some group $G$, a set of generators $S$ (depending only on $k$) and a subgroup $H$. The goal of this paper is to begin to develop such a framework for $k$-regular simplicial complexes of general dimension $d$. Our approach does not directly generalize the concept of a Schreier graph, but still presents an extensive family of $k$-regular simplicial complexes as quotients of one universal object: the $k$-regular $d$-dimensional arboreal complex, which is its"},"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":"1607.07734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-26T14:50:51Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"22b6f54f69932286db818a3af9aa2cd26e9233c0ccc5a192f274e51dcaa40958","abstract_canon_sha256":"074c1d9a2392f7126696576ad17804df141772a4b944c6dd7fc7c860baedfe2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:25.390308Z","signature_b64":"dwwRRBKwvTKE5tFShK0SlfRmlgfFi53X9PTUaO50bS/Xj3xKDnHhQ06qcJX048+ed3F9chm5YEmG+OTrhWCECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b394c1dd39f52699263ffb0b002c7ca0a0a2ff86205629532103df3919c29948","last_reissued_at":"2026-05-18T01:10:25.389875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:25.389875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On groups and simplicial complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Alexander Lubotzky, Ron Rosenthal, Zur Luria","submitted_at":"2016-07-26T14:50:51Z","abstract_excerpt":"The theory of $k$-regular graphs is closely related to group theory. Every $k$-regular, bipartite graph is a Schreier graph with respect to some group $G$, a set of generators $S$ (depending only on $k$) and a subgroup $H$. The goal of this paper is to begin to develop such a framework for $k$-regular simplicial complexes of general dimension $d$. Our approach does not directly generalize the concept of a Schreier graph, but still presents an extensive family of $k$-regular simplicial complexes as quotients of one universal object: the $k$-regular $d$-dimensional arboreal complex, which is its"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07734","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":"1607.07734","created_at":"2026-05-18T01:10:25.389933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.07734v1","created_at":"2026-05-18T01:10:25.389933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07734","created_at":"2026-05-18T01:10:25.389933+00:00"},{"alias_kind":"pith_short_12","alias_value":"WOKMDXJZ6UTJ","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"WOKMDXJZ6UTJSJR7","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"WOKMDXJZ","created_at":"2026-05-18T12:30:51.357362+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/WOKMDXJZ6UTJSJR77MFQALD4UC","json":"https://pith.science/pith/WOKMDXJZ6UTJSJR77MFQALD4UC.json","graph_json":"https://pith.science/api/pith-number/WOKMDXJZ6UTJSJR77MFQALD4UC/graph.json","events_json":"https://pith.science/api/pith-number/WOKMDXJZ6UTJSJR77MFQALD4UC/events.json","paper":"https://pith.science/paper/WOKMDXJZ"},"agent_actions":{"view_html":"https://pith.science/pith/WOKMDXJZ6UTJSJR77MFQALD4UC","download_json":"https://pith.science/pith/WOKMDXJZ6UTJSJR77MFQALD4UC.json","view_paper":"https://pith.science/paper/WOKMDXJZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.07734&json=true","fetch_graph":"https://pith.science/api/pith-number/WOKMDXJZ6UTJSJR77MFQALD4UC/graph.json","fetch_events":"https://pith.science/api/pith-number/WOKMDXJZ6UTJSJR77MFQALD4UC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WOKMDXJZ6UTJSJR77MFQALD4UC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WOKMDXJZ6UTJSJR77MFQALD4UC/action/storage_attestation","attest_author":"https://pith.science/pith/WOKMDXJZ6UTJSJR77MFQALD4UC/action/author_attestation","sign_citation":"https://pith.science/pith/WOKMDXJZ6UTJSJR77MFQALD4UC/action/citation_signature","submit_replication":"https://pith.science/pith/WOKMDXJZ6UTJSJR77MFQALD4UC/action/replication_record"}},"created_at":"2026-05-18T01:10:25.389933+00:00","updated_at":"2026-05-18T01:10:25.389933+00:00"}