{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BSO2D6PL4PYOB3QCQGFY6RHSWW","short_pith_number":"pith:BSO2D6PL","canonical_record":{"source":{"id":"1508.06673","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-26T21:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"08dd7cf740290d87cd06aefdbc9a9bab33e6fe43094dda5d9039ae481c625497","abstract_canon_sha256":"c28a1ca914b5ac2844f40c7d5d9dca9df8114c3f5e5f00436425e318e718006e"},"schema_version":"1.0"},"canonical_sha256":"0c9da1f9ebe3f0e0ee02818b8f44f2b5ac8b19b014a2c1dfb70a38bda908c0a1","source":{"kind":"arxiv","id":"1508.06673","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06673","created_at":"2026-05-18T01:33:41Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06673v2","created_at":"2026-05-18T01:33:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06673","created_at":"2026-05-18T01:33:41Z"},{"alias_kind":"pith_short_12","alias_value":"BSO2D6PL4PYO","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BSO2D6PL4PYOB3QC","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BSO2D6PL","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BSO2D6PL4PYOB3QCQGFY6RHSWW","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06673","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-26T21:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"08dd7cf740290d87cd06aefdbc9a9bab33e6fe43094dda5d9039ae481c625497","abstract_canon_sha256":"c28a1ca914b5ac2844f40c7d5d9dca9df8114c3f5e5f00436425e318e718006e"},"schema_version":"1.0"},"canonical_sha256":"0c9da1f9ebe3f0e0ee02818b8f44f2b5ac8b19b014a2c1dfb70a38bda908c0a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:41.719788Z","signature_b64":"5ljhmfaoq356K1LsFFUKsPaf/lpAsZVvCeDFTC7gt7EAOpmjQEKpYI3WYYPD7HYBYaOwXsnA2qT0o7eJ/5/2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c9da1f9ebe3f0e0ee02818b8f44f2b5ac8b19b014a2c1dfb70a38bda908c0a1","last_reissued_at":"2026-05-18T01:33:41.719332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:41.719332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06673","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":"2026-05-18T01:33:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LWfVUp+ywOObEXE4rbAPo77jKU0JqVz8Wn2CcN1wHzydzPCrC58DsqdIuWHi8UYl2O0G52jiiJcWDm+rdujPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:22:32.775361Z"},"content_sha256":"5d164a1370e23eaebe57636a530dc0bd32a0c009fb9cd0ab18f99f27a0c8a11a","schema_version":"1.0","event_id":"sha256:5d164a1370e23eaebe57636a530dc0bd32a0c009fb9cd0ab18f99f27a0c8a11a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BSO2D6PL4PYOB3QCQGFY6RHSWW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Change of variable and the rapidity of decrease of Fourier coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Vladimir Lebedev","submitted_at":"2015-08-26T21:54:16Z","abstract_excerpt":"We consider the class $C(T)$ of continuous real-valued functions on the circle. For certain classes of functions naturally characterised by the rapidity of decrease of Fourier coefficients we investigate whether it is possible to bring families of functions in $C(T)$ into these classes by a change of variable. This paper was originally published in Matematicheski\\v{\\i} Sbornik, 181:8 (1990), 1099--1113 (Russian). The English translation, published in Mathematics of the USSR, Sbornik, 70:2 (1991), 541--555, is to a large extent inconsistent with the original text. Herein the author provides a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06673","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":"2026-05-18T01:33:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uCFHn9qQin7CybkFBH2mOUklRZuJjfGCSk+fiSSndrpgjwmV4978VjZrsoHYjGFATGm5pH2i3bz8uBH3EKLfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:22:32.775710Z"},"content_sha256":"048ffe06994658b30704602c107e1110c0521baecf98fc90b0c27bd348228c0a","schema_version":"1.0","event_id":"sha256:048ffe06994658b30704602c107e1110c0521baecf98fc90b0c27bd348228c0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSO2D6PL4PYOB3QCQGFY6RHSWW/bundle.json","state_url":"https://pith.science/pith/