Pith Number

pith:RGGAKFDI

pith:2012:RGGAKFDIRZCETHXN3MMQ2HDNXR

not attested not anchored not stored refs pending

The Freiman--Ruzsa Theorem over Finite Fields

Chaim Even-Zohar, Shachar Lovett

arxiv:1212.5738 v3 · 2012-12-22 · 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{RGGAKFDIRZCETHXN3MMQ2HDNXR}

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	2026-05-18T00:14:07.161020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

898c0514688e44499eeddb190d1c6dbc712104e6190098718e6252d6b2be43d4

Aliases

arxiv: 1212.5738 · arxiv_version: 1212.5738v3 · doi: 10.48550/arxiv.1212.5738 · pith_short_12: RGGAKFDIRZCE · pith_short_16: RGGAKFDIRZCETHXN · pith_short_8: RGGAKFDI

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/RGGAKFDIRZCETHXN3MMQ2HDNXR \
  | 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: 898c0514688e44499eeddb190d1c6dbc712104e6190098718e6252d6b2be43d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1412f7dc3ad5198c20f268d26fe77ebd5e7c64e40d968b47ccd28ea1e865be2e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-22T23:12:07Z",
    "title_canon_sha256": "d435aabf5b1a15fded6c66f5896c0d938cae833239cc6053c9e2e0b94d71ffbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5738",
    "kind": "arxiv",
    "version": 3
  }
}