Pith Number

pith:DV37HZ3O

pith:2009:DV37HZ3OBQY7NNDQNYWU6VGY5A

not attested not anchored not stored refs pending

The z-Classes of Isometries

Krishnendu Gongopadhyay, Ravi S. Kulkarni

arxiv:0906.0563 v2 · 2009-06-02 · 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{DV37HZ3OBQY7NNDQNYWU6VGY5A}

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	2026-05-18T02:28:55.556752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d77f3e76e0c31f6b4706e2d4f54d8e81cdfa049b6054f61e10d07d966c3bd68

Aliases

arxiv: 0906.0563 · arxiv_version: 0906.0563v2 · doi: 10.48550/arxiv.0906.0563 · pith_short_12: DV37HZ3OBQY7 · pith_short_16: DV37HZ3OBQY7NNDQ · pith_short_8: DV37HZ3O

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/DV37HZ3OBQY7NNDQNYWU6VGY5A \
  | 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: 1d77f3e76e0c31f6b4706e2d4f54d8e81cdfa049b6054f61e10d07d966c3bd68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78d5863e722bb1b05f5d133642b9cceae132a205a1a266729f70e9de95d96e05",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-06-02T19:30:16Z",
    "title_canon_sha256": "dce7de41d1f5ccaec4f6516921910bf28eb39afebe31c43a01818d2f53f5569c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.0563",
    "kind": "arxiv",
    "version": 2
  }
}