Pith Number

pith:FIE5RZGQ

pith:2011:FIE5RZGQF2N65Q27VKAVSA3AZ3

not attested not anchored not stored refs pending

A nilpotent Freiman dimension lemma

Ben Green, Emmanuel Breuillard, Terence Tao

arxiv:1112.4174 v1 · 2011-12-18 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FIE5RZGQF2N65Q27VKAVSA3AZ3}

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	2026-05-18T04:06:06.900567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a09d8e4d02e9beec35faa81590360ced58d487df82ae6f77bed09236bd2ba4b

Aliases

arxiv: 1112.4174 · arxiv_version: 1112.4174v1 · doi: 10.48550/arxiv.1112.4174 · pith_short_12: FIE5RZGQF2N6 · pith_short_16: FIE5RZGQF2N65Q27 · pith_short_8: FIE5RZGQ

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/FIE5RZGQF2N65Q27VKAVSA3AZ3 \
  | 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: 2a09d8e4d02e9beec35faa81590360ced58d487df82ae6f77bed09236bd2ba4b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13e48435ae13be8cd7e682f5c6317553ef1846ce97377296e52bdf0a416c5193",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-18T18:21:48Z",
    "title_canon_sha256": "bd557fcff76cc1016ccdb24cff892ac4d49ab8a00dc555c15c059bf71e7ae280"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4174",
    "kind": "arxiv",
    "version": 1
  }
}