{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:U4TOS5AUPQV3F46J6ZICN2CJSF","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":"9cef0c5dbe8794ac5f9f835a7cfd6889a55a3091c98ca1530c054b29881b850e","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-01-20T17:36:00Z","title_canon_sha256":"2260c7f0d03acd7ac27d4ac7097fddb205fbf3e8297301377d66dcf9c747ce5b"},"schema_version":"1.0","source":{"id":"2501.11620","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.11620","created_at":"2026-07-05T11:03:02Z"},{"alias_kind":"arxiv_version","alias_value":"2501.11620v3","created_at":"2026-07-05T11:03:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.11620","created_at":"2026-07-05T11:03:02Z"},{"alias_kind":"pith_short_12","alias_value":"U4TOS5AUPQV3","created_at":"2026-07-05T11:03:02Z"},{"alias_kind":"pith_short_16","alias_value":"U4TOS5AUPQV3F46J","created_at":"2026-07-05T11:03:02Z"},{"alias_kind":"pith_short_8","alias_value":"U4TOS5AU","created_at":"2026-07-05T11:03:02Z"}],"graph_snapshots":[{"event_id":"sha256:4ce85cb6705c3b478c45874f8ff75392600c0d366794b58ea656559f5320b097","target":"graph","created_at":"2026-07-05T11:03:02Z","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/2501.11620/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define a naturality construction for the operations of weak omega-categories, as a meta-operation in a dependent type theory. Our construction has a geometrical motivation as a local tensor product with a directed interval, and behaves logically as a globular analogue of Reynolds parametricity. Our construction operates as a ``power tool'' to support construction of terms with geometrical structure, and we use it to define composition operations for cylinders and cones in omega-categories. The machinery can generate terms of high complexity, and we have implemented our construction in a pro","authors_text":"Chiara Sarti, Ioannis Markakis, Jamie Vicary, Thibaut Benjamin, Wilfred Offord","cross_cats":["cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-01-20T17:36:00Z","title":"Naturality for higher-dimensional path types"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.11620","kind":"arxiv","version":3},"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":"sha256:8e676d32675fcf89555ce0b5e1748e53bdd621b5e00d73ba1640d47c94ee88c6","target":"record","created_at":"2026-07-05T11:03:02Z","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":"9cef0c5dbe8794ac5f9f835a7cfd6889a55a3091c98ca1530c054b29881b850e","cross_cats_sorted":["cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-01-20T17:36:00Z","title_canon_sha256":"2260c7f0d03acd7ac27d4ac7097fddb205fbf3e8297301377d66dcf9c747ce5b"},"schema_version":"1.0","source":{"id":"2501.11620","kind":"arxiv","version":3}},"canonical_sha256":"a726e974147c2bb2f3c9f65026e849917724dd28bdd0ee83851616514d6d08db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a726e974147c2bb2f3c9f65026e849917724dd28bdd0ee83851616514d6d08db","first_computed_at":"2026-07-05T11:03:02.842380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:03:02.842380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ykSCXW0reot8Jk4fOs5iMcsbBeGbM2BfkFu5PEQuz4eNWhLcAA/07FNdUVEIlUlXLzHTbil/vFZ/tSjRkKcGCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:03:02.842963Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.11620","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e676d32675fcf89555ce0b5e1748e53bdd621b5e00d73ba1640d47c94ee88c6","sha256:4ce85cb6705c3b478c45874f8ff75392600c0d366794b58ea656559f5320b097"],"state_sha256":"c0c4a7441414bdf80b808abdf371e5750f6cbfe6c8a4cf73c1ad391ff177ecc3"}