{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:54B4HL56XY7CO6RGW6OKV62F75","short_pith_number":"pith:54B4HL56","schema_version":"1.0","canonical_sha256":"ef03c3afbebe3e277a26b79caafb45ff7fd92325939bc59f3a51bf1ed29d3ad3","source":{"kind":"arxiv","id":"1706.02756","version":1},"attestation_state":"computed","paper":{"title":"On Some Applications of Group Representation Theory to Algebraic Problems Related to the Congruence Principle for Equivariant Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hao-pin Wu, Mikhail Muzychuk, Zalman Balanov","submitted_at":"2017-06-08T20:28:06Z","abstract_excerpt":"Given a finite group $G$ and two unitary $G$-representations $V$ and $W$, possible restrictions on Brouwer degrees of equivariant maps between representation spheres $S(V)$ and $S(W)$ are usually expressed in a form of congruences modulo the greatest common divisor of lengths of orbits in $S(V)$ (denoted $\\alpha(V)$). Effective applications of these congruences is limited by answers to the following questions: (i) under which conditions, is ${\\alpha}(V)>1$? and (ii) does there exist an equivariant map with the degree easy to calculate? In the present paper, we address both questions. We show t"},"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":"1706.02756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-06-08T20:28:06Z","cross_cats_sorted":[],"title_canon_sha256":"467a3e7325eaab35cbe2dd8b67023b12ba02b5d1875c252ba711a0ae38ecb882","abstract_canon_sha256":"ccbb198563a2d712e87a8388baa7bb0f501eebf09189f6ec501013721ff6dc66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:41.068027Z","signature_b64":"v8Brd+ctmNZHyrw/XAhxslbWi4utyI9HsBPUyDAEIpy5/TOyF+Siy4UuBy3l8aCTUCt/yciVNEksTQuHLTapBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef03c3afbebe3e277a26b79caafb45ff7fd92325939bc59f3a51bf1ed29d3ad3","last_reissued_at":"2026-05-18T00:42:41.067434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:41.067434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Some Applications of Group Representation Theory to Algebraic Problems Related to the Congruence Principle for Equivariant Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hao-pin Wu, Mikhail Muzychuk, Zalman Balanov","submitted_at":"2017-06-08T20:28:06Z","abstract_excerpt":"Given a finite group $G$ and two unitary $G$-representations $V$ and $W$, possible restrictions on Brouwer degrees of equivariant maps between representation spheres $S(V)$ and $S(W)$ are usually expressed in a form of congruences modulo the greatest common divisor of lengths of orbits in $S(V)$ (denoted $\\alpha(V)$). Effective applications of these congruences is limited by answers to the following questions: (i) under which conditions, is ${\\alpha}(V)>1$? and (ii) does there exist an equivariant map with the degree easy to calculate? In the present paper, we address both questions. We show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02756","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":"1706.02756","created_at":"2026-05-18T00:42:41.067538+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.02756v1","created_at":"2026-05-18T00:42:41.067538+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02756","created_at":"2026-05-18T00:42:41.067538+00:00"},{"alias_kind":"pith_short_12","alias_value":"54B4HL56XY7C","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"54B4HL56XY7CO6RG","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"54B4HL56","created_at":"2026-05-18T12:31:00.734936+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/54B4HL56XY7CO6RGW6OKV62F75","json":"https://pith.science/pith/54B4HL56XY7CO6RGW6OKV62F75.json","graph_json":"https://pith.science/api/pith-number/54B4HL56XY7CO6RGW6OKV62F75/graph.json","events_json":"https://pith.science/api/pith-number/54B4HL56XY7CO6RGW6OKV62F75/events.json","paper":"https://pith.science/paper/54B4HL56"},"agent_actions":{"view_html":"https://pith.science/pith/54B4HL56XY7CO6RGW6OKV62F75","download_json":"https://pith.science/pith/54B4HL56XY7CO6RGW6OKV62F75.json","view_paper":"https://pith.science/paper/54B4HL56","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.02756&json=true","fetch_graph":"https://pith.science/api/pith-number/54B4HL56XY7CO6RGW6OKV62F75/graph.json","fetch_events":"https://pith.science/api/pith-number/54B4HL56XY7CO6RGW6OKV62F75/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/54B4HL56XY7CO6RGW6OKV62F75/action/timestamp_anchor","attest_storage":"https://pith.science/pith/54B4HL56XY7CO6RGW6OKV62F75/action/storage_attestation","attest_author":"https://pith.science/pith/54B4HL56XY7CO6RGW6OKV62F75/action/author_attestation","sign_citation":"https://pith.science/pith/54B4HL56XY7CO6RGW6OKV62F75/action/citation_signature","submit_replication":"https://pith.science/pith/54B4HL56XY7CO6RGW6OKV62F75/action/replication_record"}},"created_at":"2026-05-18T00:42:41.067538+00:00","updated_at":"2026-05-18T00:42:41.067538+00:00"}