{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2LLBIFZHGM23IZMGPQF2YOBS77","short_pith_number":"pith:2LLBIFZH","schema_version":"1.0","canonical_sha256":"d2d61417273335b465867c0bac3832ffcd870df6cb500448bf93677cbc70354d","source":{"kind":"arxiv","id":"2605.23195","version":1},"attestation_state":"computed","paper":{"title":"Complex Representations of Groups and Involutions of its Automorphisms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.RT","authors_text":"Ajay Kumar Shukla, Rahul Dixit, Venkata Subbaiah Yerrapati","submitted_at":"2026-05-22T03:27:13Z","abstract_excerpt":"In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these quantities in the context of inner automorphisms and the symmetric group $\\mathfrak{S}_n$. As an application, we provide a criterion for identifying groups that possess complex (non-real) irreducible representations and explore the structural consequences arising from these results."},"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":"2605.23195","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-05-22T03:27:13Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"2fd011acd78979ff893a26b57c4dc9555e3213786cb471e337bc5baa65fa257d","abstract_canon_sha256":"67286f49022eec1ad75edd1def550b5f73fce8a9664ba88aee4ed8be0444a0c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:42.561007Z","signature_b64":"TX0zhuxOv3pNZyJHQ5h4A/UsF+wWuWprn8JqApYdVfXK38cn7c6G0YY4s1Nc/yEXkQjlt2p610ar1NVx+64bDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2d61417273335b465867c0bac3832ffcd870df6cb500448bf93677cbc70354d","last_reissued_at":"2026-05-25T02:01:42.560277Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:42.560277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complex Representations of Groups and Involutions of its Automorphisms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.RT","authors_text":"Ajay Kumar Shukla, Rahul Dixit, Venkata Subbaiah Yerrapati","submitted_at":"2026-05-22T03:27:13Z","abstract_excerpt":"In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these quantities in the context of inner automorphisms and the symmetric group $\\mathfrak{S}_n$. As an application, we provide a criterion for identifying groups that possess complex (non-real) irreducible representations and explore the structural consequences arising from these results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23195","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23195/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.23195","created_at":"2026-05-25T02:01:42.560416+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.23195v1","created_at":"2026-05-25T02:01:42.560416+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23195","created_at":"2026-05-25T02:01:42.560416+00:00"},{"alias_kind":"pith_short_12","alias_value":"2LLBIFZHGM23","created_at":"2026-05-25T02:01:42.560416+00:00"},{"alias_kind":"pith_short_16","alias_value":"2LLBIFZHGM23IZMG","created_at":"2026-05-25T02:01:42.560416+00:00"},{"alias_kind":"pith_short_8","alias_value":"2LLBIFZH","created_at":"2026-05-25T02:01:42.560416+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/2LLBIFZHGM23IZMGPQF2YOBS77","json":"https://pith.science/pith/2LLBIFZHGM23IZMGPQF2YOBS77.json","graph_json":"https://pith.science/api/pith-number/2LLBIFZHGM23IZMGPQF2YOBS77/graph.json","events_json":"https://pith.science/api/pith-number/2LLBIFZHGM23IZMGPQF2YOBS77/events.json","paper":"https://pith.science/paper/2LLBIFZH"},"agent_actions":{"view_html":"https://pith.science/pith/2LLBIFZHGM23IZMGPQF2YOBS77","download_json":"https://pith.science/pith/2LLBIFZHGM23IZMGPQF2YOBS77.json","view_paper":"https://pith.science/paper/2LLBIFZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.23195&json=true","fetch_graph":"https://pith.science/api/pith-number/2LLBIFZHGM23IZMGPQF2YOBS77/graph.json","fetch_events":"https://pith.science/api/pith-number/2LLBIFZHGM23IZMGPQF2YOBS77/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2LLBIFZHGM23IZMGPQF2YOBS77/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2LLBIFZHGM23IZMGPQF2YOBS77/action/storage_attestation","attest_author":"https://pith.science/pith/2LLBIFZHGM23IZMGPQF2YOBS77/action/author_attestation","sign_citation":"https://pith.science/pith/2LLBIFZHGM23IZMGPQF2YOBS77/action/citation_signature","submit_replication":"https://pith.science/pith/2LLBIFZHGM23IZMGPQF2YOBS77/action/replication_record"}},"created_at":"2026-05-25T02:01:42.560416+00:00","updated_at":"2026-05-25T02:01:42.560416+00:00"}