{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XMBW3KX5C3KW2MVFPOX6TJOIRS","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":"5adf413916a1932d8c130bcdf7ccc93ea42eede81d13d20dbd5455396edd063c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-07-14T18:55:33Z","title_canon_sha256":"84d6b7f0c4ed97c0843e91a028c3a8bd6c15b1478c94f70f7b1397b161da241f"},"schema_version":"1.0","source":{"id":"1607.04248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04248","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04248v2","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04248","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"XMBW3KX5C3KW","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XMBW3KX5C3KW2MVF","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XMBW3KX5","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:593525ea32040c0346d0df78d5f9421d8bce2de6e43e662ca0f31f354cab3c21","target":"graph","created_at":"2026-05-18T00:49:42Z","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 gerbe $L$, on the holonomy groupoid $\\mathcal G$ of the foliation $(M, \\mathcal F)$, whose pull-back to $M$ is torsion, we construct a Connes $\\Phi$-map from the twisted Dupont-Sullivan bicomplex of $\\mathcal G$ to the cyclic complex of the $L$-projective leafwise smoothing operators on $(M, \\mathcal F)$. Our construction allows to couple the $K$-theory analytic indices of $L$-projective leafwise elliptic operators with the twisted cohomology of $B\\mathcal G$ producing scalar higher invariants. Finally by adapting the Bismut-Quillen superconnection approach, we compute these higher twi","authors_text":"Alexander Gorokhovsky, Eric Leichtnam, Moulay-Tahar Benameur","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-07-14T18:55:33Z","title":"The higher twisted index theorem for foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04248","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":"sha256:1df5ef8b2c23d878e4cda77575f125cef0ffbcc0e243262f93027de2acfb671f","target":"record","created_at":"2026-05-18T00:49:42Z","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":"5adf413916a1932d8c130bcdf7ccc93ea42eede81d13d20dbd5455396edd063c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-07-14T18:55:33Z","title_canon_sha256":"84d6b7f0c4ed97c0843e91a028c3a8bd6c15b1478c94f70f7b1397b161da241f"},"schema_version":"1.0","source":{"id":"1607.04248","kind":"arxiv","version":2}},"canonical_sha256":"bb036daafd16d56d32a57bafe9a5c88c995a7d84321ad7401a96b6e20f0ee41e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb036daafd16d56d32a57bafe9a5c88c995a7d84321ad7401a96b6e20f0ee41e","first_computed_at":"2026-05-18T00:49:42.270329Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:42.270329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DLwhBY4C3urhElD96GB1VwqOAyrzatT73+1CFX701VOKXWc9j1CFy620JzVyyTnqfELoYB6GsHWOdPUdRrhfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:42.270790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1df5ef8b2c23d878e4cda77575f125cef0ffbcc0e243262f93027de2acfb671f","sha256:593525ea32040c0346d0df78d5f9421d8bce2de6e43e662ca0f31f354cab3c21"],"state_sha256":"df4c56889253e7915b93311701f1818864eed8ed78da8606deda4b4134e0cf31"}