{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TBER2AJOPURQJDINRGWICMDQBI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d12e1efe4c06e442ad0af3bbce947ce6cdb6d473c5126e98a3eed2ad29157979","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-07-07T20:08:58Z","title_canon_sha256":"c5821b456320d589b16c28b389ecd953c8f409680dfd2a209a0e653b1b57a55e"},"schema_version":"1.0","source":{"id":"1107.1506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1506","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1506v1","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1506","created_at":"2026-05-18T04:18:35Z"},{"alias_kind":"pith_short_12","alias_value":"TBER2AJOPURQ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TBER2AJOPURQJDIN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TBER2AJO","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:c1657535117014db581e96e9a32e4f6e4f33f94ecab0baf4ee2b5977d6419687","target":"graph","created_at":"2026-05-18T04:18:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra $C_f$ of a ternary cubic form $f$ and certain vector bundles (called Ulrich bundles) on a cubic surface $X$. We study general properties of Ulrich bundles, and using a recent classification of Casanellas and Hartshorne, deduce the existence of irreducible representations of $C_f$ of every possible dimension.","authors_text":"Emre Coskun, Rajesh S. Kulkarni, Yusuf Mustopa","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-07-07T20:08:58Z","title":"On representations of Clifford algebras of ternary cubic forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1506","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b68ac4335db81c453b241d2565c868e4a0246093bcc501a99dd2635f3280b05d","target":"record","created_at":"2026-05-18T04:18:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d12e1efe4c06e442ad0af3bbce947ce6cdb6d473c5126e98a3eed2ad29157979","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-07-07T20:08:58Z","title_canon_sha256":"c5821b456320d589b16c28b389ecd953c8f409680dfd2a209a0e653b1b57a55e"},"schema_version":"1.0","source":{"id":"1107.1506","kind":"arxiv","version":1}},"canonical_sha256":"98491d012e7d23048d0d89ac8130700a1205d4c2f631591988eba08a5582ae84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98491d012e7d23048d0d89ac8130700a1205d4c2f631591988eba08a5582ae84","first_computed_at":"2026-05-18T04:18:35.529992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:35.529992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BN620aS3AU03biJoZxf6g/2masx0Ybom/TsRLAtCYRbD4Oqzya2n45S8Pk6CMATuiY9MLB5wnAhqeHWSumHnCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:35.530516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b68ac4335db81c453b241d2565c868e4a0246093bcc501a99dd2635f3280b05d","sha256:c1657535117014db581e96e9a32e4f6e4f33f94ecab0baf4ee2b5977d6419687"],"state_sha256":"838bb2a516c5fbca869c394d291dbbe5d99a7a54206537d4a101d2e91c81f32b"}