{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7ZIJYUPANFHA2HWGGVREBQWHED","short_pith_number":"pith:7ZIJYUPA","canonical_record":{"source":{"id":"1409.3968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-09-13T17:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"a8c5c0c3e742004b74b3b3cd4e99ab9a736e12d651684b13c0ca2927079d3964","abstract_canon_sha256":"ebd33336c47dae10a67e4c678c98158d732f2cff17f2e84a3a43c2b295374460"},"schema_version":"1.0"},"canonical_sha256":"fe509c51e0694e0d1ec6356240c2c720e69d1c27bfa144eb605207878d05da1a","source":{"kind":"arxiv","id":"1409.3968","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3968","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3968v1","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3968","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"7ZIJYUPANFHA","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7ZIJYUPANFHA2HWG","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7ZIJYUPA","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7ZIJYUPANFHA2HWGGVREBQWHED","target":"record","payload":{"canonical_record":{"source":{"id":"1409.3968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-09-13T17:09:12Z","cross_cats_sorted":[],"title_canon_sha256":"a8c5c0c3e742004b74b3b3cd4e99ab9a736e12d651684b13c0ca2927079d3964","abstract_canon_sha256":"ebd33336c47dae10a67e4c678c98158d732f2cff17f2e84a3a43c2b295374460"},"schema_version":"1.0"},"canonical_sha256":"fe509c51e0694e0d1ec6356240c2c720e69d1c27bfa144eb605207878d05da1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:53.319654Z","signature_b64":"t6u8D6pF4qGjB3nv3d1nD5Q5bab5vXZiVZPmdzT4R822UI56rpTXGwvKp6dFCh1HXX/qe44hs7sAYGA2KMuYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe509c51e0694e0d1ec6356240c2c720e69d1c27bfa144eb605207878d05da1a","last_reissued_at":"2026-05-18T02:42:53.319277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:53.319277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.3968","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":"2026-05-18T02:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qe7D1j1tbHnN1o168yp0iOR9BtyRo+XlZ2GX4UVn1vmojwTF0Ec00jhv7Uzr5aeNf+aWGz6TGVo7bcQ3R2fzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:27:41.169831Z"},"content_sha256":"776400ce3494feaa029021cdd8abc28cb711be7dc1678a2d8647545bef74d783","schema_version":"1.0","event_id":"sha256:776400ce3494feaa029021cdd8abc28cb711be7dc1678a2d8647545bef74d783"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7ZIJYUPANFHA2HWGGVREBQWHED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complementability of exponential systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Yurii Belov","submitted_at":"2014-09-13T17:09:12Z","abstract_excerpt":"We prove that any incomplete system of complex exponentials $\\{e^{i\\lambda_n t}\\}$ in $L^2(-\\pi,\\pi)$ is a subset of some complete and minimal system of exponentials. In addition, we prove analogous statement for systems of reproducing kernels in de Branges spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3968","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":"2026-05-18T02:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOoKEDyrK3ANZ9ckOvRPug0nLp38ayTG7lI+275uIzseBANHmoSy2ul7RHWCrdpB29G5I1MjNqH75XECTHM/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:27:41.170172Z"},"content_sha256":"740446a925390401f20db76ce6c6ca43b709198de8d5e0252b4ffbf571ad9998","schema_version":"1.0","event_id":"sha256:740446a925390401f20db76ce6c6ca43b709198de8d5e0252b4ffbf571ad9998"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ZIJYUPANFHA2HWGGVREBQWHED/bundle.json","state_url":"https://pith.science/pith/7ZIJYUPANFHA2HWGGVREBQWHED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ZIJYUPANFHA2HWGGVREBQWHED/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":"2026-06-29T05:27:41Z","links":{"resolver":"https://pith.science/pith/7ZIJYUPANFHA2HWGGVREBQWHED","bundle":"https://pith.science/pith/7ZIJYUPANFHA2HWGGVREBQWHED/bundle.json","state":"https://pith.science/pith/7ZIJYUPANFHA2HWGGVREBQWHED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ZIJYUPANFHA2HWGGVREBQWHED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7ZIJYUPANFHA2HWGGVREBQWHED","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":"ebd33336c47dae10a67e4c678c98158d732f2cff17f2e84a3a43c2b295374460","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-09-13T17:09:12Z","title_canon_sha256":"a8c5c0c3e742004b74b3b3cd4e99ab9a736e12d651684b13c0ca2927079d3964"},"schema_version":"1.0","source":{"id":"1409.3968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3968","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3968v1","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3968","created_at":"2026-05-18T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"7ZIJYUPANFHA","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7ZIJYUPANFHA2HWG","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7ZIJYUPA","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:740446a925390401f20db76ce6c6ca43b709198de8d5e0252b4ffbf571ad9998","target":"graph","created_at":"2026-05-18T02:42:53Z","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 prove that any incomplete system of complex exponentials $\\{e^{i\\lambda_n t}\\}$ in $L^2(-\\pi,\\pi)$ is a subset of some complete and minimal system of exponentials. In addition, we prove analogous statement for systems of reproducing kernels in de Branges spaces.","authors_text":"Yurii Belov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-09-13T17:09:12Z","title":"Complementability of exponential systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3968","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":"sha256:776400ce3494feaa029021cdd8abc28cb711be7dc1678a2d8647545bef74d783","target":"record","created_at":"2026-05-18T02:42:53Z","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":"ebd33336c47dae10a67e4c678c98158d732f2cff17f2e84a3a43c2b295374460","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-09-13T17:09:12Z","title_canon_sha256":"a8c5c0c3e742004b74b3b3cd4e99ab9a736e12d651684b13c0ca2927079d3964"},"schema_version":"1.0","source":{"id":"1409.3968","kind":"arxiv","version":1}},"canonical_sha256":"fe509c51e0694e0d1ec6356240c2c720e69d1c27bfa144eb605207878d05da1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe509c51e0694e0d1ec6356240c2c720e69d1c27bfa144eb605207878d05da1a","first_computed_at":"2026-05-18T02:42:53.319277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:53.319277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6u8D6pF4qGjB3nv3d1nD5Q5bab5vXZiVZPmdzT4R822UI56rpTXGwvKp6dFCh1HXX/qe44hs7sAYGA2KMuYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:53.319654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:776400ce3494feaa029021cdd8abc28cb711be7dc1678a2d8647545bef74d783","sha256:740446a925390401f20db76ce6c6ca43b709198de8d5e0252b4ffbf571ad9998"],"state_sha256":"8eadc868da8c2f8251b3adf4a374ef6055d523d6c511cd6438adf3ba003b1f66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1r10aYaYELCO68unYiLDGmx15lGvphezXD3WT49cEB25wDO+LrlJwfQepo8yctV6PLve+RILUSkoSzUxMDnkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T05:27:41.172047Z","bundle_sha256":"42b7d1e68325e2f0ed5e9df0c97cc326255b6d6b90f37d065de5b454c30a47eb"}}