Pith Number

pith:3UN5TXTB

pith:2018:3UN5TXTBT4RHJ2TLH2YAXQLLLN

not attested not anchored not stored refs pending

A criterion for residual $p$-finiteness of arbitrary graphs of finite $p$-groups

Gareth Wilkes

arxiv:1810.13222 v1 · 2018-10-31 · 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{3UN5TXTBT4RHJ2TLH2YAXQLLLN}

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	2026-05-18T00:01:51.870988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd1bd9de619f2274ea6b3eb00bc16b5b6cc9da8866475b91fd6d577e4fbee00e

Aliases

arxiv: 1810.13222 · arxiv_version: 1810.13222v1 · doi: 10.48550/arxiv.1810.13222 · pith_short_12: 3UN5TXTBT4RH · pith_short_16: 3UN5TXTBT4RHJ2TL · pith_short_8: 3UN5TXTB

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/3UN5TXTBT4RHJ2TLH2YAXQLLLN \
  | 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: dd1bd9de619f2274ea6b3eb00bc16b5b6cc9da8866475b91fd6d577e4fbee00e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e048952a3d144b9e1a16fbb9d781116b8e79c9df1b6f7ad2db3b250b19d323a2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-10-31T11:34:21Z",
    "title_canon_sha256": "3d0cdf27f73024088745657e60a733a9d062a16ae0addda4268fc88df65b7ad7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.13222",
    "kind": "arxiv",
    "version": 1
  }
}