{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZPVJOPEBRESTZYXCGHJOPDQEPD","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":"43cd9c71e1be37054dbfeed3d42f33fb9bd8c1dcbb53ea5ea91b7e39c53247b2","cross_cats_sorted":["math.NT","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-29T10:53:39Z","title_canon_sha256":"21a01019c9148a37a63549ddf9ffd1180af7f9214483d632c59f633ca5a9c9a9"},"schema_version":"1.0","source":{"id":"2505.23335","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.23335","created_at":"2026-07-05T11:11:59Z"},{"alias_kind":"arxiv_version","alias_value":"2505.23335v1","created_at":"2026-07-05T11:11:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23335","created_at":"2026-07-05T11:11:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZPVJOPEBREST","created_at":"2026-07-05T11:11:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZPVJOPEBRESTZYXC","created_at":"2026-07-05T11:11:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZPVJOPEB","created_at":"2026-07-05T11:11:59Z"}],"graph_snapshots":[{"event_id":"sha256:b0fedfcb8448c65f2d26b00c11e0ec3bea34a4d7d0c6fb587223fffa230033e9","target":"graph","created_at":"2026-07-05T11:11:59Z","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/2505.23335/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a degree-$d$ polynomial $f(\\xi_1,\\dots,\\xi_n)$ of independent Rademacher random variables $\\xi_1,\\dots,\\xi_n$. To what extent can $f(\\xi_1,\\dots,\\xi_n)$ concentrate on a single point? This is the so-called polynomial Littlewood-Offord problem. A nearly optimal bound was proved by Meka, Nguyen and Vu: the point probabilities are always at most about $1/\\sqrt n$, unless $f$ is \"close to the zero polynomial\" (having only $o(n^d)$ nonzero coefficients).\n  In this paper we prove several results supporting the general philosophy that the Meka-Nguyen-Vu bound can be significantly improved un","authors_text":"Lisa Sauermann, Matthew Kwan, Yiting Wang, Zhihan Jin","cross_cats":["math.NT","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-29T10:53:39Z","title":"Algebraic aspects of the polynomial Littlewood-Offord problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23335","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":"sha256:04ef9e1798ab6b6d097eede3dc6f4818ae2389e3f0c4a57c26bbdb69012ff146","target":"record","created_at":"2026-07-05T11:11:59Z","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":"43cd9c71e1be37054dbfeed3d42f33fb9bd8c1dcbb53ea5ea91b7e39c53247b2","cross_cats_sorted":["math.NT","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-29T10:53:39Z","title_canon_sha256":"21a01019c9148a37a63549ddf9ffd1180af7f9214483d632c59f633ca5a9c9a9"},"schema_version":"1.0","source":{"id":"2505.23335","kind":"arxiv","version":1}},"canonical_sha256":"cbea973c8189253ce2e231d2e78e0478d09f3435f97f2ebc2706ff687c137a6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbea973c8189253ce2e231d2e78e0478d09f3435f97f2ebc2706ff687c137a6a","first_computed_at":"2026-07-05T11:11:59.847294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:59.847294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cEGDQUKO38qY8yAB1Nm55yhFCrDqJATHPJoH8M185X1Lw6xXbBmCvA4hWxeI7y/tm4sODlqeMM/om2khjySwDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:59.847833Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.23335","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04ef9e1798ab6b6d097eede3dc6f4818ae2389e3f0c4a57c26bbdb69012ff146","sha256:b0fedfcb8448c65f2d26b00c11e0ec3bea34a4d7d0c6fb587223fffa230033e9"],"state_sha256":"7a3a5e0c36d80ff8666fad281015089f266a3d816b8fd91c993c6301eea020f1"}