Pith Number

pith:DD4CZPOY

pith:2016:DD4CZPOYZXNICY7KLNQJG4HB3F

not attested not anchored not stored refs pending

Hall polynomials for the torsion free groups of Hirsch length at most 5

Ann-Kristin Engel, Bettina Eick

arxiv:1605.01591 v2 · 2016-05-05 · 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{DD4CZPOYZXNICY7KLNQJG4HB3F}

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	2026-05-18T01:06:28.637865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18f82cbdd8cdda8163ea5b609370e1d9626ff7dbc85513550922bcb1ef915d1c

Aliases

arxiv: 1605.01591 · arxiv_version: 1605.01591v2 · doi: 10.48550/arxiv.1605.01591 · pith_short_12: DD4CZPOYZXNI · pith_short_16: DD4CZPOYZXNICY7K · pith_short_8: DD4CZPOY

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/DD4CZPOYZXNICY7KLNQJG4HB3F \
  | 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: 18f82cbdd8cdda8163ea5b609370e1d9626ff7dbc85513550922bcb1ef915d1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d0a1a87c097eb2df199ad70ac2b769e3c125fa7190c0f68e00fdd88462998d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-05-05T13:43:43Z",
    "title_canon_sha256": "60424dfeddc7555c7d3157aada3a1f2348350c3c0607451b8b59d7941bb5e238"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.01591",
    "kind": "arxiv",
    "version": 2
  }
}