Pith Number

pith:Y4M7YKKM

pith:2011:Y4M7YKKMYR3DV3V5TU2K6R5U3G

not attested not anchored not stored refs pending

Groups of given intermediate word growth

Anna Erschler, Laurent Bartholdi

arxiv:1110.3650 v3 · 2011-10-17 · 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{Y4M7YKKMYR3DV3V5TU2K6R5U3G}

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	2026-05-18T01:11:55.592828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c719fc294cc4763aeebd9d34af47b4d9bc9cbab2d47abbca4bb280f95f58545b

Aliases

arxiv: 1110.3650 · arxiv_version: 1110.3650v3 · doi: 10.48550/arxiv.1110.3650 · pith_short_12: Y4M7YKKMYR3D · pith_short_16: Y4M7YKKMYR3DV3V5 · pith_short_8: Y4M7YKKM

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/Y4M7YKKMYR3DV3V5TU2K6R5U3G \
  | 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: c719fc294cc4763aeebd9d34af47b4d9bc9cbab2d47abbca4bb280f95f58545b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad86ea42e4a017895f1c537eee42cc5e8dffa14ccf46a239db0ae726221e1f57",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-10-17T12:24:38Z",
    "title_canon_sha256": "b7b4eb887bd47813da6c6706720467853a9e28731eb2c836201c9e76592546a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3650",
    "kind": "arxiv",
    "version": 3
  }
}