Pith Number

pith:XFFO2HQ5

pith:2011:XFFO2HQ5YQZQW6EUUOSANF3LMJ

not attested not anchored not stored refs pending

Growth rate of an endomorphism of a group

Benjamin Fine, Delaram Kahrobaei, Kenneth Falconer

arxiv:1103.5622 v1 · 2011-03-29 · 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{XFFO2HQ5YQZQW6EUUOSANF3LMJ}

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	2026-05-18T04:25:37.222872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b94aed1e1dc4330b7894a3a406976b62485f83fe38d46f2840d5bb264a7fbde8

Aliases

arxiv: 1103.5622 · arxiv_version: 1103.5622v1 · doi: 10.48550/arxiv.1103.5622 · pith_short_12: XFFO2HQ5YQZQ · pith_short_16: XFFO2HQ5YQZQW6EU · pith_short_8: XFFO2HQ5

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/XFFO2HQ5YQZQW6EUUOSANF3LMJ \
  | 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: b94aed1e1dc4330b7894a3a406976b62485f83fe38d46f2840d5bb264a7fbde8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e605352f50cf7c2213ff49d20fd8c9584090fd4957e74be0537b241e39b1b9c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-03-29T13:06:00Z",
    "title_canon_sha256": "185cc77cbf437494671016b069637bafcf0cbecbce45f298d309937542a5fafa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5622",
    "kind": "arxiv",
    "version": 1
  }
}