Pith Number

pith:QFS26YBG

pith:2012:QFS26YBG6PA3YVSPCKETWY5TOR

not attested not anchored not stored refs pending

Growth in linear groups

Endre Szab\'o, L\'aszl\'o Pyber

arxiv:1208.2538 v1 · 2012-08-13 · 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{QFS26YBG6PA3YVSPCKETWY5TOR}

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	2026-05-18T03:48:57.590667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8165af6026f3c1bc564f12893b63b3745cea790a5e5991d2864917324b3990b1

Aliases

arxiv: 1208.2538 · arxiv_version: 1208.2538v1 · doi: 10.48550/arxiv.1208.2538 · pith_short_12: QFS26YBG6PA3 · pith_short_16: QFS26YBG6PA3YVSP · pith_short_8: QFS26YBG

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/QFS26YBG6PA3YVSPCKETWY5TOR \
  | 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: 8165af6026f3c1bc564f12893b63b3745cea790a5e5991d2864917324b3990b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12fa8fd257265cb2d6f1ea659df3cc5da37c2cf9166f32b80f6abf38fabe12ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-08-13T09:57:21Z",
    "title_canon_sha256": "9f05286e4f0957899b19d7072fb5ed49717b8d5f201ad223b6cb574bf9ea944b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2538",
    "kind": "arxiv",
    "version": 1
  }
}