{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FP2I5XL6B2YWJXWAQU33HRSWPR","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":"3e67c9df6cc6a61127fed383779861ed620978dc53eff55b8f72327f13a5c8af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-03-29T16:50:24Z","title_canon_sha256":"3ab8faf06774b91cf423a9b90b76fba59fab4224f8d83fea9c516b51562f3589"},"schema_version":"1.0","source":{"id":"1803.11148","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.11148","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1803.11148v2","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.11148","created_at":"2026-05-17T23:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"FP2I5XL6B2YW","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FP2I5XL6B2YWJXWA","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FP2I5XL6","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:24d5b080f281f7580648abadbab128e218bf7c891fa047fd62d4bc83d46f7fd9","target":"graph","created_at":"2026-05-17T23:48:01Z","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 define and study the index map for families of $G$-transversally elliptic operators and introduce the multiplicity for a given irreducible representation as a virtual bundle over the base of the fibration. We then prove the usual axiomatic properties for the index map extending the Atiyah-Singer results [1]. Finally, we compute the Kasparov intersection product of our index class against the K-homology class of an elliptic operator on the base. Our approach is based on the functorial properties of the intersection product, and relies on some constructions due to Connes-Skandalis and to Hils","authors_text":"Alexandre Baldare","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-03-29T16:50:24Z","title":"The index of G-transversally elliptic families I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11148","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":"sha256:0e2ca947a587bce0c7fbe3b32b5f3a970e5fcb9411427383ac327169260ebc94","target":"record","created_at":"2026-05-17T23:48:01Z","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":"3e67c9df6cc6a61127fed383779861ed620978dc53eff55b8f72327f13a5c8af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-03-29T16:50:24Z","title_canon_sha256":"3ab8faf06774b91cf423a9b90b76fba59fab4224f8d83fea9c516b51562f3589"},"schema_version":"1.0","source":{"id":"1803.11148","kind":"arxiv","version":2}},"canonical_sha256":"2bf48edd7e0eb164dec08537b3c6567c40ad613f0bfc73382a059b23a4247d91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bf48edd7e0eb164dec08537b3c6567c40ad613f0bfc73382a059b23a4247d91","first_computed_at":"2026-05-17T23:48:01.970600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:01.970600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FCTIoPDe/Wr2EJmd8X7TxiDFTcW/c9YLDp219MGCAtYOqPuVuCoouKWusH8sIa5MIffVh/qpW6LvjDRrkIMQCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:01.971069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.11148","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e2ca947a587bce0c7fbe3b32b5f3a970e5fcb9411427383ac327169260ebc94","sha256:24d5b080f281f7580648abadbab128e218bf7c891fa047fd62d4bc83d46f7fd9"],"state_sha256":"4396dede951f9c4d5ca8d7dba407857d19d55aec878ec0da9f3d301b053fd0b8"}