Pith Number

pith:XYAYUDK2

pith:2009:XYAYUDK2OLK4VBPGD3MLOGSOKP

not attested not anchored not stored refs pending

Bilinear and Quadratic Variants on the Littlewood-Offord Problem

Kevin P. Costello

arxiv:0902.1538 v1 · 2009-02-09 · math.PR · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XYAYUDK2OLK4VBPGD3MLOGSOKP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:37:29.142991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be018a0d5a72d5ca85e61ed8b71a4e53e96ebe497c6043cf610f8dca64f4fba8

Aliases

arxiv: 0902.1538 · arxiv_version: 0902.1538v1 · doi: 10.48550/arxiv.0902.1538 · pith_short_12: XYAYUDK2OLK4 · pith_short_16: XYAYUDK2OLK4VBPG · pith_short_8: XYAYUDK2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XYAYUDK2OLK4VBPGD3MLOGSOKP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: be018a0d5a72d5ca85e61ed8b71a4e53e96ebe497c6043cf610f8dca64f4fba8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d88b7aaa73be29a1ed08e6b760f72a6cee07315a9c51eb7463679c8069342115",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-02-09T21:06:57Z",
    "title_canon_sha256": "539b452e127bd57009cb47e6a39e38df3640e86fd494a5f00a00a2a301766e8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1538",
    "kind": "arxiv",
    "version": 1
  }
}