{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:B6TQBC6FWMJAJXRHLKRYM6Y3LA","short_pith_number":"pith:B6TQBC6F","schema_version":"1.0","canonical_sha256":"0fa7008bc5b31204de275aa3867b1b5814ec66b856a2bdd3ce16f5ca6d6c1bef","source":{"kind":"arxiv","id":"1411.6120","version":1},"attestation_state":"computed","paper":{"title":"On Tensor Spaces for Rook Monoid Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.RA","authors_text":"Zhankui Xiao","submitted_at":"2014-11-22T12:03:22Z","abstract_excerpt":"Let $m,n\\in \\mathbb{N}$, and $V$ be a $m$-dimensional vector space over a field $F$ of characteristic $0$. Let $U=F\\oplus V$ and $R_n$ be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of $U^{\\otimes n}$ in $FR_n$, which comes from some one-dimensional two-sided ideal of rook monoid algebra. We show that the two-sided ideal generated by this element is indeed the whole annihilator of $U^{\\otimes n}$ in $FR_n$."},"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":"1411.6120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-11-22T12:03:22Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"40824422ee84dd7dc4f38997ae65efe3518c90590c66889156a7c564540683bc","abstract_canon_sha256":"2fb948fe151e52e17cc5cb92d8ed88a7d1b85acc03b5c115146b2301dec61df0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:00.654179Z","signature_b64":"0XlQ67aF5vusdNxIOx+etkNGQSYL+leX/lfyf8FSyerPY2/RutwD0PERcSiN9NDRHLjTTY9jEkhrhbBXEqvhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fa7008bc5b31204de275aa3867b1b5814ec66b856a2bdd3ce16f5ca6d6c1bef","last_reissued_at":"2026-05-18T02:33:00.653842Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:00.653842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Tensor Spaces for Rook Monoid Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.RA","authors_text":"Zhankui Xiao","submitted_at":"2014-11-22T12:03:22Z","abstract_excerpt":"Let $m,n\\in \\mathbb{N}$, and $V$ be a $m$-dimensional vector space over a field $F$ of characteristic $0$. Let $U=F\\oplus V$ and $R_n$ be the rook monoid. In this paper, we construct a certain quasi-idempotent in the annihilator of $U^{\\otimes n}$ in $FR_n$, which comes from some one-dimensional two-sided ideal of rook monoid algebra. We show that the two-sided ideal generated by this element is indeed the whole annihilator of $U^{\\otimes n}$ in $FR_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6120","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":"1411.6120","created_at":"2026-05-18T02:33:00.653904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.6120v1","created_at":"2026-05-18T02:33:00.653904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6120","created_at":"2026-05-18T02:33:00.653904+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6TQBC6FWMJA","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6TQBC6FWMJAJXRH","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6TQBC6F","created_at":"2026-05-18T12:28:22.404517+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/B6TQBC6FWMJAJXRHLKRYM6Y3LA","json":"https://pith.science/pith/B6TQBC6FWMJAJXRHLKRYM6Y3LA.json","graph_json":"https://pith.science/api/pith-number/B6TQBC6FWMJAJXRHLKRYM6Y3LA/graph.json","events_json":"https://pith.science/api/pith-number/B6TQBC6FWMJAJXRHLKRYM6Y3LA/events.json","paper":"https://pith.science/paper/B6TQBC6F"},"agent_actions":{"view_html":"https://pith.science/pith/B6TQBC6FWMJAJXRHLKRYM6Y3LA","download_json":"https://pith.science/pith/B6TQBC6FWMJAJXRHLKRYM6Y3LA.json","view_paper":"https://pith.science/paper/B6TQBC6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.6120&json=true","fetch_graph":"https://pith.science/api/pith-number/B6TQBC6FWMJAJXRHLKRYM6Y3LA/graph.json","fetch_events":"https://pith.science/api/pith-number/B6TQBC6FWMJAJXRHLKRYM6Y3LA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6TQBC6FWMJAJXRHLKRYM6Y3LA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6TQBC6FWMJAJXRHLKRYM6Y3LA/action/storage_attestation","attest_author":"https://pith.science/pith/B6TQBC6FWMJAJXRHLKRYM6Y3LA/action/author_attestation","sign_citation":"https://pith.science/pith/B6TQBC6FWMJAJXRHLKRYM6Y3LA/action/citation_signature","submit_replication":"https://pith.science/pith/B6TQBC6FWMJAJXRHLKRYM6Y3LA/action/replication_record"}},"created_at":"2026-05-18T02:33:00.653904+00:00","updated_at":"2026-05-18T02:33:00.653904+00:00"}