{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:35NRWVTIRQB6X7A7NYZ6YZAKDM","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":"2d6c849e24e08f2a844a8fa179003f25e970fe519a461c85238805019ad74840","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-02T14:44:26Z","title_canon_sha256":"17b06b4b541c80281f5aa686ef1a08824991d917b45f884d5c5691d81932118d"},"schema_version":"1.0","source":{"id":"1502.00494","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00494","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00494v3","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00494","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"35NRWVTIRQB6","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"35NRWVTIRQB6X7A7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"35NRWVTI","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:9511780d8e9d50296b074d521689d1bb238cd5d54d56beefc99cea55a0a401e0","target":"graph","created_at":"2026-05-18T00:04:24Z","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 generalize Roe's index theorem for graded generalized Dirac operators on amenable manifolds to multigraded elliptic uniform pseudodifferential operators.\n  This generalization will follow as a corollary from a local index theorem that is valid on any manifold of bounded geometry. This local formula incorporates the uniform estimates that are present in the definition of our class of pseudodifferential operators which is more general than similar classes defined by other authors.\n  We will revisit Spakula's uniform K-homology and show that multigraded elliptic uniform pseudodifferential oper","authors_text":"Alexander Engel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-02T14:44:26Z","title":"Index theory of uniform pseudodifferential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00494","kind":"arxiv","version":3},"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":"sha256:1de063ce87bbdb760ce08089a778a903e63cf9e25cc7abddde3989bdc58e39c9","target":"record","created_at":"2026-05-18T00:04:24Z","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":"2d6c849e24e08f2a844a8fa179003f25e970fe519a461c85238805019ad74840","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-02-02T14:44:26Z","title_canon_sha256":"17b06b4b541c80281f5aa686ef1a08824991d917b45f884d5c5691d81932118d"},"schema_version":"1.0","source":{"id":"1502.00494","kind":"arxiv","version":3}},"canonical_sha256":"df5b1b56688c03ebfc1f6e33ec640a1b14f70d48651d679f8cefb8feb2d483cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df5b1b56688c03ebfc1f6e33ec640a1b14f70d48651d679f8cefb8feb2d483cd","first_computed_at":"2026-05-18T00:04:24.483663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:24.483663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nF5ICL1Y7M/6xYes/QToehpb+fvJH2hX5Aofoe40f4xJH72mI5WQrGVHVhNJXo3owZdgbrrBLNED7nc2M+ikCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:24.484322Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00494","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1de063ce87bbdb760ce08089a778a903e63cf9e25cc7abddde3989bdc58e39c9","sha256:9511780d8e9d50296b074d521689d1bb238cd5d54d56beefc99cea55a0a401e0"],"state_sha256":"09c89e739513e554e55b27a5cb92f23b5b07d5b4736c0cb1585fa2b19874ad42"}