Pith Number

pith:42CXYOQG

pith:2011:42CXYOQGJXZJHECSQ6DMB3C3V7

not attested not anchored not stored refs pending

On $p$-deficiency in groups

Jan-Christoph Schlage-Puchta, Yiftach Barnea

arxiv:1106.3255 v2 · 2011-06-16 · 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{42CXYOQGJXZJHECSQ6DMB3C3V7}

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	2026-05-18T00:57:42.839578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6857c3a064df29390528786c0ec5bafcdf74e7647faf295396f108e41a179ea

Aliases

arxiv: 1106.3255 · arxiv_version: 1106.3255v2 · doi: 10.48550/arxiv.1106.3255 · pith_short_12: 42CXYOQGJXZJ · pith_short_16: 42CXYOQGJXZJHECS · pith_short_8: 42CXYOQG

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/42CXYOQGJXZJHECSQ6DMB3C3V7 \
  | 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: e6857c3a064df29390528786c0ec5bafcdf74e7647faf295396f108e41a179ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70360ad1b5b3ccfd56a996e18a8d6582aa43418aa46d7d1f0f82c490d2339a39",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-06-16T15:25:47Z",
    "title_canon_sha256": "97bac4382b4f8d175ca9e4c3553b72e8910dc0fe52e75a2bbd9dfb41a98fed5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3255",
    "kind": "arxiv",
    "version": 2
  }
}