{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:3TAADHNAT5VYWETA5NHNBHVDAH","short_pith_number":"pith:3TAADHNA","canonical_record":{"source":{"id":"2010.00812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-10-02T07:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"62dd79c236c7142efe528daf92ff4acebc16df7e2b392218a569295147a39174","abstract_canon_sha256":"4280696ae8326377aa4eed46313ae25e3cba52d06419b039be07294485d0849c"},"schema_version":"1.0"},"canonical_sha256":"dcc0019da09f6b8b1260eb4ed09ea301d54f3177423a9cfbbc58c6bd1c63bbc6","source":{"kind":"arxiv","id":"2010.00812","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.00812","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"2010.00812v1","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.00812","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"3TAADHNAT5VY","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"pith_short_16","alias_value":"3TAADHNAT5VYWETA","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"pith_short_8","alias_value":"3TAADHNA","created_at":"2026-07-05T01:39:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:3TAADHNAT5VYWETA5NHNBHVDAH","target":"record","payload":{"canonical_record":{"source":{"id":"2010.00812","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-10-02T07:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"62dd79c236c7142efe528daf92ff4acebc16df7e2b392218a569295147a39174","abstract_canon_sha256":"4280696ae8326377aa4eed46313ae25e3cba52d06419b039be07294485d0849c"},"schema_version":"1.0"},"canonical_sha256":"dcc0019da09f6b8b1260eb4ed09ea301d54f3177423a9cfbbc58c6bd1c63bbc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:39:47.786952Z","signature_b64":"VI7sYW5q8Dxyrls3VIodBjgeKAqoV2udphXI9672jel/s8F9lZdxsEfKuEE4jqzCxbd6Czp684S8gvQfwyldDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcc0019da09f6b8b1260eb4ed09ea301d54f3177423a9cfbbc58c6bd1c63bbc6","last_reissued_at":"2026-07-05T01:39:47.786568Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:39:47.786568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.00812","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":"2026-07-05T01:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fYy4uJT+55OyIf1ARGM5eE/c/hHPbRjpJrCRw7FgqdnsbttsoOYujHyiALNXvODENMnD+tn6iTfHEd+gFSuqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:07:32.674274Z"},"content_sha256":"6074361bc39faa2023bd9b9351424bb0e8f9ef48849f5a2f2a015b6c777c3eb3","schema_version":"1.0","event_id":"sha256:6074361bc39faa2023bd9b9351424bb0e8f9ef48849f5a2f2a015b6c777c3eb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:3TAADHNAT5VYWETA5NHNBHVDAH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variable coefficient multi-frequency lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Pavel Zorin-Kranich, Shaoming Guo","submitted_at":"2020-10-02T07:07:26Z","abstract_excerpt":"We show a variable coefficient version of Bourgain's multi-frequency lemma. It can be used to obtain major arc estimates for a discrete Stein--Wainger type operator considered by Krause arXiv:1803.09431 and Roos arXiv:1907.00405."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00812","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.00812/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:39:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80hUn2WVnq/W4k8n79KQ5zeZntZ1JUjlnxcjnBgNrDn0LFQHvUstqfWSnLH/fSxGkrN1EDoGLZzq+ovA2zZxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:07:32.674926Z"},"content_sha256":"18bfa49f3a9fbcd28bffbe4de51d37f45802769960a7c1a6401d0be590d89189","schema_version":"1.0","event_id":"sha256:18bfa49f3a9fbcd28bffbe4de51d37f45802769960a7c1a6401d0be590d89189"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TAADHNAT5VYWETA5NHNBHVDAH/bundle.json","state_url":"https://pith.science/pith/3TAADHNAT5VYWETA5NHNBHVDAH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TAADHNAT5VYWETA5NHNBHVDAH/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":"2026-08-11T21:07:32Z","links":{"resolver":"https://pith.science/pith/3TAADHNAT5VYWETA5NHNBHVDAH","bundle":"https://pith.science/pith/3TAADHNAT5VYWETA5NHNBHVDAH/bundle.json","state":"https://pith.science/pith/3TAADHNAT5VYWETA5NHNBHVDAH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TAADHNAT5VYWETA5NHNBHVDAH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3TAADHNAT5VYWETA5NHNBHVDAH","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":"4280696ae8326377aa4eed46313ae25e3cba52d06419b039be07294485d0849c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-10-02T07:07:26Z","title_canon_sha256":"62dd79c236c7142efe528daf92ff4acebc16df7e2b392218a569295147a39174"},"schema_version":"1.0","source":{"id":"2010.00812","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.00812","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"arxiv_version","alias_value":"2010.00812v1","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.00812","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"pith_short_12","alias_value":"3TAADHNAT5VY","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"pith_short_16","alias_value":"3TAADHNAT5VYWETA","created_at":"2026-07-05T01:39:47Z"},{"alias_kind":"pith_short_8","alias_value":"3TAADHNA","created_at":"2026-07-05T01:39:47Z"}],"graph_snapshots":[{"event_id":"sha256:18bfa49f3a9fbcd28bffbe4de51d37f45802769960a7c1a6401d0be590d89189","target":"graph","created_at":"2026-07-05T01:39:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.00812/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show a variable coefficient version of Bourgain's multi-frequency lemma. It can be used to obtain major arc estimates for a discrete Stein--Wainger type operator considered by Krause arXiv:1803.09431 and Roos arXiv:1907.00405.","authors_text":"Pavel Zorin-Kranich, Shaoming Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-10-02T07:07:26Z","title":"A variable coefficient multi-frequency lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.00812","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":"sha256:6074361bc39faa2023bd9b9351424bb0e8f9ef48849f5a2f2a015b6c777c3eb3","target":"record","created_at":"2026-07-05T01:39:47Z","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":"4280696ae8326377aa4eed46313ae25e3cba52d06419b039be07294485d0849c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2020-10-02T07:07:26Z","title_canon_sha256":"62dd79c236c7142efe528daf92ff4acebc16df7e2b392218a569295147a39174"},"schema_version":"1.0","source":{"id":"2010.00812","kind":"arxiv","version":1}},"canonical_sha256":"dcc0019da09f6b8b1260eb4ed09ea301d54f3177423a9cfbbc58c6bd1c63bbc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcc0019da09f6b8b1260eb4ed09ea301d54f3177423a9cfbbc58c6bd1c63bbc6","first_computed_at":"2026-07-05T01:39:47.786568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:39:47.786568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VI7sYW5q8Dxyrls3VIodBjgeKAqoV2udphXI9672jel/s8F9lZdxsEfKuEE4jqzCxbd6Czp684S8gvQfwyldDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:39:47.786952Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.00812","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6074361bc39faa2023bd9b9351424bb0e8f9ef48849f5a2f2a015b6c777c3eb3","sha256:18bfa49f3a9fbcd28bffbe4de51d37f45802769960a7c1a6401d0be590d89189"],"state_sha256":"f969a3de318ebfb4ccabf2924d389d4582846bd2edd4636b0c3212d38def766e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"59dH1Qk4N46Q4EXCmQcyPZMTyQJPuiEafzzvYSrC9+xhoJCHENJzJXsRiaSYN6wY9FdzgzM+GnMgcWggBUxnCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T21:07:32.680954Z","bundle_sha256":"8c138426ddc5d6c0d440b1b628c7350eb279b4d9c28a1025683697b57134bf4d"}}