{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RGHHBSFKNIJVTR6SSM6I2ETP2B","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":"725b204f9fae6f32e3f0ed9dd6d282f3890a3454e9ea9ff558a40c49a5bdf195","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-11-28T14:55:04Z","title_canon_sha256":"b1dc198b66d51a56714911359510b362b05883c08e6136f24d71e88d1feeee43"},"schema_version":"1.0","source":{"id":"2211.15392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.15392","created_at":"2026-07-05T05:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"2211.15392v2","created_at":"2026-07-05T05:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.15392","created_at":"2026-07-05T05:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"RGHHBSFKNIJV","created_at":"2026-07-05T05:31:04Z"},{"alias_kind":"pith_short_16","alias_value":"RGHHBSFKNIJVTR6S","created_at":"2026-07-05T05:31:04Z"},{"alias_kind":"pith_short_8","alias_value":"RGHHBSFK","created_at":"2026-07-05T05:31:04Z"}],"graph_snapshots":[{"event_id":"sha256:3cfab0077ae582cf59d75e8532d07993ec267b096e2b2d6422cfb50fec825ca6","target":"graph","created_at":"2026-07-05T05:31:04Z","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/2211.15392/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be the group of all order-preserving self-maps of the real line. In previous work, the first two authors constructed a pre-Tannakian category $\\underline{\\mathrm{Rep}}(G)$ associated to $G$. The present paper is a detailed study of this category, which we name the Delannoy category. We classify the simple objects, determine branching rules to open subgroups, and give a combinatorial rule for tensor products. The Delannoy category has some remarkable features: it is semi-simple in all characteristics; all simples have categorical dimension $\\pm 1$; and the Adams operations on its Grothe","authors_text":"Andrew Snowden, Nate Harman, Noah Snyder","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-11-28T14:55:04Z","title":"The Delannoy category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.15392","kind":"arxiv","version":2},"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":"sha256:8ff524783b390c4aefbaac90a665340d1d2ecff6eca3ca669dce514b94e0fbdd","target":"record","created_at":"2026-07-05T05:31:04Z","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":"725b204f9fae6f32e3f0ed9dd6d282f3890a3454e9ea9ff558a40c49a5bdf195","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-11-28T14:55:04Z","title_canon_sha256":"b1dc198b66d51a56714911359510b362b05883c08e6136f24d71e88d1feeee43"},"schema_version":"1.0","source":{"id":"2211.15392","kind":"arxiv","version":2}},"canonical_sha256":"898e70c8aa6a1359c7d2933c8d126fd05e734abf377e3c1be9998982d20c58a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"898e70c8aa6a1359c7d2933c8d126fd05e734abf377e3c1be9998982d20c58a0","first_computed_at":"2026-07-05T05:31:04.016575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:31:04.016575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QidzY79nu2lcqDrh6vdOeC2kQEW8UiiFbPAZ6VmkOS0+Ms40yOvvTc7c2ubizH/XCs5jqN+NWBX/dQiwJB3FCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:31:04.017031Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.15392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ff524783b390c4aefbaac90a665340d1d2ecff6eca3ca669dce514b94e0fbdd","sha256:3cfab0077ae582cf59d75e8532d07993ec267b096e2b2d6422cfb50fec825ca6"],"state_sha256":"6617e91a1538dbbb7f7bc5d3bed93a70051182b0b14c5b5ad7d58165ae6bcbd2"}