BSO2D6PL4PYOB3QCQGFY6RHSWW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSO2D6PL4PYOB3QCQGFY6RHSWW/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":"2026-06-01T14:22:32Z","links":{"resolver":"https://pith.science/pith/BSO2D6PL4PYOB3QCQGFY6RHSWW","bundle":"https://pith.science/pith/BSO2D6PL4PYOB3QCQGFY6RHSWW/bundle.json","state":"https://pith.science/pith/BSO2D6PL4PYOB3QCQGFY6RHSWW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSO2D6PL4PYOB3QCQGFY6RHSWW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BSO2D6PL4PYOB3QCQGFY6RHSWW","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":"c28a1ca914b5ac2844f40c7d5d9dca9df8114c3f5e5f00436425e318e718006e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-26T21:54:16Z","title_canon_sha256":"08dd7cf740290d87cd06aefdbc9a9bab33e6fe43094dda5d9039ae481c625497"},"schema_version":"1.0","source":{"id":"1508.06673","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06673","created_at":"2026-05-18T01:33:41Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06673v2","created_at":"2026-05-18T01:33:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06673","created_at":"2026-05-18T01:33:41Z"},{"alias_kind":"pith_short_12","alias_value":"BSO2D6PL4PYO","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BSO2D6PL4PYOB3QC","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BSO2D6PL","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:048ffe06994658b30704602c107e1110c0521baecf98fc90b0c27bd348228c0a","target":"graph","created_at":"2026-05-18T01:33:41Z","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 consider the class $C(T)$ of continuous real-valued functions on the circle. For certain classes of functions naturally characterised by the rapidity of decrease of Fourier coefficients we investigate whether it is possible to bring families of functions in $C(T)$ into these classes by a change of variable. This paper was originally published in Matematicheski\\v{\\i} Sbornik, 181:8 (1990), 1099--1113 (Russian). The English translation, published in Mathematics of the USSR, Sbornik, 70:2 (1991), 541--555, is to a large extent inconsistent with the original text. Herein the author provides a c","authors_text":"Vladimir Lebedev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-26T21:54:16Z","title":"Change of variable and the rapidity of decrease of Fourier coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06673","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":"sha256:5d164a1370e23eaebe57636a530dc0bd32a0c009fb9cd0ab18f99f27a0c8a11a","target":"record","created_at":"2026-05-18T01:33:41Z","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":"c28a1ca914b5ac2844f40c7d5d9dca9df8114c3f5e5f00436425e318e718006e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-08-26T21:54:16Z","title_canon_sha256":"08dd7cf740290d87cd06aefdbc9a9bab33e6fe43094dda5d9039ae481c625497"},"schema_version":"1.0","source":{"id":"1508.06673","kind":"arxiv","version":2}},"canonical_sha256":"0c9da1f9ebe3f0e0ee02818b8f44f2b5ac8b19b014a2c1dfb70a38bda908c0a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c9da1f9ebe3f0e0ee02818b8f44f2b5ac8b19b014a2c1dfb70a38bda908c0a1","first_computed_at":"2026-05-18T01:33:41.719332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:41.719332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ljhmfaoq356K1LsFFUKsPaf/lpAsZVvCeDFTC7gt7EAOpmjQEKpYI3WYYPD7HYBYaOwXsnA2qT0o7eJ/5/2BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:41.719788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06673","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d164a1370e23eaebe57636a530dc0bd32a0c009fb9cd0ab18f99f27a0c8a11a","sha256:048ffe06994658b30704602c107e1110c0521baecf98fc90b0c27bd348228c0a"],"state_sha256":"2800af54ba07679ccff117cadd9d493b43a2d7266f9939dae0f3b45aa1c246b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"12e/7tw3EUT2ieFqy97HDEAe8+yvgx5ad7OZM3JXljhsVAND8ZENFKwdNP1cxOb94KP6JIAUq+/IYuNK7MAvAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:22:32.777630Z","bundle_sha256":"7d259715243d8702380f77ab72ee1a9af1fa3022ed78c7376cc5dfb9308316ac"}}