{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PG5OT45GYL7IEEUNIXF2WMTTIM","short_pith_number":"pith:PG5OT45G","schema_version":"1.0","canonical_sha256":"79bae9f3a6c2fe82128d45cbab3273430326e71467a8bdc718c241ed71a05094","source":{"kind":"arxiv","id":"1910.10612","version":2},"attestation_state":"computed","paper":{"title":"Combinatorial study of stable categories of graded Cohen--Macaulay modules over skew quadric hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.RA","authors_text":"Akihiro Higashitani, Kenta Ueyama","submitted_at":"2019-10-23T15:29:43Z","abstract_excerpt":"In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let $S$ be a graded ($\\pm 1$)-skew polynomial algebra in $n$ variables of degree $1$ and $f =x_1^2 + \\cdots +x_n^2 \\in S$. We prove that the stable category $\\mathsf{\\underline{CM}}^{\\mathbb Z}(S/(f))$ of graded maximal Cohen--Macaulay module over $S/(f)$ can be completely computed using the four graphical operations. As a consequence, $\\mathsf{\\underline{CM}}^{\\mathbb Z}(S/(f))$ is equivalent to the derived category $\\mathsf{D^b}(\\operatorname{\\mathsf{mod}} k^{2^r})$, an"},"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":"1910.10612","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-10-23T15:29:43Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"e90532f86684f1552dc0557dd82369e2748e2b738fa6aeb854c3099ced0d6d1b","abstract_canon_sha256":"87132473fa84024a805b14bb0122b55bb60bb55a1a377a9f9201e796f674993a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:59:26.857370Z","signature_b64":"aTuqhKF1hjfgMuKmPX+VlhufgP9wOD3Xw0lcHbsjMA1BraSNPaa/xdwutyV1Na9fVEk7ZEwckGTTKAnuY3ZLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79bae9f3a6c2fe82128d45cbab3273430326e71467a8bdc718c241ed71a05094","last_reissued_at":"2026-07-05T01:59:26.856857Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:59:26.856857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorial study of stable categories of graded Cohen--Macaulay modules over skew quadric hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"math.RA","authors_text":"Akihiro Higashitani, Kenta Ueyama","submitted_at":"2019-10-23T15:29:43Z","abstract_excerpt":"In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let $S$ be a graded ($\\pm 1$)-skew polynomial algebra in $n$ variables of degree $1$ and $f =x_1^2 + \\cdots +x_n^2 \\in S$. We prove that the stable category $\\mathsf{\\underline{CM}}^{\\mathbb Z}(S/(f))$ of graded maximal Cohen--Macaulay module over $S/(f)$ can be completely computed using the four graphical operations. As a consequence, $\\mathsf{\\underline{CM}}^{\\mathbb Z}(S/(f))$ is equivalent to the derived category $\\mathsf{D^b}(\\operatorname{\\mathsf{mod}} k^{2^r})$, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.10612","kind":"arxiv","version":2},"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/1910.10612/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":"1910.10612","created_at":"2026-07-05T01:59:26.856914+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.10612v2","created_at":"2026-07-05T01:59:26.856914+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.10612","created_at":"2026-07-05T01:59:26.856914+00:00"},{"alias_kind":"pith_short_12","alias_value":"PG5OT45GYL7I","created_at":"2026-07-05T01:59:26.856914+00:00"},{"alias_kind":"pith_short_16","alias_value":"PG5OT45GYL7IEEUN","created_at":"2026-07-05T01:59:26.856914+00:00"},{"alias_kind":"pith_short_8","alias_value":"PG5OT45G","created_at":"2026-07-05T01:59:26.856914+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/PG5OT45GYL7IEEUNIXF2WMTTIM","json":"https://pith.science/pith/PG5OT45GYL7IEEUNIXF2WMTTIM.json","graph_json":"https://pith.science/api/pith-number/PG5OT45GYL7IEEUNIXF2WMTTIM/graph.json","events_json":"https://pith.science/api/pith-number/PG5OT45GYL7IEEUNIXF2WMTTIM/events.json","paper":"https://pith.science/paper/PG5OT45G"},"agent_actions":{"view_html":"https://pith.science/pith/PG5OT45GYL7IEEUNIXF2WMTTIM","download_json":"https://pith.science/pith/PG5OT45GYL7IEEUNIXF2WMTTIM.json","view_paper":"https://pith.science/paper/PG5OT45G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.10612&json=true","fetch_graph":"https://pith.science/api/pith-number/PG5OT45GYL7IEEUNIXF2WMTTIM/graph.json","fetch_events":"https://pith.science/api/pith-number/PG5OT45GYL7IEEUNIXF2WMTTIM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PG5OT45GYL7IEEUNIXF2WMTTIM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PG5OT45GYL7IEEUNIXF2WMTTIM/action/storage_attestation","attest_author":"https://pith.science/pith/PG5OT45GYL7IEEUNIXF2WMTTIM/action/author_attestation","sign_citation":"https://pith.science/pith/PG5OT45GYL7IEEUNIXF2WMTTIM/action/citation_signature","submit_replication":"https://pith.science/pith/PG5OT45GYL7IEEUNIXF2WMTTIM/action/replication_record"}},"created_at":"2026-07-05T01:59:26.856914+00:00","updated_at":"2026-07-05T01:59:26.856914+00:00"}