Pith Number

pith:2TV3CMNT

pith:2013:2TV3CMNTHSZU26HJBLBDJ27H3F

not attested not anchored not stored refs pending

Groups whose prime graphs have no triangles

Hung P. Tong-Viet

arxiv:1303.3457 v1 · 2013-03-14 · math.GR · math.CO · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2TV3CMNTHSZU26HJBLBDJ27H3F}

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	2026-05-18T03:30:54.545979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4ebb131b33cb34d78e90ac234ebe7d9496a600ce29886c6f3c1e2ae68b460c5

Aliases

arxiv: 1303.3457 · arxiv_version: 1303.3457v1 · doi: 10.48550/arxiv.1303.3457 · pith_short_12: 2TV3CMNTHSZU · pith_short_16: 2TV3CMNTHSZU26HJ · pith_short_8: 2TV3CMNT

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/2TV3CMNTHSZU26HJBLBDJ27H3F \
  | 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: d4ebb131b33cb34d78e90ac234ebe7d9496a600ce29886c6f3c1e2ae68b460c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c03d6f4be078cb33cc2d861d2fddbb5a08c47864d34bf9cfc32e4b83c62e4d2",
    "cross_cats_sorted": [
      "math.CO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-03-14T14:28:28Z",
    "title_canon_sha256": "48e109ce141c8b342d15672096c3180ffb345928cdc364d95edc436878c20245"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3457",
    "kind": "arxiv",
    "version": 1
  }
}