{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZIQKJ5APNFSRBHSKKDB3KKGCS6","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":"9de16c09f5e31a137cfb0b23db695a0479cc9be22e4b26fd8525784f1288993f","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-12-04T02:54:24Z","title_canon_sha256":"9cbd0d09ebaa933bce9b9df049416d45dd369a21d3d98ebd3b0a6d39741a11f2"},"schema_version":"1.0","source":{"id":"2512.05155","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.05155","created_at":"2026-06-02T02:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"2512.05155v2","created_at":"2026-06-02T02:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.05155","created_at":"2026-06-02T02:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"ZIQKJ5APNFSR","created_at":"2026-06-02T02:04:11Z"},{"alias_kind":"pith_short_16","alias_value":"ZIQKJ5APNFSRBHSK","created_at":"2026-06-02T02:04:11Z"},{"alias_kind":"pith_short_8","alias_value":"ZIQKJ5AP","created_at":"2026-06-02T02:04:11Z"}],"graph_snapshots":[{"event_id":"sha256:6cfb1fcbc89daf02be562ae27cf6161f0a2c5ea1d06649fc4d35a63fd31a7288","target":"graph","created_at":"2026-06-02T02:04:11Z","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/2512.05155/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Surface holonomy plays a central role in higher gauge theory, bundle gerbes and the geometric formulation of Wess--Zumino terms in string theory. In this work, we consider the relation between surface holonomy and nonabelian multiplicative integration on surfaces. In this framework, we interpret the local Stokes law as a curvature obstruction law for higher holonomy and investigate its consequences in the abelian setting. We derive a global three-dimensional Stokes relation and show that it reproduces the familiar Wess-Zumino phase formula. In particular, the phase difference between two surfa","authors_text":"Hollis Williams","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-12-04T02:54:24Z","title":"Nonabelian multiplicative integration and curvature obstructions for surface holonomy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.05155","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:b3d21c54f8aa9bd043a01e0ca2397dee271a69bf9ea5ec2d7e160015fbe12f24","target":"record","created_at":"2026-06-02T02:04:11Z","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":"9de16c09f5e31a137cfb0b23db695a0479cc9be22e4b26fd8525784f1288993f","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-12-04T02:54:24Z","title_canon_sha256":"9cbd0d09ebaa933bce9b9df049416d45dd369a21d3d98ebd3b0a6d39741a11f2"},"schema_version":"1.0","source":{"id":"2512.05155","kind":"arxiv","version":2}},"canonical_sha256":"ca20a4f40f6965109e4a50c3b528c297acf493d11995a05d596c1792ba5b43a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca20a4f40f6965109e4a50c3b528c297acf493d11995a05d596c1792ba5b43a2","first_computed_at":"2026-06-02T02:04:11.922508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:11.922508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lQedP4nWb7xZDMKyijPARIGbzVrBimOXrh2ZFuS/ay1xjKDVlbxk62uUYT5tJVv9Hbo9BJxkhdKGrEoQ7ljyCw==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:11.923020Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.05155","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3d21c54f8aa9bd043a01e0ca2397dee271a69bf9ea5ec2d7e160015fbe12f24","sha256:6cfb1fcbc89daf02be562ae27cf6161f0a2c5ea1d06649fc4d35a63fd31a7288"],"state_sha256":"bafe675dc623fe0b84c1f9e853fed0c931c3669b3d108b1563b0d2300a6e7c10"}