Pith Number

pith:HKYH7CB7

pith:2012:HKYH7CB7VFFWYIYHQY4DDYUNRV

not attested not anchored not stored refs pending

Groups with a base property analogous to that of vector spaces

Benjamin Klopsch, Paul Apisa

arxiv:1211.6137 v1 · 2012-11-26 · 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{HKYH7CB7VFFWYIYHQY4DDYUNRV}

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	2026-05-18T03:39:52.492072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ab07f883fa94b6c2307863831e28d8d61d8be1e79336ae9bd81c230e90738aa

Aliases

arxiv: 1211.6137 · arxiv_version: 1211.6137v1 · doi: 10.48550/arxiv.1211.6137 · pith_short_12: HKYH7CB7VFFW · pith_short_16: HKYH7CB7VFFWYIYH · pith_short_8: HKYH7CB7

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/HKYH7CB7VFFWYIYHQY4DDYUNRV \
  | 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: 3ab07f883fa94b6c2307863831e28d8d61d8be1e79336ae9bd81c230e90738aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f790e7917ec46506a81bbd00ed90b34ab1aabb07ce81ac5966c6e9cf8c97fda",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-11-26T21:29:38Z",
    "title_canon_sha256": "78fadfeb164a126a136f4c97adbab9c8299589b77acc3f2d1877e37284701e85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6137",
    "kind": "arxiv",
    "version": 1
  }
}