{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:56J32NWRRRKL6I6M6FEEKDVMNT","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":"5af70722ea16cb5dc95366bad3e337acfb7f51079cd09b00ba17ab13686426ea","cross_cats_sorted":["hep-th","math.DG"],"license":"","primary_cat":"math.KT","submitted_at":"2005-07-21T04:36:49Z","title_canon_sha256":"97a7c3e7d7a7ab9801f8613236a17c9d0e472fce6ea551d8828ed37cc0b0331b"},"schema_version":"1.0","source":{"id":"math/0507414","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0507414","created_at":"2026-07-04T14:50:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/0507414v4","created_at":"2026-07-04T14:50:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0507414","created_at":"2026-07-04T14:50:35Z"},{"alias_kind":"pith_short_12","alias_value":"56J32NWRRRKL","created_at":"2026-07-04T14:50:35Z"},{"alias_kind":"pith_short_16","alias_value":"56J32NWRRRKL6I6M","created_at":"2026-07-04T14:50:35Z"},{"alias_kind":"pith_short_8","alias_value":"56J32NWR","created_at":"2026-07-04T14:50:35Z"}],"graph_snapshots":[{"event_id":"sha256:a231a8a6cc08a2e270f3839c63bd02c87dc8317d8f42f00ee19b83cae59dae57","target":"graph","created_at":"2026-07-04T14:50:35Z","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/math/0507414/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable proper map $f: X\\to Y$ (not necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any $K$-oriented differentiable proper map and the Atiyah-Singer index theorem of Dirac operators on Clifford modules. For $D$-branes satisfying Freed-Witten's anomaly cancellation condition in a manifold with a non-trivial $B$-field, we associate a canonical element in the twisted K-group to get the so-called","authors_text":"Alan L. Carey, Bai-Ling Wang","cross_cats":["hep-th","math.DG"],"headline":"","license":"","primary_cat":"math.KT","submitted_at":"2005-07-21T04:36:49Z","title":"Thom isomorphism and Push-forward map in twisted K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507414","kind":"arxiv","version":4},"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":"sha256:8e3e5c7d5478723e97f392ead5d7d4a95a7b7fe5ef403d09d3ca7fb255bd9e59","target":"record","created_at":"2026-07-04T14:50:35Z","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":"5af70722ea16cb5dc95366bad3e337acfb7f51079cd09b00ba17ab13686426ea","cross_cats_sorted":["hep-th","math.DG"],"license":"","primary_cat":"math.KT","submitted_at":"2005-07-21T04:36:49Z","title_canon_sha256":"97a7c3e7d7a7ab9801f8613236a17c9d0e472fce6ea551d8828ed37cc0b0331b"},"schema_version":"1.0","source":{"id":"math/0507414","kind":"arxiv","version":4}},"canonical_sha256":"ef93bd36d18c54bf23ccf148450eac6ce9e3066289f5faab33858540833eb200","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef93bd36d18c54bf23ccf148450eac6ce9e3066289f5faab33858540833eb200","first_computed_at":"2026-07-04T14:50:35.909764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:50:35.909764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TlE2KOqCSH5sO5FJmSF+jB3/dt6UQdzt+Qpj3uQn8A+jJe2Fcdtx+fvbDlZ0KlXifxdsQp8kT+exoArl42S+CA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:50:35.910098Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0507414","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e3e5c7d5478723e97f392ead5d7d4a95a7b7fe5ef403d09d3ca7fb255bd9e59","sha256:a231a8a6cc08a2e270f3839c63bd02c87dc8317d8f42f00ee19b83cae59dae57"],"state_sha256":"29611c5121e5522bc7fee7d2c4fd3ff493432edb4bef389d6ad934b424e3a973"}