Pith Number

pith:UBOB4TYY

pith:2013:UBOB4TYY2ZZUGLF5HREFAB4GVI

not attested not anchored not stored refs pending

Co-prolongations of a group extension

Doan Trong Tuyen, Nguyen Thi Thu Thuy, Nguyen Tien Quang

arxiv:1309.3167 v1 · 2013-09-12 · 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{UBOB4TYY2ZZUGLF5HREFAB4GVI}

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	2026-05-18T03:13:32.661572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a05c1e4f18d673432cbd3c48500786aa0f520308369a027f261641a2fc419453

Aliases

arxiv: 1309.3167 · arxiv_version: 1309.3167v1 · doi: 10.48550/arxiv.1309.3167 · pith_short_12: UBOB4TYY2ZZU · pith_short_16: UBOB4TYY2ZZUGLF5 · pith_short_8: UBOB4TYY

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/UBOB4TYY2ZZUGLF5HREFAB4GVI \
  | 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: a05c1e4f18d673432cbd3c48500786aa0f520308369a027f261641a2fc419453

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e258fb047bc9b6d7a848476e2332844c88be7bdeee14fe6bebf885817bd7905",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-12T14:21:17Z",
    "title_canon_sha256": "beaabe0d1171edf699a4ef7c6866a0856518220a56a60f6122340ce10ee58eb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3167",
    "kind": "arxiv",
    "version": 1
  }
}