Pith Number

pith:ZFKMB2XP

pith:2004:ZFKMB2XPHTHBXS3W2OBYINZN2H

not attested not anchored not stored refs pending

A tighter bound for the number of words of minimum length in an automorphic orbit

Donghi Lee

arxiv:math/0401269 v3 · 2004-01-21 · 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{ZFKMB2XPHTHBXS3W2OBYINZN2H}

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	2026-05-18T04:23:11.850000Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c954c0eaef3cce1bcb76d38384372dd1e9c31ecdd0e87dd49a32bd7dce71bdfa

Aliases

arxiv: math/0401269 · arxiv_version: math/0401269v3 · doi: 10.48550/arxiv.math/0401269 · pith_short_12: ZFKMB2XPHTHB · pith_short_16: ZFKMB2XPHTHBXS3W · pith_short_8: ZFKMB2XP

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/ZFKMB2XPHTHBXS3W2OBYINZN2H \
  | 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: c954c0eaef3cce1bcb76d38384372dd1e9c31ecdd0e87dd49a32bd7dce71bdfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ad346286eef0dd757ffbd144fceea4601515832497fe3a18034f66e3fa4c544",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2004-01-21T07:29:45Z",
    "title_canon_sha256": "cc5489cad3b71a223bf7564d351b9de4af0c5d07047f1cb2a196c9aa17c042a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0401269",
    "kind": "arxiv",
    "version": 3
  }
}