{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TNHKLIPFNZ6GFMB66WJ7VWDXVE","short_pith_number":"pith:TNHKLIPF","canonical_record":{"source":{"id":"1410.2637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-09T21:42:33Z","cross_cats_sorted":[],"title_canon_sha256":"6f9ea4a203fc60561a76e7c9ac7d71aa3c931ce9fcc15b3c5e35bd0655752688","abstract_canon_sha256":"7267d46ff66c2c18ec2244f708875636d193a3d38a63040c369dfca9733638d4"},"schema_version":"1.0"},"canonical_sha256":"9b4ea5a1e56e7c62b03ef593fad877a933cd0fb4b3f828f266e0c3896ed39da5","source":{"kind":"arxiv","id":"1410.2637","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2637","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2637v2","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2637","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"TNHKLIPFNZ6G","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TNHKLIPFNZ6GFMB6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TNHKLIPF","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TNHKLIPFNZ6GFMB66WJ7VWDXVE","target":"record","payload":{"canonical_record":{"source":{"id":"1410.2637","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-09T21:42:33Z","cross_cats_sorted":[],"title_canon_sha256":"6f9ea4a203fc60561a76e7c9ac7d71aa3c931ce9fcc15b3c5e35bd0655752688","abstract_canon_sha256":"7267d46ff66c2c18ec2244f708875636d193a3d38a63040c369dfca9733638d4"},"schema_version":"1.0"},"canonical_sha256":"9b4ea5a1e56e7c62b03ef593fad877a933cd0fb4b3f828f266e0c3896ed39da5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:08.815775Z","signature_b64":"vGIMAh/N8cVqzoO7EGhWycQiEY6hvhBtaC+XnPZYYNbv0ACCBbtDZe3Ga75OwDYjMkQGVoor1mdBxmKIV6m+Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b4ea5a1e56e7c62b03ef593fad877a933cd0fb4b3f828f266e0c3896ed39da5","last_reissued_at":"2026-05-18T01:23:08.815227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:08.815227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.2637","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":"2026-05-18T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GP6nLj9R6gWbMVlZ/y5WSyxBZAJv9OOZE+x3JvYOmpSnDI3e52mj09aLk4R0zyTVnJxjvLdayCviTJ9RERtQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:29:51.548858Z"},"content_sha256":"c62086dab68b8756f8ab8d582d15045945a7ee658d4e08bda69b6cb57cd73d01","schema_version":"1.0","event_id":"sha256:c62086dab68b8756f8ab8d582d15045945a7ee658d4e08bda69b6cb57cd73d01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TNHKLIPFNZ6GFMB66WJ7VWDXVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenfunction expansions of ultradifferentiable functions and ultradistributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Aparajita Dasgupta, Michael Ruzhansky","submitted_at":"2014-10-09T21:42:33Z","abstract_excerpt":"In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold $X$. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on $X$. This extends the result for analytic functions on compact manifold by Seeley, and the characterisation of Gevrey functions and Gevrey ultradistributions on compact Lie groups and homogeneous spaces by the authors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2637","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":"2026-05-18T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+3cQl6//jugm4Jy6L8BUwrbtAoo7gAm4Ygnyc6rzN5znMJhhtwsbfhtswcips3mzX2rk/XBMn8NLK68Ke9AAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:29:51.549203Z"},"content_sha256":"5c8f0b8f677be328a5ac9fc61d5da731292bfd1f36950980fb46be4e454377d7","schema_version":"1.0","event_id":"sha256:5c8f0b8f677be328a5ac9fc61d5da731292bfd1f36950980fb46be4e454377d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNHKLIPFNZ6GFMB66WJ7VWDXVE/bundle.json","state_url":"https://pith.science/pith/TNHKLIPFNZ6GFMB66WJ7VWDXVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNHKLIPFNZ6GFMB66WJ7VWDXVE/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":"2026-06-09T15:29:51Z","links":{"resolver":"https://pith.science/pith/TNHKLIPFNZ6GFMB66WJ7VWDXVE","bundle":"https://pith.science/pith/TNHKLIPFNZ6GFMB66WJ7VWDXVE/bundle.json","state":"https://pith.science/pith/TNHKLIPFNZ6GFMB66WJ7VWDXVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNHKLIPFNZ6GFMB66WJ7VWDXVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TNHKLIPFNZ6GFMB66WJ7VWDXVE","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":"7267d46ff66c2c18ec2244f708875636d193a3d38a63040c369dfca9733638d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-09T21:42:33Z","title_canon_sha256":"6f9ea4a203fc60561a76e7c9ac7d71aa3c931ce9fcc15b3c5e35bd0655752688"},"schema_version":"1.0","source":{"id":"1410.2637","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2637","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2637v2","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2637","created_at":"2026-05-18T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"TNHKLIPFNZ6G","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TNHKLIPFNZ6GFMB6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TNHKLIPF","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:5c8f0b8f677be328a5ac9fc61d5da731292bfd1f36950980fb46be4e454377d7","target":"graph","created_at":"2026-05-18T01:23:08Z","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":"In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold $X$. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on $X$. This extends the result for analytic functions on compact manifold by Seeley, and the characterisation of Gevrey functions and Gevrey ultradistributions on compact Lie groups and homogeneous spaces by the authors.","authors_text":"Aparajita Dasgupta, Michael Ruzhansky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-09T21:42:33Z","title":"Eigenfunction expansions of ultradifferentiable functions and ultradistributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2637","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:c62086dab68b8756f8ab8d582d15045945a7ee658d4e08bda69b6cb57cd73d01","target":"record","created_at":"2026-05-18T01:23:08Z","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":"7267d46ff66c2c18ec2244f708875636d193a3d38a63040c369dfca9733638d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-09T21:42:33Z","title_canon_sha256":"6f9ea4a203fc60561a76e7c9ac7d71aa3c931ce9fcc15b3c5e35bd0655752688"},"schema_version":"1.0","source":{"id":"1410.2637","kind":"arxiv","version":2}},"canonical_sha256":"9b4ea5a1e56e7c62b03ef593fad877a933cd0fb4b3f828f266e0c3896ed39da5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b4ea5a1e56e7c62b03ef593fad877a933cd0fb4b3f828f266e0c3896ed39da5","first_computed_at":"2026-05-18T01:23:08.815227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:08.815227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vGIMAh/N8cVqzoO7EGhWycQiEY6hvhBtaC+XnPZYYNbv0ACCBbtDZe3Ga75OwDYjMkQGVoor1mdBxmKIV6m+Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:08.815775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2637","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c62086dab68b8756f8ab8d582d15045945a7ee658d4e08bda69b6cb57cd73d01","sha256:5c8f0b8f677be328a5ac9fc61d5da731292bfd1f36950980fb46be4e454377d7"],"state_sha256":"00c1e61adc037311988c7c97d35386f2c1b0db87526ca6f56c43e0875aab487d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLFKMXORy+KyqMNsNZOlM2nJ5h95L6lcZDX8qNmV/ATKKuWAADKLBg/Hj40v5ZMJm7kr8A4k1s8lhxatYfJoBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:29:51.551310Z","bundle_sha256":"03066c039e46ae204cf1479cbecbccc66d13c8cac18660932d1545e7ed484d34"}}