Pith Number

pith:4KHLJHGT

pith:2007:4KHLJHGTDEG52CG2J6T3VCI6IK

not attested not anchored not stored refs pending

The rank gradient from a combinatorial viewpoint

Andrei Jaikin-Zapirain, Miklos Abert, Nikolay Nikolov

arxiv:math/0701925 v3 · 2007-01-31 · 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{4KHLJHGTDEG52CG2J6T3VCI6IK}

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	2026-05-18T04:28:37.151641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e28eb49cd3190ddd08da4fa7ba891e42816bba94ba2c42ebe391aa1d64b137ce

Aliases

arxiv: math/0701925 · arxiv_version: math/0701925v3 · doi: 10.48550/arxiv.math/0701925 · pith_short_12: 4KHLJHGTDEG5 · pith_short_16: 4KHLJHGTDEG52CG2 · pith_short_8: 4KHLJHGT

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/4KHLJHGTDEG52CG2J6T3VCI6IK \
  | 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: e28eb49cd3190ddd08da4fa7ba891e42816bba94ba2c42ebe391aa1d64b137ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5f79e78b22175b85994fe414cae07faabc0afc8ab15e4d3158c8fa5c318c6b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2007-01-31T14:50:04Z",
    "title_canon_sha256": "9d3d554b1160b7aa98404501cbcd67fea19ffceaa42e80f105dc373c66526af6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0701925",
    "kind": "arxiv",
    "version": 3
  }
}