Pith Number

pith:PIYBSMSB

pith:2013:PIYBSMSB6TCQ4DHCH3EYX43WB5

not attested not anchored not stored refs pending

Expansion in finite simple groups of Lie type

Ben Green, Emmanuel Breuillard, Robert Guralnick, Terence Tao

arxiv:1309.1975 v2 · 2013-09-08 · math.GR · 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{PIYBSMSB6TCQ4DHCH3EYX43WB5}

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	2026-05-18T02:59:47.768725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a30193241f4c50e0ce23ec98bf3760f5ecdb336ea046e66c1bc2f68b28b7b88

Aliases

arxiv: 1309.1975 · arxiv_version: 1309.1975v2 · doi: 10.48550/arxiv.1309.1975 · pith_short_12: PIYBSMSB6TCQ · pith_short_16: PIYBSMSB6TCQ4DHC · pith_short_8: PIYBSMSB

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/PIYBSMSB6TCQ4DHCH3EYX43WB5 \
  | 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: 7a30193241f4c50e0ce23ec98bf3760f5ecdb336ea046e66c1bc2f68b28b7b88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "049ea5dfce7f47bfe242f8c33d90bbfea440b4d237333b958023d0ccbd03c2b5",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-08T16:38:54Z",
    "title_canon_sha256": "f5cf1f7d823f42b2a6586b938f98dd9224cf8a13b9bf1d44ee3632df471e9ab4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1975",
    "kind": "arxiv",
    "version": 2
  }
}