{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5PJ5KSM7HPMTJLLQ4EPU2EMBXV","short_pith_number":"pith:5PJ5KSM7","schema_version":"1.0","canonical_sha256":"ebd3d5499f3bd934ad70e11f4d1181bd427411f63cc8787fe07bb2dd9ae344ed","source":{"kind":"arxiv","id":"2507.20521","version":1},"attestation_state":"computed","paper":{"title":"Some calculations of centralizer rings of a complex reflection group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Manabu Oura, Masashi Kosuda, Sarbaini","submitted_at":"2025-07-28T05:09:41Z","abstract_excerpt":"Let H1 be the complex reflection group of order 96. For the tensor products of faithful transitive permutation representations of H1, we determine the structures of the centralizer rings. This complements the work of Imamura-Kosuda-Oura."},"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":"2507.20521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-07-28T05:09:41Z","cross_cats_sorted":[],"title_canon_sha256":"6e01ae212259e0b7666893642889d19b9be9c8b56e4ee223d60c22256bc3336a","abstract_canon_sha256":"79488470f9268a242efa74d6a390e545b020577c34b54aa7ce3022525be1ac9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:20.933853Z","signature_b64":"ranJkjRk5WR4pV4LRev1f50sYF6z1hKGf8sdL42qANTRgWFOrs8lxeDP9eJeGsqrcOEhJOAI8iylTNAEtO/gDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebd3d5499f3bd934ad70e11f4d1181bd427411f63cc8787fe07bb2dd9ae344ed","last_reissued_at":"2026-07-05T11:44:20.933397Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:20.933397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some calculations of centralizer rings of a complex reflection group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Manabu Oura, Masashi Kosuda, Sarbaini","submitted_at":"2025-07-28T05:09:41Z","abstract_excerpt":"Let H1 be the complex reflection group of order 96. For the tensor products of faithful transitive permutation representations of H1, we determine the structures of the centralizer rings. This complements the work of Imamura-Kosuda-Oura."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20521","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/2507.20521/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":"2507.20521","created_at":"2026-07-05T11:44:20.933456+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.20521v1","created_at":"2026-07-05T11:44:20.933456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20521","created_at":"2026-07-05T11:44:20.933456+00:00"},{"alias_kind":"pith_short_12","alias_value":"5PJ5KSM7HPMT","created_at":"2026-07-05T11:44:20.933456+00:00"},{"alias_kind":"pith_short_16","alias_value":"5PJ5KSM7HPMTJLLQ","created_at":"2026-07-05T11:44:20.933456+00:00"},{"alias_kind":"pith_short_8","alias_value":"5PJ5KSM7","created_at":"2026-07-05T11:44:20.933456+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/5PJ5KSM7HPMTJLLQ4EPU2EMBXV","json":"https://pith.science/pith/5PJ5KSM7HPMTJLLQ4EPU2EMBXV.json","graph_json":"https://pith.science/api/pith-number/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/graph.json","events_json":"https://pith.science/api/pith-number/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/events.json","paper":"https://pith.science/paper/5PJ5KSM7"},"agent_actions":{"view_html":"https://pith.science/pith/5PJ5KSM7HPMTJLLQ4EPU2EMBXV","download_json":"https://pith.science/pith/5PJ5KSM7HPMTJLLQ4EPU2EMBXV.json","view_paper":"https://pith.science/paper/5PJ5KSM7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.20521&json=true","fetch_graph":"https://pith.science/api/pith-number/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/graph.json","fetch_events":"https://pith.science/api/pith-number/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/action/storage_attestation","attest_author":"https://pith.science/pith/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/action/author_attestation","sign_citation":"https://pith.science/pith/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/action/citation_signature","submit_replication":"https://pith.science/pith/5PJ5KSM7HPMTJLLQ4EPU2EMBXV/action/replication_record"}},"created_at":"2026-07-05T11:44:20.933456+00:00","updated_at":"2026-07-05T11:44:20.933456+00:00"}