{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C3SFUUE64IYJAM7JRKMGZWAPOM","short_pith_number":"pith:C3SFUUE6","canonical_record":{"source":{"id":"1602.04603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-02-15T10:02:31Z","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP","math.SP"],"title_canon_sha256":"3e3a03fddb308704a6639f78f0d3e1995c8d2e3faac3e72848dffedcd484ee9d","abstract_canon_sha256":"86a78b5af3d4bd1b7815c92a45eb877ed3a0cc9f70f0ff97a48a8ceccbf93e19"},"schema_version":"1.0"},"canonical_sha256":"16e45a509ee2309033e98a986cd80f730cdac131fcb32046f7c2618cb544a883","source":{"kind":"arxiv","id":"1602.04603","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04603","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04603v1","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04603","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"C3SFUUE64IYJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C3SFUUE64IYJAM7J","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C3SFUUE6","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C3SFUUE64IYJAM7JRKMGZWAPOM","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04603","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-02-15T10:02:31Z","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP","math.SP"],"title_canon_sha256":"3e3a03fddb308704a6639f78f0d3e1995c8d2e3faac3e72848dffedcd484ee9d","abstract_canon_sha256":"86a78b5af3d4bd1b7815c92a45eb877ed3a0cc9f70f0ff97a48a8ceccbf93e19"},"schema_version":"1.0"},"canonical_sha256":"16e45a509ee2309033e98a986cd80f730cdac131fcb32046f7c2618cb544a883","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:49.558299Z","signature_b64":"HoDG+IhpbsLAxbllTJwdlmHPzW6H1xxJdljtpyXAj8O37+pbid3oRO9u0MEumjrcgI6qIhBQo5bsJoEfseDyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16e45a509ee2309033e98a986cd80f730cdac131fcb32046f7c2618cb544a883","last_reissued_at":"2026-05-18T01:20:49.557902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:49.557902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04603","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":"2026-05-18T01:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qck0N4sn111f7QQCk9daYLLGCRg/mU9CgIpvNYq7DyhPdKRRH73kt0FZuRK/HOiJzbk34PhT1Ma18nWac/L8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:29:48.948600Z"},"content_sha256":"94c20a0a7fce27223f40d17530824c731312a22eba228879294f57532bd84172","schema_version":"1.0","event_id":"sha256:94c20a0a7fce27223f40d17530824c731312a22eba228879294f57532bd84172"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C3SFUUE64IYJAM7JRKMGZWAPOM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fredholm criteria for pseudodifferential operators and induced representations of groupoid algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.FA","math.MP","math.SP"],"primary_cat":"math.OA","authors_text":"Victor Nistor","submitted_at":"2016-02-15T10:02:31Z","abstract_excerpt":"We characterize the groupoids for which an operator is Fredholm if, and only if, its principal symbol and all its boundary restrictions are invertible. A groupoid with this property is called {\\em Fredholm}. Using results on the Effros-Hahn conjecture, we show that an almost amenable, Hausdorff, second countable groupoid is Fredholm. Many groupoids, and hence many pseudodifferential operators appearing in practice, fit into this framework. In particular, one can use these results to characterize the Fredholm operators on manifolds with cylindrical and poly-cylindrical ends, on manifolds that a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04603","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":"2026-05-18T01:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3E7+Xubgm/MWbwIkAQhsbyBBok4rCxQZNLSkfqitPRJTIWeo4AF6Ncg+jxRTtYokj8qW9VHlfC7mPHPVUnVdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:29:48.948936Z"},"content_sha256":"1bd0bb59fd7ff4f9003a833a2bc347477b3bb09fae5c5577410ed3bc4f56d0a0","schema_version":"1.0","event_id":"sha256:1bd0bb59fd7ff4f9003a833a2bc347477b3bb09fae5c5577410ed3bc4f56d0a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3SFUUE64IYJAM7JRKMGZWAPOM/bundle.json","state