{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TLJFN5PJHEAPW2TSD7J6U5OD4S","short_pith_number":"pith:TLJFN5PJ","canonical_record":{"source":{"id":"1711.03083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-08T18:28:59Z","cross_cats_sorted":["math.AP","math.RT"],"title_canon_sha256":"5007d003b67b8221fec2e968f01c22131ef42dd23a7e62fe8da7fa00c91b088f","abstract_canon_sha256":"9a076f665a510c93c636221bab4807b3a27f9ef5d3b23a91847f7b9934cbf661"},"schema_version":"1.0"},"canonical_sha256":"9ad256f5e93900fb6a721fd3ea75c3e488360da12280f1219de79430cbc07688","source":{"kind":"arxiv","id":"1711.03083","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03083","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03083v2","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03083","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"TLJFN5PJHEAP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TLJFN5PJHEAPW2TS","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TLJFN5PJ","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TLJFN5PJHEAPW2TSD7J6U5OD4S","target":"record","payload":{"canonical_record":{"source":{"id":"1711.03083","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-08T18:28:59Z","cross_cats_sorted":["math.AP","math.RT"],"title_canon_sha256":"5007d003b67b8221fec2e968f01c22131ef42dd23a7e62fe8da7fa00c91b088f","abstract_canon_sha256":"9a076f665a510c93c636221bab4807b3a27f9ef5d3b23a91847f7b9934cbf661"},"schema_version":"1.0"},"canonical_sha256":"9ad256f5e93900fb6a721fd3ea75c3e488360da12280f1219de79430cbc07688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:08.137767Z","signature_b64":"m6LvvRiu2k5an+KB2raAfLJi8Z4/trklyMst2b2YYzbjbteOGwTiNSlDy6GzS1zA7sk4OYunSox38CYAPqvICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ad256f5e93900fb6a721fd3ea75c3e488360da12280f1219de79430cbc07688","last_reissued_at":"2026-05-18T00:04:08.137136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:08.137136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.03083","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eofq8EKP7a0qSX0qTuGl5eSjxrF/AMm2fbEtRxu7xT6breZWP42ITBbM4v3egd5/kcPsyy4vMfL2CnSigrm9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:47:52.621366Z"},"content_sha256":"a81cd2ba7d31596a32b94d910a256e49479bc85c50c42761d715ef5248755669","schema_version":"1.0","event_id":"sha256:a81cd2ba7d31596a32b94d910a256e49479bc85c50c42761d715ef5248755669"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TLJFN5PJHEAPW2TSD7J6U5OD4S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local and global symbols on compact Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.RT"],"primary_cat":"math.FA","authors_text":"Veronique Fischer","submitted_at":"2017-11-08T18:28:59Z","abstract_excerpt":"On the torus, it is possible to assign a global symbol to a pseudodifferential operator using Fourier series. In this paper we investigate the relations between the local and global symbols for the operators in the classical H\\\"ormander calculus and describe the principal symbols, the non-commutative residue and the canonical trace of an operator in terms of its global symbol. We also generalise these results to any compact Lie group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03083","kind":"arxiv","version":2},"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":"2026-05-18T00:04:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1o4dlE/7KGB+/97R7rqqP/XGHe6ICB6+E09QauC/tyt9VZoqhBQJSKOG8659fmOo4fs/qa/tXHuSGj33iBEdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:47:52.621757Z"},"content_sha256":"a501a4507d48bd30c39142bc280da208477c9c9da699ec8d8c0f36c022767b1b","schema_version":"1.0","event_id":"sha256:a501a4507d48bd30c39142bc280da208477c9c9da699ec8d8c0f36c022767b1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLJFN5PJHEAPW2TSD7J6U5OD4S/bundle.json","state_url":"https://pith.science/pith/TLJFN5PJHEAPW2TSD7J6U5OD4S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLJFN5PJHEAPW2TSD7J6U5OD4S/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":"2026-06-25T22:47:52Z","links":{"resolver":"https://pith.science/pith/TLJFN5PJHEAPW2TSD7J6U5OD4S","bundle":"https://pith.science/pith/TLJFN5PJHEAPW2TSD7J6U5OD4S/bundle.json","state":"https://pith.science/pith/TLJFN5PJHEAPW2TSD7J6U5OD4S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLJFN5PJHEAPW2TSD7J6U5OD4S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TLJFN5PJHEAPW2TSD7J6U5OD4S","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":"9a076f665a510c93c636221bab4807b3a27f9ef5d3b23a91847f7b9934cbf661","cross_cats_sorted":["math.AP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-08T18:28:59Z","title_canon_sha256":"5007d003b67b8221fec2e968f01c22131ef42dd23a7e62fe8da7fa00c91b088f"},"schema_version":"1.0","source":{"id":"1711.03083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03083","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03083v2","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03083","created_at":"2026-05-18T00:04:08Z"},{"alias_kind":"pith_short_12","alias_value":"TLJFN5PJHEAP","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TLJFN5PJHEAPW2TS","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TLJFN5PJ","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:a501a4507d48bd30c39142bc280da208477c9c9da699ec8d8c0f36c022767b1b","target":"graph","created_at":"2026-05-18T00:04:08Z","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":"On the torus, it is possible to assign a global symbol to a pseudodifferential operator using Fourier series. In this paper we investigate the relations between the local and global symbols for the operators in the classical H\\\"ormander calculus and describe the principal symbols, the non-commutative residue and the canonical trace of an operator in terms of its global symbol. We also generalise these results to any compact Lie group.","authors_text":"Veronique Fischer","cross_cats":["math.AP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-08T18:28:59Z","title":"Local and global symbols on compact Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03083","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:a81cd2ba7d31596a32b94d910a256e49479bc85c50c42761d715ef5248755669","target":"record","created_at":"2026-05-18T00:04:08Z","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":"9a076f665a510c93c636221bab4807b3a27f9ef5d3b23a91847f7b9934cbf661","cross_cats_sorted":["math.AP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-08T18:28:59Z","title_canon_sha256":"5007d003b67b8221fec2e968f01c22131ef42dd23a7e62fe8da7fa00c91b088f"},"schema_version":"1.0","source":{"id":"1711.03083","kind":"arxiv","version":2}},"canonical_sha256":"9ad256f5e93900fb6a721fd3ea75c3e488360da12280f1219de79430cbc07688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ad256f5e93900fb6a721fd3ea75c3e488360da12280f1219de79430cbc07688","first_computed_at":"2026-05-18T00:04:08.137136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:08.137136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m6LvvRiu2k5an+KB2raAfLJi8Z4/trklyMst2b2YYzbjbteOGwTiNSlDy6GzS1zA7sk4OYunSox38CYAPqvICA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:08.137767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.03083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a81cd2ba7d31596a32b94d910a256e49479bc85c50c42761d715ef5248755669","sha256:a501a4507d48bd30c39142bc280da208477c9c9da699ec8d8c0f36c022767b1b"],"state_sha256":"fb9529fa6e7f7db9b0f56491215e5433869b317bd015d73f0774a676d821d938"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eic/Wli1a3lZiAgyO2+7eQmxZHwChYbHn/GEwPmO9/tFAHLOT7AtwYpF3Il1P+WY4BGDSy2ECNlp5TFrWgHzDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:47:52.623723Z","bundle_sha256":"80ad487a056a6c39bd4cc996d83f94bc0f975aa38ff3fd90a341f61be6478ec9"}}