{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4UST5PRBBDIJKLDXM2IRUF33QD","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":"7e73df1aaf67e6730319e29395d0f248633e5ed010822ef6be9c407745d6a492","cross_cats_sorted":["cond-mat.str-el","hep-th","math.AT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-30T14:55:00Z","title_canon_sha256":"8caa968e26ef91e4c3d9e792048e02f5ebcae9a08202459a5b9fee16a32febf8"},"schema_version":"1.0","source":{"id":"2501.18399","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.18399","created_at":"2026-07-05T10:12:26Z"},{"alias_kind":"arxiv_version","alias_value":"2501.18399v1","created_at":"2026-07-05T10:12:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18399","created_at":"2026-07-05T10:12:26Z"},{"alias_kind":"pith_short_12","alias_value":"4UST5PRBBDIJ","created_at":"2026-07-05T10:12:26Z"},{"alias_kind":"pith_short_16","alias_value":"4UST5PRBBDIJKLDX","created_at":"2026-07-05T10:12:26Z"},{"alias_kind":"pith_short_8","alias_value":"4UST5PRB","created_at":"2026-07-05T10:12:26Z"}],"graph_snapshots":[{"event_id":"sha256:da0559a8b8700c30f5a8aede3e49f593d3bd0763c3f2903524b8e50673963993","target":"graph","created_at":"2026-07-05T10:12:26Z","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/2501.18399/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the global structure of topological defects which wrap a submanifold $F\\subset M$ in a quantum field theory defined on a closed manifold $M$. The Pontryagin-Thom construction oversees the interplay between the global structure of $F$ and the global structure of $M$. We will employ this construction to two distinct mathematical frameworks with physical applications. The first framework is the concept of a characteristic structure, consisting of the data of pairs of manifolds $(M,F)$ where $F$ is Poincar\\'e dual to some characteristic class. This concept is discussed in the mathem","authors_text":"Arun Debray, Matthew Yu, Weicheng Ye","cross_cats":["cond-mat.str-el","hep-th","math.AT","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-30T14:55:00Z","title":"Global Structure in the Presence of a Topological Defect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18399","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:dc379a888e94977c3a9c4fa3040284b224a02d3f2fbc1fa5858009da63f869ca","target":"record","created_at":"2026-07-05T10:12:26Z","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":"7e73df1aaf67e6730319e29395d0f248633e5ed010822ef6be9c407745d6a492","cross_cats_sorted":["cond-mat.str-el","hep-th","math.AT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-30T14:55:00Z","title_canon_sha256":"8caa968e26ef91e4c3d9e792048e02f5ebcae9a08202459a5b9fee16a32febf8"},"schema_version":"1.0","source":{"id":"2501.18399","kind":"arxiv","version":1}},"canonical_sha256":"e5253ebe2108d0952c7766911a177b80d4b13e27a8e418fc1f4332044402258e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5253ebe2108d0952c7766911a177b80d4b13e27a8e418fc1f4332044402258e","first_computed_at":"2026-07-05T10:12:26.021295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:12:26.021295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GTDsbe1RUWkJCirGx3U0eIQM+Gxnnlxsh6kF9gFcjiyhQH3zX7vURE5V9W1tp2udNYX2CzmQc7rZYPF+rikHAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:12:26.021788Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.18399","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc379a888e94977c3a9c4fa3040284b224a02d3f2fbc1fa5858009da63f869ca","sha256:da0559a8b8700c30f5a8aede3e49f593d3bd0763c3f2903524b8e50673963993"],"state_sha256":"c5b9e993c785c8aba25705ed88250f3c5bb70bc98f9d22438eb23aabd486579a"}