_url":"https://pith.science/pith/C3SFUUE64IYJAM7JRKMGZWAPOM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3SFUUE64IYJAM7JRKMGZWAPOM/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":"2026-06-02T00:29:48Z","links":{"resolver":"https://pith.science/pith/C3SFUUE64IYJAM7JRKMGZWAPOM","bundle":"https://pith.science/pith/C3SFUUE64IYJAM7JRKMGZWAPOM/bundle.json","state":"https://pith.science/pith/C3SFUUE64IYJAM7JRKMGZWAPOM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3SFUUE64IYJAM7JRKMGZWAPOM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C3SFUUE64IYJAM7JRKMGZWAPOM","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":"86a78b5af3d4bd1b7815c92a45eb877ed3a0cc9f70f0ff97a48a8ceccbf93e19","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-02-15T10:02:31Z","title_canon_sha256":"3e3a03fddb308704a6639f78f0d3e1995c8d2e3faac3e72848dffedcd484ee9d"},"schema_version":"1.0","source":{"id":"1602.04603","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04603","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04603v1","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04603","created_at":"2026-05-18T01:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"C3SFUUE64IYJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C3SFUUE64IYJAM7J","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C3SFUUE6","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:1bd0bb59fd7ff4f9003a833a2bc347477b3bb09fae5c5577410ed3bc4f56d0a0","target":"graph","created_at":"2026-05-18T01:20:49Z","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 characterize the groupoids for which an operator is Fredholm if, and only if, its principal symbol and all its boundary restrictions are invertible. A groupoid with this property is called {\\em Fredholm}. Using results on the Effros-Hahn conjecture, we show that an almost amenable, Hausdorff, second countable groupoid is Fredholm. Many groupoids, and hence many pseudodifferential operators appearing in practice, fit into this framework. In particular, one can use these results to characterize the Fredholm operators on manifolds with cylindrical and poly-cylindrical ends, on manifolds that a","authors_text":"Victor Nistor","cross_cats":["math-ph","math.AP","math.FA","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-02-15T10:02:31Z","title":"Fredholm criteria for pseudodifferential operators and induced representations of groupoid algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04603","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":"sha256:94c20a0a7fce27223f40d17530824c731312a22eba228879294f57532bd84172","target":"record","created_at":"2026-05-18T01:20:49Z","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":"86a78b5af3d4bd1b7815c92a45eb877ed3a0cc9f70f0ff97a48a8ceccbf93e19","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-02-15T10:02:31Z","title_canon_sha256":"3e3a03fddb308704a6639f78f0d3e1995c8d2e3faac3e72848dffedcd484ee9d"},"schema_version":"1.0","source":{"id":"1602.04603","kind":"arxiv","version":1}},"canonical_sha256":"16e45a509ee2309033e98a986cd80f730cdac131fcb32046f7c2618cb544a883","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16e45a509ee2309033e98a986cd80f730cdac131fcb32046f7c2618cb544a883","first_computed_at":"2026-05-18T01:20:49.557902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:49.557902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HoDG+IhpbsLAxbllTJwdlmHPzW6H1xxJdljtpyXAj8O37+pbid3oRO9u0MEumjrcgI6qIhBQo5bsJoEfseDyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:49.558299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04603","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94c20a0a7fce27223f40d17530824c731312a22eba228879294f57532bd84172","sha256:1bd0bb59fd7ff4f9003a833a2bc347477b3bb09fae5c5577410ed3bc4f56d0a0"],"state_sha256":"7a586d4477d9d0f38bbad317b4c9609f430e18cccf595dccdf9f4eed3ad75bc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f3ryX23SK+2IUaMBIzGaevwJBx2eVpQDD1NTSkRpPodVdeRxwSc88y8mPv0BfaA1NXA9a7mjGp24dwJc8KELBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:29:48.950844Z","bundle_sha256":"4df6ed123934d1c0865bc07e6fa4ec712604f775e2b3bf3e2a7565c6f5e78fbc"}}