{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZCCO6R4BPOFSSNN5C6SUGSOW6L","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":"dfb7dab03576050dda7107ed874736a8a961388896f66b0c4b77705f13c9fcd5","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-02T12:23:44Z","title_canon_sha256":"a007aae420fe79df77cf9c24127d56bba088751cbd62e8ad2098250e35478e97"},"schema_version":"1.0","source":{"id":"1304.0613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0613","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0613v1","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0613","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZCCO6R4BPOFS","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZCCO6R4BPOFSSNN5","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZCCO6R4B","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:4ba22744f057367bc553ff024aa8472bdfa71fdb01f6dcb1fb23ad7cac309287","target":"graph","created_at":"2026-05-18T03:29:14Z","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"},"paper":{"abstract_excerpt":"Given a principal bundle over a closed manifold, G --> P --> M, let P^{Ad} --> M be the associated adjoint bundle. Gruher and Salvatore showed that the Thom spectrum (P^{Ad})^{-TM} is a ring spectrum whose corresponding product in homology is a Chas-Sullivan type string topology product. We refer to this spectrum as the `string topology spectrum of P\", S (P). In the universal case when P is contractible, S(P) is equivalent to LM^{-TM} where LM is the free loop space of the manifold. This ring spectrum was introduced by the authors as a homotopy theoretic realization of the Chas-Sullivan string","authors_text":"John D.S. Jones, Ralph L. Cohen","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-02T12:23:44Z","title":"Gauge theory and string topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0613","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":"sha256:9dfd10af47af88d86e8de9aff5156a31fb23d9718feb7cfc609c565ec0daee42","target":"record","created_at":"2026-05-18T03:29:14Z","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":"dfb7dab03576050dda7107ed874736a8a961388896f66b0c4b77705f13c9fcd5","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-04-02T12:23:44Z","title_canon_sha256":"a007aae420fe79df77cf9c24127d56bba088751cbd62e8ad2098250e35478e97"},"schema_version":"1.0","source":{"id":"1304.0613","kind":"arxiv","version":1}},"canonical_sha256":"c884ef47817b8b2935bd17a54349d6f2f1828d07b1e08a4b1fdac19464542cf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c884ef47817b8b2935bd17a54349d6f2f1828d07b1e08a4b1fdac19464542cf0","first_computed_at":"2026-05-18T03:29:14.878494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:14.878494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P1EuEXw3zvUxew/7b5qPon5JSUs/+aUSKLQVSyQQsM9umJgsfegKjmDbLmjj7Is3+LLYtss/EWpdHDAIhyWFCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:14.879068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9dfd10af47af88d86e8de9aff5156a31fb23d9718feb7cfc609c565ec0daee42","sha256:4ba22744f057367bc553ff024aa8472bdfa71fdb01f6dcb1fb23ad7cac309287"],"state_sha256":"e0f17e2e3ce80a8d6a511fbe438792ed597c2c97b38a0d4fcd7321163918607a"}