{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2CRBV32XMUF2552X3FWYJ3RNHD","short_pith_number":"pith:2CRBV32X","canonical_record":{"source":{"id":"1810.10272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-10-24T09:49:48Z","cross_cats_sorted":[],"title_canon_sha256":"4d60a340bb134142382660aa44958901f4eddd8175d9159f20a2ce78f47b15a9","abstract_canon_sha256":"11550b73f737f340598daacc808d279279a7ce135d755d9bd9da8d9a28ebf56a"},"schema_version":"1.0"},"canonical_sha256":"d0a21aef57650baef757d96d84ee2d38e83653de9b780c541a445692159bc1e4","source":{"kind":"arxiv","id":"1810.10272","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10272","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10272v1","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10272","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"2CRBV32XMUF2","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2CRBV32XMUF2552X","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2CRBV32X","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2CRBV32XMUF2552X3FWYJ3RNHD","target":"record","payload":{"canonical_record":{"source":{"id":"1810.10272","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-10-24T09:49:48Z","cross_cats_sorted":[],"title_canon_sha256":"4d60a340bb134142382660aa44958901f4eddd8175d9159f20a2ce78f47b15a9","abstract_canon_sha256":"11550b73f737f340598daacc808d279279a7ce135d755d9bd9da8d9a28ebf56a"},"schema_version":"1.0"},"canonical_sha256":"d0a21aef57650baef757d96d84ee2d38e83653de9b780c541a445692159bc1e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:23.691533Z","signature_b64":"jUWANq6Y+MWuXHTzJjdOMzfWwh8aL0xpyShjo1UKRWKm3NcOCNpUb8lMscNBZNmEHFK93BlLTt1fH5RLbzO/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0a21aef57650baef757d96d84ee2d38e83653de9b780c541a445692159bc1e4","last_reissued_at":"2026-05-18T00:02:23.691046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:23.691046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.10272","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":"2026-05-18T00:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DUg8aNvDxOno9cCyrRMJ42ViEe/+mXFArUFHpt8WzybipU6TV79VuHfteDF+7fAO6G/tD/hhuNSGKsAN4AhMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:56:24.627559Z"},"content_sha256":"546ed6c816dea705471c69894286436007e1aa27de979d30c439157d7f9ca954","schema_version":"1.0","event_id":"sha256:546ed6c816dea705471c69894286436007e1aa27de979d30c439157d7f9ca954"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2CRBV32XMUF2552X3FWYJ3RNHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On pseudodifferential operators on filtered and multifiltered manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Robert Yuncken","submitted_at":"2018-10-24T09:49:48Z","abstract_excerpt":"This memoir is a summary of recent work, including collaborations with Erik van Erp, Christian Voigt and Marco Matassa, compiled for the \"Habilitation \\`a diriger des recherches\".\n  We present various different approaches to constructing algebras of pseudodifferential operators adapted to filtered and multifiltered manifolds and some quantum analogues. A general goal is the study of index problems in situations where standard elliptic theory is insufficient. We also present some applications of these constructions.\n  We begin by presenting a characterization of pseudodifferential operators on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10272","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":"2026-05-18T00:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ob4/+w7nqGnmXsYXEaE2fdKGN3WHuFKydTsKF1+xz1D48KFscQgXCzXW0YM0E7dgQBBFUOhDsLzzkCvB12tBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:56:24.627899Z"},"content_sha256":"61b9c80fa5dbb82d3912e101f94bf34a7bb590bb7da3851d305cf5df42099197","schema_version":"1.0","event_id":"sha256:61b9c80fa5dbb82d3912e101f94bf34a7bb590bb7da3851d305cf5df42099197"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2CRBV32XMUF2552X3FWYJ3RNHD/bundle.json","state_url":"https://pith.science/pith/2CRBV32XMUF2552X3FWYJ3RNHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2CRBV32XMUF2552X3FWYJ3RNHD/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":"2026-06-29T15:56:24Z","links":{"resolver":"https://pith.science/pith/2CRBV32XMUF2552X3FWYJ3RNHD","bundle":"https://pith.science/pith/2CRBV32XMUF2552X3FWYJ3RNHD/bundle.json","state":"https://pith.science/pith/2CRBV32XMUF2552X3FWYJ3RNHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2CRBV32XMUF2552X3FWYJ3RNHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2CRBV32XMUF2552X3FWYJ3RNHD","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":"11550b73f737f340598daacc808d279279a7ce135d755d9bd9da8d9a28ebf56a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-10-24T09:49:48Z","title_canon_sha256":"4d60a340bb134142382660aa44958901f4eddd8175d9159f20a2ce78f47b15a9"},"schema_version":"1.0","source":{"id":"1810.10272","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10272","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10272v1","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10272","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"2CRBV32XMUF2","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2CRBV32XMUF2552X","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2CRBV32X","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:61b9c80fa5dbb82d3912e101f94bf34a7bb590bb7da3851d305cf5df42099197","target":"graph","created_at":"2026-05-18T00:02:23Z","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":"This memoir is a summary of recent work, including collaborations with Erik van Erp, Christian Voigt and Marco Matassa, compiled for the \"Habilitation \\`a diriger des recherches\".\n  We present various different approaches to constructing algebras of pseudodifferential operators adapted to filtered and multifiltered manifolds and some quantum analogues. A general goal is the study of index problems in situations where standard elliptic theory is insufficient. We also present some applications of these constructions.\n  We begin by presenting a characterization of pseudodifferential operators on ","authors_text":"Robert Yuncken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-10-24T09:49:48Z","title":"On pseudodifferential operators on filtered and multifiltered manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10272","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":"sha256:546ed6c816dea705471c69894286436007e1aa27de979d30c439157d7f9ca954","target":"record","created_at":"2026-05-18T00:02:23Z","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":"11550b73f737f340598daacc808d279279a7ce135d755d9bd9da8d9a28ebf56a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-10-24T09:49:48Z","title_canon_sha256":"4d60a340bb134142382660aa44958901f4eddd8175d9159f20a2ce78f47b15a9"},"schema_version":"1.0","source":{"id":"1810.10272","kind":"arxiv","version":1}},"canonical_sha256":"d0a21aef57650baef757d96d84ee2d38e83653de9b780c541a445692159bc1e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0a21aef57650baef757d96d84ee2d38e83653de9b780c541a445692159bc1e4","first_computed_at":"2026-05-18T00:02:23.691046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:23.691046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jUWANq6Y+MWuXHTzJjdOMzfWwh8aL0xpyShjo1UKRWKm3NcOCNpUb8lMscNBZNmEHFK93BlLTt1fH5RLbzO/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:23.691533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10272","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:546ed6c816dea705471c69894286436007e1aa27de979d30c439157d7f9ca954","sha256:61b9c80fa5dbb82d3912e101f94bf34a7bb590bb7da3851d305cf5df42099197"],"state_sha256":"fe6e4120fb2cf4f59d8f8abda14bed95e71ace575fff9411b131e00f6732e376"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8qSX/RIvebvug6hu0SQDTOo6JqkyAT+Nko8BKHbNiGBEBIb5hnFn6s+qJhyqV/Jah9GBs80AER2iZO8awl7pCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T15:56:24.629730Z","bundle_sha256":"d8878cecfa83dd716e291f19bfb247c7d1ab9cc0d4bc60e4094766984b2ff29a"}}