Pith Number

pith:PMEYS7JI

pith:2019:PMEYS7JI2ZQCX2FHG2BQ7PFA45

not attested not anchored not stored refs pending

On the counting problem in inverse Littlewood--Offord theory

Asaf Ferber, Kyle Luh, Vishesh Jain, Wojciech Samotij

arxiv:1904.10425 v1 · 2019-04-23 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PMEYS7JI2ZQCX2FHG2BQ7PFA45}

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	2026-05-17T23:47:54.204633Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b09897d28d6602be8a736830fbca0e765f77218a5375fc04e39c2a18338cb58

Aliases

arxiv: 1904.10425 · arxiv_version: 1904.10425v1 · doi: 10.48550/arxiv.1904.10425 · pith_short_12: PMEYS7JI2ZQC · pith_short_16: PMEYS7JI2ZQCX2FH · pith_short_8: PMEYS7JI

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/PMEYS7JI2ZQCX2FHG2BQ7PFA45 \
  | 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: 7b09897d28d6602be8a736830fbca0e765f77218a5375fc04e39c2a18338cb58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee69640e073508243213e0513507fca87fc1ea0787a8aa70b00d2b1c1b82a410",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-04-23T17:05:13Z",
    "title_canon_sha256": "cfa16b0e0cb1a1a83f20d6b8e856ed870da2e110e88b9cd2aad80123d5cc4973"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.10425",
    "kind": "arxiv",
    "version": 1
  }
}