{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z23F44SJJ52Q3RMG4XQKE2P5DR","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":"20af5356541d3e5aa0940313b733cf24c3740b6361949b62c90d8131b0094c72","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-06-02T14:24:50Z","title_canon_sha256":"17157392b93c3780a449c5afddbda68243caca332829557ecdea38bba7350d57"},"schema_version":"1.0","source":{"id":"2506.01717","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01717","created_at":"2026-07-05T11:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01717v1","created_at":"2026-07-05T11:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01717","created_at":"2026-07-05T11:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"Z23F44SJJ52Q","created_at":"2026-07-05T11:14:18Z"},{"alias_kind":"pith_short_16","alias_value":"Z23F44SJJ52Q3RMG","created_at":"2026-07-05T11:14:18Z"},{"alias_kind":"pith_short_8","alias_value":"Z23F44SJ","created_at":"2026-07-05T11:14:18Z"}],"graph_snapshots":[{"event_id":"sha256:b56f2ce77315649c25b9b26bd5c1f063925f6f918d48db2083a2bee012074c80","target":"graph","created_at":"2026-07-05T11:14:18Z","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/2506.01717/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The category fat Delta, introduced by J. Kock, is a modification of the simplex category where the degeneracies behave weakly. The objective of this note is to provide tools for working with fat Delta. In particular, we identify three types of morphisms: degenerated, standard and vertical faces, and establish six relations between these classes. We then show that fat Delta is generated by these morphisms and relations.","authors_text":"Sti\\'ephen Pradal","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-06-02T14:24:50Z","title":"On combinatorial aspects of fat Delta"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01717","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":"sha256:40b13c6ffd608bebfcaca338ad4b3b16140f0f8564cc7886f499965e805116d7","target":"record","created_at":"2026-07-05T11:14:18Z","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":"20af5356541d3e5aa0940313b733cf24c3740b6361949b62c90d8131b0094c72","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-06-02T14:24:50Z","title_canon_sha256":"17157392b93c3780a449c5afddbda68243caca332829557ecdea38bba7350d57"},"schema_version":"1.0","source":{"id":"2506.01717","kind":"arxiv","version":1}},"canonical_sha256":"ceb65e72494f750dc586e5e0a269fd1c7e5d5ae723037bda6bc47a1fc9dcc114","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ceb65e72494f750dc586e5e0a269fd1c7e5d5ae723037bda6bc47a1fc9dcc114","first_computed_at":"2026-07-05T11:14:18.299587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:14:18.299587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ADMguXOtNAq+aEEC3hegbnsFzbOY1kATkRHjWlglG7tN+a83eHllZaW7IMgnKENwamy7LybKLHWxuU5NimnbDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:14:18.300060Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01717","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40b13c6ffd608bebfcaca338ad4b3b16140f0f8564cc7886f499965e805116d7","sha256:b56f2ce77315649c25b9b26bd5c1f063925f6f918d48db2083a2bee012074c80"],"state_sha256":"452ad6754ad7214c195896081369183af6c8e281e6b5e726d28a5318307edbc2"}