Pith Number

pith:Y7YNMCOG

pith:2013:Y7YNMCOGLT3C4YLA3M6LWU4XHG

not attested not anchored not stored refs pending

On locally graded groups with a word whose values are Engel

Antonio Tortora, Maria Tota, Pavel Shumyatsky

arxiv:1305.3045 v2 · 2013-05-14 · 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{Y7YNMCOGLT3C4YLA3M6LWU4XHG}

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	2026-05-18T02:29:53.291698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7f0d609c65cf62e6160db3cbb539739adb8968037777bf778f759320f08dc52

Aliases

arxiv: 1305.3045 · arxiv_version: 1305.3045v2 · doi: 10.48550/arxiv.1305.3045 · pith_short_12: Y7YNMCOGLT3C · pith_short_16: Y7YNMCOGLT3C4YLA · pith_short_8: Y7YNMCOG

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/Y7YNMCOGLT3C4YLA3M6LWU4XHG \
  | 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: c7f0d609c65cf62e6160db3cbb539739adb8968037777bf778f759320f08dc52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "837e0a99577a069a77af8b0f479ee7b664c4633147bc970ea87455b5108b745d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-05-14T07:39:03Z",
    "title_canon_sha256": "752baca3d112c1c5f350468b56136f2a7bfb4146bdb8f9016397bb7ca23a6313"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.3045",
    "kind": "arxiv",
    "version": 2
  }
}