{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NEC32FALHEZCHX57KSHHF7KCKJ","short_pith_number":"pith:NEC32FAL","schema_version":"1.0","canonical_sha256":"6905bd140b393223dfbf548e72fd42525d93d353a38c31c9a46f1326ecd7ed63","source":{"kind":"arxiv","id":"1710.05473","version":1},"attestation_state":"computed","paper":{"title":"On the decomposition numbers of $\\mathrm{SO}_8^+(2^f)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alessandro Paolini","submitted_at":"2017-10-16T02:42:53Z","abstract_excerpt":"Let $q=2^f$, and let $G=\\mathrm{SO}_8^+(q)$ and $U$ be a Sylow $2$-subgroup of $G$. We first describe the fusion of the conjugacy classes of $U$ in $G$. We then use this information to prove the unitriangularity of the $\\ell$-decomposition matrices of $G$ for all $\\ell \\ne 2$ by inducing certain irreducible characters of $U$ to $G$; the characters of $U$ of degree $q^3/2$ play here a major role. We then determine the $\\ell$-decomposition matrix of $G$ in the case $\\ell \\mid q+1$, when $\\ell \\ge 5$ and $(q+1)_\\ell>5$, up to two non-negative indeterminates in one column."},"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":"1710.05473","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-10-16T02:42:53Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ba64881c90eb976eb9a452233f00e5d27741fcafe886259bfc2105d87cc49ff9","abstract_canon_sha256":"31cf38a15bfd6e9aeff80b4e116b0128a0322614794b1fff55e6cb8739f9d0f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:49.307767Z","signature_b64":"AR2B2psp6r1Y2KeV8SZ1vWxJc5mPcRK1zUGXB9KG41wKaxWH/2RjkNqML5c1B4K5qzCCnelCIuxQSGBjY3rjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6905bd140b393223dfbf548e72fd42525d93d353a38c31c9a46f1326ecd7ed63","last_reissued_at":"2026-05-18T00:32:49.307009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:49.307009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the decomposition numbers of $\\mathrm{SO}_8^+(2^f)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alessandro Paolini","submitted_at":"2017-10-16T02:42:53Z","abstract_excerpt":"Let $q=2^f$, and let $G=\\mathrm{SO}_8^+(q)$ and $U$ be a Sylow $2$-subgroup of $G$. We first describe the fusion of the conjugacy classes of $U$ in $G$. We then use this information to prove the unitriangularity of the $\\ell$-decomposition matrices of $G$ for all $\\ell \\ne 2$ by inducing certain irreducible characters of $U$ to $G$; the characters of $U$ of degree $q^3/2$ play here a major role. We then determine the $\\ell$-decomposition matrix of $G$ in the case $\\ell \\mid q+1$, when $\\ell \\ge 5$ and $(q+1)_\\ell>5$, up to two non-negative indeterminates in one column."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05473","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":"1710.05473","created_at":"2026-05-18T00:32:49.307129+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.05473v1","created_at":"2026-05-18T00:32:49.307129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05473","created_at":"2026-05-18T00:32:49.307129+00:00"},{"alias_kind":"pith_short_12","alias_value":"NEC32FALHEZC","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NEC32FALHEZCHX57","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NEC32FAL","created_at":"2026-05-18T12:31:31.346846+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/NEC32FALHEZCHX57KSHHF7KCKJ","json":"https://pith.science/pith/NEC32FALHEZCHX57KSHHF7KCKJ.json","graph_json":"https://pith.science/api/pith-number/NEC32FALHEZCHX57KSHHF7KCKJ/graph.json","events_json":"https://pith.science/api/pith-number/NEC32FALHEZCHX57KSHHF7KCKJ/events.json","paper":"https://pith.science/paper/NEC32FAL"},"agent_actions":{"view_html":"https://pith.science/pith/NEC32FALHEZCHX57KSHHF7KCKJ","download_json":"https://pith.science/pith/NEC32FALHEZCHX57KSHHF7KCKJ.json","view_paper":"https://pith.science/paper/NEC32FAL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.05473&json=true","fetch_graph":"https://pith.science/api/pith-number/NEC32FALHEZCHX57KSHHF7KCKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/NEC32FALHEZCHX57KSHHF7KCKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NEC32FALHEZCHX57KSHHF7KCKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NEC32FALHEZCHX57KSHHF7KCKJ/action/storage_attestation","attest_author":"https://pith.science/pith/NEC32FALHEZCHX57KSHHF7KCKJ/action/author_attestation","sign_citation":"https://pith.science/pith/NEC32FALHEZCHX57KSHHF7KCKJ/action/citation_signature","submit_replication":"https://pith.science/pith/NEC32FALHEZCHX57KSHHF7KCKJ/action/replication_record"}},"created_at":"2026-05-18T00:32:49.307129+00:00","updated_at":"2026-05-18T00:32:49.307129+00:00"}