{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:Q4GH5Y256673F2VM3CWFMUU6MB","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":"d1bd2db573bb782308037ac2ed962b30cf99fba1c56095cecc89ae2bbf072e08","cross_cats_sorted":["cs.LO","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2020-04-14T14:57:13Z","title_canon_sha256":"0a5ed62a19426e3d34d0d878dcc1de8b80941acc5538882fb3b61f977b08661b"},"schema_version":"1.0","source":{"id":"2004.06572","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.06572","created_at":"2026-07-05T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"2004.06572v3","created_at":"2026-07-05T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.06572","created_at":"2026-07-05T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"Q4GH5Y256673","created_at":"2026-07-05T01:12:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q4GH5Y256673F2VM","created_at":"2026-07-05T01:12:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q4GH5Y25","created_at":"2026-07-05T01:12:43Z"}],"graph_snapshots":[{"event_id":"sha256:8cbafe50bb1e591059239f0df9aab5f5d4ea28d8e182c1e2b011b5534394cdb7","target":"graph","created_at":"2026-07-05T01:12:43Z","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/2004.06572/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant under isomorphism: more specifically, identifications of structures coincide with isomorphisms. We prove a version of this principle for a wide range of higher-categorical structures, adapting FOLDS-signatures to specify a general class of structures, and using two-level type theory to treat all categorical dimensions uniformly. As in the previously known case of 1-categories (which is an instance of our theory), the st","authors_text":"Benedikt Ahrens, Dimitris Tsementzis, Michael Shulman, Paige Randall North","cross_cats":["cs.LO","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2020-04-14T14:57:13Z","title":"A Higher Structure Identity Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.06572","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:c08c5d16fec6444e19e434c48cd5af41ac6e8092762f498d7b1325d56b394bc4","target":"record","created_at":"2026-07-05T01:12:43Z","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":"d1bd2db573bb782308037ac2ed962b30cf99fba1c56095cecc89ae2bbf072e08","cross_cats_sorted":["cs.LO","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2020-04-14T14:57:13Z","title_canon_sha256":"0a5ed62a19426e3d34d0d878dcc1de8b80941acc5538882fb3b61f977b08661b"},"schema_version":"1.0","source":{"id":"2004.06572","kind":"arxiv","version":3}},"canonical_sha256":"870c7ee35df7bfb2eaacd8ac56529e6064b759d55996fa2ddbc817e65e42aaa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"870c7ee35df7bfb2eaacd8ac56529e6064b759d55996fa2ddbc817e65e42aaa6","first_computed_at":"2026-07-05T01:12:43.768250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:12:43.768250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hzl9zumw6jB01ASt7FzqnwiSYOtgAfVijKpG1HzC3emBO6Tcr1q3BeWN42bTguQUU5zx3A9OZ02oh9e8ZavbBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:12:43.768670Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.06572","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c08c5d16fec6444e19e434c48cd5af41ac6e8092762f498d7b1325d56b394bc4","sha256:8cbafe50bb1e591059239f0df9aab5f5d4ea28d8e182c1e2b011b5534394cdb7"],"state_sha256":"94d9f3ac0151d5a1581da5e0491ddaff97584362da2ad5716c57c5011ea856f6"}