Pith Number

pith:3ZDWHA4C

pith:2018:3ZDWHA4CYGNNI5NNVPYMXMKVCJ

not attested not anchored not stored refs pending

If $A+A$ is small then $AAA$ is superquadratic

Ilya D. Shkredov, Oliver Roche-Newton

arxiv:1810.10842 v2 · 2018-10-25 · 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{3ZDWHA4CYGNNI5NNVPYMXMKVCJ}

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	2026-05-17T23:49:40.799047Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de47638382c19ad475adabf0cbb1551253d2acf68449f2737c4b9d4d1c711624

Aliases

arxiv: 1810.10842 · arxiv_version: 1810.10842v2 · doi: 10.48550/arxiv.1810.10842 · pith_short_12: 3ZDWHA4CYGNN · pith_short_16: 3ZDWHA4CYGNNI5NN · pith_short_8: 3ZDWHA4C

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/3ZDWHA4CYGNNI5NNVPYMXMKVCJ \
  | 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: de47638382c19ad475adabf0cbb1551253d2acf68449f2737c4b9d4d1c711624

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d20dd227068931f01a179cffbca0a566c20ee555fee0438c7bbef09e80599c06",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-10-25T12:18:03Z",
    "title_canon_sha256": "9c574256126fab9c7d2a716d23ac6f010ab01d38077f5c555f8d174a3c016e29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.10842",
    "kind": "arxiv",
    "version": 2
  }
}