Pith Number

pith:VH5JRLF5

pith:2016:VH5JRLF5E4FXIG7TF3V7EC53HK

not attested not anchored not stored refs pending

The abelian arithmetic regularity lemma

Sean Eberhard

arxiv:1606.09303 v1 · 2016-06-29 · math.NT · 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{VH5JRLF5E4FXIG7TF3V7EC53HK}

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.

Cited by

2 papers in Pith

A structure theorem for sets with doubling $4+\delta$

The sum-product phenomenon for dense subsets of finite fields

Receipt and verification

First computed	2026-05-18T01:11:40.670425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9fa98acbd270b741bf32eebf20bbb3ab6b0ef633ebf8471bee2a6ea91272873

Aliases

arxiv: 1606.09303 · arxiv_version: 1606.09303v1 · doi: 10.48550/arxiv.1606.09303 · pith_short_12: VH5JRLF5E4FX · pith_short_16: VH5JRLF5E4FXIG7T · pith_short_8: VH5JRLF5

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/VH5JRLF5E4FXIG7TF3V7EC53HK \
  | 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: a9fa98acbd270b741bf32eebf20bbb3ab6b0ef633ebf8471bee2a6ea91272873

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "553c6cac5b6d76b58b57c564b69add2ecfcad27779fb983059e850e2f71d7d00",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-29T22:27:44Z",
    "title_canon_sha256": "23d5dd3dd88e28e5bad88b463fc3f9672530ae920918966a1563762436ae12e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.09303",
    "kind": "arxiv",
    "version": 1
  }
}