{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:376QZDSOYM6PTGWX4JXZ7O5NXG","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":"18549e85986e25660e57f9379d76b86d5a565a6f31051388c3b2d9e5a9ec86d3","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2020-03-23T19:17:39Z","title_canon_sha256":"3eb98ba69a340e80a60a7592780e4ddd544393977fbd38b169c3d70185175fbf"},"schema_version":"1.0","source":{"id":"2003.10499","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.10499","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"arxiv_version","alias_value":"2003.10499v4","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.10499","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_12","alias_value":"376QZDSOYM6P","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"376QZDSOYM6PTGWX","created_at":"2026-07-05T03:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"376QZDSO","created_at":"2026-07-05T03:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:3282dfe54977dd3ef9652346f722d4e981dab53dc9e9b1691c8e0560adbd39fc","target":"graph","created_at":"2026-07-05T03:30:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2003.10499/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a method of constructing abelian envelopes of symmetric rigid monoidal Karoubian categories over an algebraically closed field $\\bf k$. If ${\\rm char}({\\bf k})=p>0$, we use this method to construct generalizations ${\\rm Ver}_{p^n}$, ${\\rm Ver}_{p^n}^+$ of the incompressible abelian symmetric tensor categories defined in arXiv:1807.05549 for $p=2$ and by Gelfand-Kazhdan and Georgiev-Mathieu for $n=1$. Namely, ${\\rm Ver}_{p^n}$ is the abelian envelope of the quotient of the category of tilting modules for $SL_2(\\bf k)$ by the $n$-th Steinberg module, and ${\\rm Ver}_{p^n}^+$ is its sub","authors_text":"Dave Benson, Pavel Etingof, Victor Ostrik","cross_cats":["math.CT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2020-03-23T19:17:39Z","title":"New incompressible symmetric tensor categories in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.10499","kind":"arxiv","version":4},"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":"sha256:00a5ea8abb383ccce626b173551550020e818c6b66eea4849d34be57164cdf29","target":"record","created_at":"2026-07-05T03:30:36Z","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":"18549e85986e25660e57f9379d76b86d5a565a6f31051388c3b2d9e5a9ec86d3","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2020-03-23T19:17:39Z","title_canon_sha256":"3eb98ba69a340e80a60a7592780e4ddd544393977fbd38b169c3d70185175fbf"},"schema_version":"1.0","source":{"id":"2003.10499","kind":"arxiv","version":4}},"canonical_sha256":"dffd0c8e4ec33cf99ad7e26f9fbbadb987fff788edd74e4f0494563ba7740bfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dffd0c8e4ec33cf99ad7e26f9fbbadb987fff788edd74e4f0494563ba7740bfa","first_computed_at":"2026-07-05T03:30:36.894270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:30:36.894270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VaKTkaXNkZBtUuikfxzFET1jnURNvzmnHnCbXNuvgc6Gu87ygnj62CKwfdtp3rHDZgAjbdD6eQT/1MqM7YdEDw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:30:36.894828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.10499","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00a5ea8abb383ccce626b173551550020e818c6b66eea4849d34be57164cdf29","sha256:3282dfe54977dd3ef9652346f722d4e981dab53dc9e9b1691c8e0560adbd39fc"],"state_sha256":"d6c37308dba9227a68d2a90826c60c17ba979e3ae51a5208b5c4abd2bd691f4f"}