{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZCWLKSFGEMNKTAJTP23KS36FNU","short_pith_number":"pith:ZCWLKSFG","canonical_record":{"source":{"id":"1410.8030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T15:48:09Z","cross_cats_sorted":[],"title_canon_sha256":"eca5c9da62388b67137712200490f4d402b76470841b9cc24301d0baa99ed025","abstract_canon_sha256":"9dfc82d84464607a0244f6dd25726ba7cdaff4693fa49698c399e0f75a9decec"},"schema_version":"1.0"},"canonical_sha256":"c8acb548a6231aa981337eb6a96fc56d14e489b3215b8a7a19df88d5bb3679a9","source":{"kind":"arxiv","id":"1410.8030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8030","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8030v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8030","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZCWLKSFGEMNK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCWLKSFGEMNKTAJT","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCWLKSFG","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZCWLKSFGEMNKTAJTP23KS36FNU","target":"record","payload":{"canonical_record":{"source":{"id":"1410.8030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T15:48:09Z","cross_cats_sorted":[],"title_canon_sha256":"eca5c9da62388b67137712200490f4d402b76470841b9cc24301d0baa99ed025","abstract_canon_sha256":"9dfc82d84464607a0244f6dd25726ba7cdaff4693fa49698c399e0f75a9decec"},"schema_version":"1.0"},"canonical_sha256":"c8acb548a6231aa981337eb6a96fc56d14e489b3215b8a7a19df88d5bb3679a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:07.489891Z","signature_b64":"cMivLZzeN6tncpmJaalgc3OpxxWVPGvB04Lwddnx3yWRLLYh630Z3NUyDy2Ypn/fQ3wFZusjugOZX/HRTTlODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8acb548a6231aa981337eb6a96fc56d14e489b3215b8a7a19df88d5bb3679a9","last_reissued_at":"2026-05-18T02:39:07.489230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:07.489230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.8030","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wxo0f90dCMW9bJQxuSLAZnwq98b2lh1nsJzVUtoYcwt8hRacI7f30Db4w5MG49AjrwMfw+jflMLYKhf5L0hmCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:15:15.086642Z"},"content_sha256":"47a630a6bfaf4c21c2d6bb319392e47d4f41dac1c68fb3df3d5aeb8ae0e75c95","schema_version":"1.0","event_id":"sha256:47a630a6bfaf4c21c2d6bb319392e47d4f41dac1c68fb3df3d5aeb8ae0e75c95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZCWLKSFGEMNKTAJTP23KS36FNU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Indices of pseudodifferential operators on open manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexander Engel","submitted_at":"2014-10-29T15:48:09Z","abstract_excerpt":"We generalize Roe's Index Theorem for operators of Dirac type on open manifolds to elliptic pseudodifferential operators. To this end we introduce a class of pseudodifferential operators on manifolds of bounded geometry which is more general than similar classes defined by other authors. We revisit Spakula's uniform K-homology and show that our elliptic pseudodifferential operators naturally define classes there. Furthermore, we use the uniform coarse assembly map to relate these classes to the index classes of these operators in the K-theory of the uniform Roe algebra. Our investigation of un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8030","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLRIt4awnctapTpyVdfF4bV1Q9KWEAAfle8H49IQjBzoLGwQVwKMelRwVqE2B/5zsqobXjr4ZCPy7LBXyecYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:15:15.087448Z"},"content_sha256":"f8851f98d1ed8874a31ed39f83cf05a11689adeaa6b62e36162ad8bdbae7a961","schema_version":"1.0","event_id":"sha256:f8851f98d1ed8874a31ed39f83cf05a11689adeaa6b62e36162ad8bdbae7a961"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCWLKSFGEMNKTAJTP23KS36FNU/bundle.json","state_url":"https://pith.science/pith/ZCWLKSFGEMNKTAJTP23KS36FNU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCWLKSFGEMNKTAJTP23KS36FNU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T00:15:15Z","links":{"resolver":"https://pith.science/pith/ZCWLKSFGEMNKTAJTP23KS36FNU","bundle":"https://pith.science/pith/ZCWLKSFGEMNKTAJTP23KS36FNU/bundle.json","state":"https://pith.science/pith/ZCWLKSFGEMNKTAJTP23KS36FNU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCWLKSFGEMNKTAJTP23KS36FNU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZCWLKSFGEMNKTAJTP23KS36FNU","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":"9dfc82d84464607a0244f6dd25726ba7cdaff4693fa49698c399e0f75a9decec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T15:48:09Z","title_canon_sha256":"eca5c9da62388b67137712200490f4d402b76470841b9cc24301d0baa99ed025"},"schema_version":"1.0","source":{"id":"1410.8030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8030","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8030v1","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8030","created_at":"2026-05-18T02:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZCWLKSFGEMNK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCWLKSFGEMNKTAJT","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCWLKSFG","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:f8851f98d1ed8874a31ed39f83cf05a11689adeaa6b62e36162ad8bdbae7a961","target":"graph","created_at":"2026-05-18T02:39:07Z","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 operators of Dirac type on open manifolds to elliptic pseudodifferential operators. To this end we introduce a class of pseudodifferential operators on manifolds of bounded geometry which is more general than similar classes defined by other authors. We revisit Spakula's uniform K-homology and show that our elliptic pseudodifferential operators naturally define classes there. Furthermore, we use the uniform coarse assembly map to relate these classes to the index classes of these operators in the K-theory of the uniform Roe algebra. Our investigation of un","authors_text":"Alexander Engel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T15:48:09Z","title":"Indices of pseudodifferential operators on open manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8030","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":"sha256:47a630a6bfaf4c21c2d6bb319392e47d4f41dac1c68fb3df3d5aeb8ae0e75c95","target":"record","created_at":"2026-05-18T02:39:07Z","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":"9dfc82d84464607a0244f6dd25726ba7cdaff4693fa49698c399e0f75a9decec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-29T15:48:09Z","title_canon_sha256":"eca5c9da62388b67137712200490f4d402b76470841b9cc24301d0baa99ed025"},"schema_version":"1.0","source":{"id":"1410.8030","kind":"arxiv","version":1}},"canonical_sha256":"c8acb548a6231aa981337eb6a96fc56d14e489b3215b8a7a19df88d5bb3679a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8acb548a6231aa981337eb6a96fc56d14e489b3215b8a7a19df88d5bb3679a9","first_computed_at":"2026-05-18T02:39:07.489230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:07.489230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cMivLZzeN6tncpmJaalgc3OpxxWVPGvB04Lwddnx3yWRLLYh630Z3NUyDy2Ypn/fQ3wFZusjugOZX/HRTTlODQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:07.489891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47a630a6bfaf4c21c2d6bb319392e47d4f41dac1c68fb3df3d5aeb8ae0e75c95","sha256:f8851f98d1ed8874a31ed39f83cf05a11689adeaa6b62e36162ad8bdbae7a961"],"state_sha256":"b54467f3803364434fa0a0b4634147febcceff5675f3f7c32a7db3143536396e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8fLOtOEO+umcssEXa6AUqff22O7pKhMCyQp1H2nPdUUkcZtSygzZ2u+mBT4ELRXTmWYnqzwY2v1VQUVWvAZhAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:15:15.092077Z","bundle_sha256":"d0d6a05c34d181e930966e940cc6f77e15ca7484a51a006a0ee7b1ca154ca439"}}