{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ZHOZBTY6YLWPIABZS4GF2TRZWX","short_pith_number":"pith:ZHOZBTY6","schema_version":"1.0","canonical_sha256":"c9dd90cf1ec2ecf40039970c5d4e39b5f771aed092ba1a8b16f3352136328969","source":{"kind":"arxiv","id":"1105.2799","version":1},"attestation_state":"computed","paper":{"title":"Square character degree graphs yield direct products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark L. Lewis, Qingyun Meng","submitted_at":"2011-05-13T18:29:05Z","abstract_excerpt":"If $G$ is a solvable group, we take $\\Delta (G)$ to be the character degree graph for $G$ with primes as vertices. We prove that if $\\Delta (G)$ is a square, then $G$ must be a direct product."},"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":"1105.2799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-05-13T18:29:05Z","cross_cats_sorted":[],"title_canon_sha256":"2dc7f4ef010288009bf9dcc807992df2228d34065a82b58c350ee58fe7d934ab","abstract_canon_sha256":"b30d12b36e0366e047940597206b25f6b3e5af39dd9ad38c003c0af8897927a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:52.358849Z","signature_b64":"X+xN/ogvC+weBsnSm0f1HgM0TvFKkR1s/wvekjo1UMfj/uNO5JBkUCJhjX4Q1bfdfkBn5AKWx4A+iiTOMK06Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9dd90cf1ec2ecf40039970c5d4e39b5f771aed092ba1a8b16f3352136328969","last_reissued_at":"2026-05-18T02:37:52.358219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:52.358219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Square character degree graphs yield direct products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark L. Lewis, Qingyun Meng","submitted_at":"2011-05-13T18:29:05Z","abstract_excerpt":"If $G$ is a solvable group, we take $\\Delta (G)$ to be the character degree graph for $G$ with primes as vertices. We prove that if $\\Delta (G)$ is a square, then $G$ must be a direct product."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2799","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":"1105.2799","created_at":"2026-05-18T02:37:52.358331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.2799v1","created_at":"2026-05-18T02:37:52.358331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2799","created_at":"2026-05-18T02:37:52.358331+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZHOZBTY6YLWP","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZHOZBTY6YLWPIABZ","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZHOZBTY6","created_at":"2026-05-18T12:26:47.523578+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/ZHOZBTY6YLWPIABZS4GF2TRZWX","json":"https://pith.science/pith/ZHOZBTY6YLWPIABZS4GF2TRZWX.json","graph_json":"https://pith.science/api/pith-number/ZHOZBTY6YLWPIABZS4GF2TRZWX/graph.json","events_json":"https://pith.science/api/pith-number/ZHOZBTY6YLWPIABZS4GF2TRZWX/events.json","paper":"https://pith.science/paper/ZHOZBTY6"},"agent_actions":{"view_html":"https://pith.science/pith/ZHOZBTY6YLWPIABZS4GF2TRZWX","download_json":"https://pith.science/pith/ZHOZBTY6YLWPIABZS4GF2TRZWX.json","view_paper":"https://pith.science/paper/ZHOZBTY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.2799&json=true","fetch_graph":"https://pith.science/api/pith-number/ZHOZBTY6YLWPIABZS4GF2TRZWX/graph.json","fetch_events":"https://pith.science/api/pith-number/ZHOZBTY6YLWPIABZS4GF2TRZWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZHOZBTY6YLWPIABZS4GF2TRZWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZHOZBTY6YLWPIABZS4GF2TRZWX/action/storage_attestation","attest_author":"https://pith.science/pith/ZHOZBTY6YLWPIABZS4GF2TRZWX/action/author_attestation","sign_citation":"https://pith.science/pith/ZHOZBTY6YLWPIABZS4GF2TRZWX/action/citation_signature","submit_replication":"https://pith.science/pith/ZHOZBTY6YLWPIABZS4GF2TRZWX/action/replication_record"}},"created_at":"2026-05-18T02:37:52.358331+00:00","updated_at":"2026-05-18T02:37:52.358331+00:00"}