{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:6EA3MEW5ZXT6MPA47RQRFE7PLF","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":"20420b53f6c004b49487843167e623a5baf1be4c6ee7bd7ce457fac1e7f7ec0b","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AT","submitted_at":"2006-02-10T10:15:55Z","title_canon_sha256":"c125dea7a91ecf4c69bd9b04d5efaf3a7fb0ade3ddbcc8dd0139ea2e79b014c9"},"schema_version":"1.0","source":{"id":"math/0602210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0602210","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0602210v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0602210","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"6EA3MEW5ZXT6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"6EA3MEW5ZXT6MPA4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"6EA3MEW5","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:c4a4232d91ed5f941c654f51cb491ede989dec5ad0dcb9fb5849f4bd297b2c3d","target":"graph","created_at":"2026-05-18T02:57:45Z","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":"We show that the Chas-Sullivan loop product, a combination of the Pontrjagin product on the fiber and intersection product on the base, makes sense on the total space homology of any fiberwise monoid E over a closed oriented manifold M. More generally the Thom spectrum E^{-TM} is a ring spectrum. Similarly a fiberwise module over E defines a module over E^{-TM}. Fiberwise monoids include adjoint bundles of principal bundles, and the construction is natural with respect to maps of principal bundles. This naturality implies homotopy invariance of the algebra structure on H_*(LM) arising from the","authors_text":"Kate Gruher, Paolo Salvatore","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2006-02-10T10:15:55Z","title":"Generalized string topology operations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0602210","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":"sha256:8e2c396879f6df1877ce2ca7e3700a9a15ecc3c16ded5c40ecbf9ff296f3362b","target":"record","created_at":"2026-05-18T02:57:45Z","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":"20420b53f6c004b49487843167e623a5baf1be4c6ee7bd7ce457fac1e7f7ec0b","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AT","submitted_at":"2006-02-10T10:15:55Z","title_canon_sha256":"c125dea7a91ecf4c69bd9b04d5efaf3a7fb0ade3ddbcc8dd0139ea2e79b014c9"},"schema_version":"1.0","source":{"id":"math/0602210","kind":"arxiv","version":1}},"canonical_sha256":"f101b612ddcde7e63c1cfc611293ef5960f8b89b5e4c46d9afe5de5f430e7b4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f101b612ddcde7e63c1cfc611293ef5960f8b89b5e4c46d9afe5de5f430e7b4f","first_computed_at":"2026-05-18T02:57:45.654389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.654389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+jgGFDEeRJR5AsmXqnYA2QrAZt6Zyd7+M4lkAbG7pLDu80QfDaHRlrc3zct3GVCFEkHDek19ZpMTUGAfvN7tBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.654949Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0602210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e2c396879f6df1877ce2ca7e3700a9a15ecc3c16ded5c40ecbf9ff296f3362b","sha256:c4a4232d91ed5f941c654f51cb491ede989dec5ad0dcb9fb5849f4bd297b2c3d"],"state_sha256":"f9f4981290b8acb192bfae5a9d84ec24e110f37cea4c2bcdca494401615ea59f"}