{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ORZZMGDTPNOC5FSDSJFQ2GRV75","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":"a786e2f4dc449f6c55f2e2bebc8003a0d2d2af1edf0d72db057ecfddc85e25bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-23T19:36:41Z","title_canon_sha256":"d6c50ec723b0da35377d2155f741a8bac4408a6686d5a084eb06eb9f5cf40314"},"schema_version":"1.0","source":{"id":"1204.5157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5157","created_at":"2026-05-18T03:57:14Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5157v1","created_at":"2026-05-18T03:57:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5157","created_at":"2026-05-18T03:57:14Z"},{"alias_kind":"pith_short_12","alias_value":"ORZZMGDTPNOC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"ORZZMGDTPNOC5FSD","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"ORZZMGDT","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:e2d7e2deb14c716688f7105e4ef566015464a024c86e11193ee6572a9c279f00","target":"graph","created_at":"2026-05-18T03:57:14Z","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 introduce an amalgam type space, a subspace of $L^1(\\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the integrability of trigonometric series.","authors_text":"E. Liflyand","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-23T19:36:41Z","title":"Fourier transforms on an amalgam type space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5157","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":"sha256:4d8de740d68d15a284ef4ccc207803d4dbad37e8675f5d31fb83e5b4770e8a26","target":"record","created_at":"2026-05-18T03:57:14Z","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":"a786e2f4dc449f6c55f2e2bebc8003a0d2d2af1edf0d72db057ecfddc85e25bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-04-23T19:36:41Z","title_canon_sha256":"d6c50ec723b0da35377d2155f741a8bac4408a6686d5a084eb06eb9f5cf40314"},"schema_version":"1.0","source":{"id":"1204.5157","kind":"arxiv","version":1}},"canonical_sha256":"74739618737b5c2e9643924b0d1a35ff4606568bc76b5fa1f216a4da74a66b3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74739618737b5c2e9643924b0d1a35ff4606568bc76b5fa1f216a4da74a66b3c","first_computed_at":"2026-05-18T03:57:14.608633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:14.608633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lK7a5Z1MD4dUMcl1+dlJvUdwVQGRStwJhomFwMgvkCZrUpUqav1EEbybncIpJTFif9ZAZn13gBOqJrjjgwaPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:14.609204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d8de740d68d15a284ef4ccc207803d4dbad37e8675f5d31fb83e5b4770e8a26","sha256:e2d7e2deb14c716688f7105e4ef566015464a024c86e11193ee6572a9c279f00"],"state_sha256":"5f5d7b2800e8837bbbe5d0b164be18a277e2da94ea3af17267b397f2be73360b"}