Pith Number

pith:2QAV4AZP

pith:2007:2QAV4AZPQWBBHHA2DBCVEQL45F

not attested not anchored not stored refs pending

The Littlewood-Offord Problem and invertibility of random matrices

Mark Rudelson, Roman Vershynin

arxiv:math/0703503 v2 · 2007-03-16 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2QAV4AZPQWBBHHA2DBCVEQL45F}

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	2026-05-18T00:54:09.240329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4015e032f8582139c1a184552417ce9697aa08952c3ec74e031e5289b025c2e

Aliases

arxiv: math/0703503 · arxiv_version: math/0703503v2 · doi: 10.48550/arxiv.math/0703503 · pith_short_12: 2QAV4AZPQWBB · pith_short_16: 2QAV4AZPQWBBHHA2 · pith_short_8: 2QAV4AZP

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/2QAV4AZPQWBBHHA2DBCVEQL45F \
  | 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: d4015e032f8582139c1a184552417ce9697aa08952c3ec74e031e5289b025c2e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b81c4124eb0a53abf8f831f93cf92e3702547ed613cad189aa387817be11aa58",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2007-03-16T21:58:20Z",
    "title_canon_sha256": "1c4b8b9d92f90f60ab175ec898bbd537032e11da37273e825df58f08fc448764"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703503",
    "kind": "arxiv",
    "version": 2
  }
}