{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6XNO65EH6V4E4L4HJGFCCX5MTY","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":"744e545261ff543d5ad1376c435dd0587c8f9d9009d95bcc6d720bff522e41e7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-09-04T20:21:51Z","title_canon_sha256":"7496bcd44d6b374289d8f03bcfef8b8391fe7610ec7390ec83eadee5ca874188"},"schema_version":"1.0","source":{"id":"1909.02089","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.02089","created_at":"2026-07-05T01:25:52Z"},{"alias_kind":"arxiv_version","alias_value":"1909.02089v2","created_at":"2026-07-05T01:25:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.02089","created_at":"2026-07-05T01:25:52Z"},{"alias_kind":"pith_short_12","alias_value":"6XNO65EH6V4E","created_at":"2026-07-05T01:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"6XNO65EH6V4E4L4H","created_at":"2026-07-05T01:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"6XNO65EH","created_at":"2026-07-05T01:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:bbe1953e639167e14431d887992c4b440b7dadc6ca78be6fca2b6ab72870a66c","target":"graph","created_at":"2026-07-05T01:25:52Z","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/1909.02089/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a quadratic polynomial $f\\left(\\xi_{1},\\dots,\\xi_{n}\\right)$ of independent Bernoulli random variables. What can be said about the concentration of $f$ on any single value? This generalises the classical Littlewood--Offord problem, which asks the same question for linear polynomials. As in the linear case, it is known that the point probabilities of $f$ can be as large as about $1/\\sqrt{n}$, but still poorly understood is the \"inverse\" question of characterising the algebraic and arithmetic features $f$ must have if it has point probabilities comparable to this bound. In this paper we","authors_text":"Lisa Sauermann, Matthew Kwan","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-09-04T20:21:51Z","title":"An algebraic inverse theorem for the quadratic Littlewood-Offord problem, and an application to Ramsey graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02089","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":"sha256:305ac06e2168b1f04167eb00bab80e9e3a8186ef373b0b732fda50efe45d1396","target":"record","created_at":"2026-07-05T01:25:52Z","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":"744e545261ff543d5ad1376c435dd0587c8f9d9009d95bcc6d720bff522e41e7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-09-04T20:21:51Z","title_canon_sha256":"7496bcd44d6b374289d8f03bcfef8b8391fe7610ec7390ec83eadee5ca874188"},"schema_version":"1.0","source":{"id":"1909.02089","kind":"arxiv","version":2}},"canonical_sha256":"f5daef7487f5784e2f87498a215fac9e1f00c7926fe3935c1d758f23618a3a09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5daef7487f5784e2f87498a215fac9e1f00c7926fe3935c1d758f23618a3a09","first_computed_at":"2026-07-05T01:25:52.000645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:25:52.000645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g/2H4iIgTCCfF0a85y3KZAOqbB4M4UkUdCaMY6P5YyElzsYR/ehvayPJNHAkhRlzrBvfFr/QZmT3xNy0YMKNCA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:25:52.001110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.02089","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:305ac06e2168b1f04167eb00bab80e9e3a8186ef373b0b732fda50efe45d1396","sha256:bbe1953e639167e14431d887992c4b440b7dadc6ca78be6fca2b6ab72870a66c"],"state_sha256":"0336a9168feec40312edcbf81ecd14044bbec53148f1d2b99b2c867a6d763192"}