{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:O3ESZMICUFZ33Y75S6VH3LSF6T","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":"32497cfe270523f298f44e8f5819a9eca2ee35daf985f1e27edbe42491525c23","cross_cats_sorted":["math.CT","math.QA"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2025-06-30T14:10:17Z","title_canon_sha256":"f45eaa851c9094855102540d539feb54f7c9300fd60f937329ec44969a761945"},"schema_version":"1.0","source":{"id":"2506.23880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.23880","created_at":"2026-07-05T11:29:29Z"},{"alias_kind":"arxiv_version","alias_value":"2506.23880v1","created_at":"2026-07-05T11:29:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23880","created_at":"2026-07-05T11:29:29Z"},{"alias_kind":"pith_short_12","alias_value":"O3ESZMICUFZ3","created_at":"2026-07-05T11:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"O3ESZMICUFZ33Y75","created_at":"2026-07-05T11:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"O3ESZMIC","created_at":"2026-07-05T11:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:a8ad59435acee4ffe409f01cf6125dfebab16801f109a5aaa6d148c1fe269f6d","target":"graph","created_at":"2026-07-05T11:29:29Z","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/2506.23880/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building on ideas of Kohno, we develop a framework for the construction of higher holonomy functors via the transport of formal power series connections. Using these techniques, we obtain functors from the path groupoid, the path 2-groupoid, and the path 3-groupoid of a manifold. As an application, we construct a Gray functor from the path 3-groupoid of the configuration space of $m$ points in $\\mathbb{R}^n$ for $n\\geqslant 4$.","authors_text":"Matthew Cellot","cross_cats":["math.CT","math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2025-06-30T14:10:17Z","title":"Higher path groupoids and the holonomy of formal power series connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23880","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:d67de2581f32b8f5860341749054b5c4304d2c5d38e6489d03573cfa19171f33","target":"record","created_at":"2026-07-05T11:29:29Z","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":"32497cfe270523f298f44e8f5819a9eca2ee35daf985f1e27edbe42491525c23","cross_cats_sorted":["math.CT","math.QA"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2025-06-30T14:10:17Z","title_canon_sha256":"f45eaa851c9094855102540d539feb54f7c9300fd60f937329ec44969a761945"},"schema_version":"1.0","source":{"id":"2506.23880","kind":"arxiv","version":1}},"canonical_sha256":"76c92cb102a173bde3fd97aa7dae45f4ce57e01933d8d7d1e41cffaa9b0ceb92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76c92cb102a173bde3fd97aa7dae45f4ce57e01933d8d7d1e41cffaa9b0ceb92","first_computed_at":"2026-07-05T11:29:29.553896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:29.553896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OibXs7jPIvYuF//kV8Yg3Vq3flpnyRE1k4rU2sykY4A0jBDmn3YENwAXLLpS04dsHtXLRhITxarddRABnpMWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:29.554380Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.23880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d67de2581f32b8f5860341749054b5c4304d2c5d38e6489d03573cfa19171f33","sha256:a8ad59435acee4ffe409f01cf6125dfebab16801f109a5aaa6d148c1fe269f6d"],"state_sha256":"11233912654b57ecc8083098e2b74b27f787be78a636b4965b4a11a4188767c8"}