Pith Number

pith:VGZGE4K3

pith:2018:VGZGE4K3UJIVI34WZDDB3FVKAB

not attested not anchored not stored refs pending

On the size of the set $AA+A$

Chun-Yen Shen, Ilya D. Shkredov, Imre Z. Ruzsa, Oliver Roche-Newton

arxiv:1801.10431 v1 · 2018-01-31 · 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{VGZGE4K3UJIVI34WZDDB3FVKAB}

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	2026-05-18T00:04:17.645830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9b262715ba251546f96c8c61d96aa006c0519b0d29d2248a460a573d657ad52

Aliases

arxiv: 1801.10431 · arxiv_version: 1801.10431v1 · doi: 10.48550/arxiv.1801.10431 · pith_short_12: VGZGE4K3UJIV · pith_short_16: VGZGE4K3UJIVI34W · pith_short_8: VGZGE4K3

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/VGZGE4K3UJIVI34WZDDB3FVKAB \
  | 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: a9b262715ba251546f96c8c61d96aa006c0519b0d29d2248a460a573d657ad52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19c96f0eb86a803dd5def7a15cbe777513768ec8d07932b1488a7f9c2981ae75",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-01-31T13:00:32Z",
    "title_canon_sha256": "b820f72da523d400720b9956b88241efab9e8ee88bf2a468884b72696c36339f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.10431",
    "kind": "arxiv",
    "version": 1
  }
}