{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FCXSISNRXED2ZE6UPRLE7ZUE3V","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":"fb8ac8b2f333a154369c9302040d662d97f286c30a55e18e9d6f83ed943b4622","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2015-09-17T18:32:53Z","title_canon_sha256":"9034975da9591a5ad6a5d8d487c171315cebef16e07e1fe0b761498f48a4a5c1"},"schema_version":"1.0","source":{"id":"1509.05363","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05363","created_at":"2026-05-18T00:52:53Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05363v6","created_at":"2026-05-18T00:52:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05363","created_at":"2026-05-18T00:52:53Z"},{"alias_kind":"pith_short_12","alias_value":"FCXSISNRXED2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FCXSISNRXED2ZE6U","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FCXSISNR","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:cced020353afa17f03313b277ae2280c1fb28f1b076bb6d68243df061fe9c9ad","target":"graph","created_at":"2026-05-18T00:52:53Z","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 show that for any sequence $f: {\\bf N} \\to \\{-1,+1\\}$ taking values in $\\{-1,+1\\}$, the discrepancy $$ \\sup_{n,d \\in {\\bf N}} \\left|\\sum_{j=1}^n f(jd)\\right| $$ of $f$ is infinite. This answers a question of Erd\\H{o}s. In fact the argument also applies to sequences $f$ taking values in the unit sphere of a real or complex Hilbert space.\n  The argument uses three ingredients. The first is a Fourier-analytic reduction, obtained as part of the Polymath5 project on this problem, which reduces the problem to the case when $f$ is replaced by a (stochastic) completely multiplicative function ${\\bf","authors_text":"Terence Tao","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2015-09-17T18:32:53Z","title":"The Erdos discrepancy problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05363","kind":"arxiv","version":6},"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":"sha256:1fb7a89b753c82efe9ea9dd6e2ff3232e2e36d15acd1edf89dbd5c77ee1cb36d","target":"record","created_at":"2026-05-18T00:52:53Z","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":"fb8ac8b2f333a154369c9302040d662d97f286c30a55e18e9d6f83ed943b4622","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2015-09-17T18:32:53Z","title_canon_sha256":"9034975da9591a5ad6a5d8d487c171315cebef16e07e1fe0b761498f48a4a5c1"},"schema_version":"1.0","source":{"id":"1509.05363","kind":"arxiv","version":6}},"canonical_sha256":"28af2449b1b907ac93d47c564fe684dd5bffa796e2d1f3799b10cd688badeae7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28af2449b1b907ac93d47c564fe684dd5bffa796e2d1f3799b10cd688badeae7","first_computed_at":"2026-05-18T00:52:53.069629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:53.069629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SFqDMaNEo9Id+BpDGFJ6xdDdnJo37X9O6qEJ3hyr0J/b8dTlluPE/cV8vMleX0SfQLtLezYwGeZ/L2KzaI1iAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:53.070375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05363","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fb7a89b753c82efe9ea9dd6e2ff3232e2e36d15acd1edf89dbd5c77ee1cb36d","sha256:cced020353afa17f03313b277ae2280c1fb28f1b076bb6d68243df061fe9c9ad"],"state_sha256":"033cf43ac086da426806d953173ef3df8f9a5e2a69bab7a0c212c1465659b75a"}