Pith Number

pith:OPFOV4HT

pith:2013:OPFOV4HTPCHKY6WYMLZJRD4ROL

not attested not anchored not stored refs pending

Embeddings between partially commutative groups: two counterexamples

Andrew Duncan, Ilya Kazachkov, Montserrat Casals-Ruiz

arxiv:1306.3087 v1 · 2013-06-13 · 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{OPFOV4HTPCHKY6WYMLZJRD4ROL}

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	2026-05-18T03:20:59.616098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73caeaf0f3788eac7ad862f2988f9172f8fbcab3901e5e6070e5d15f7ed3e810

Aliases

arxiv: 1306.3087 · arxiv_version: 1306.3087v1 · doi: 10.48550/arxiv.1306.3087 · pith_short_12: OPFOV4HTPCHK · pith_short_16: OPFOV4HTPCHKY6WY · pith_short_8: OPFOV4HT

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/OPFOV4HTPCHKY6WYMLZJRD4ROL \
  | 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: 73caeaf0f3788eac7ad862f2988f9172f8fbcab3901e5e6070e5d15f7ed3e810

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9d498a7804e6281cfb62f5a668223b35668f738e9edcbb71e8b8b4a0701f514",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-06-13T11:47:34Z",
    "title_canon_sha256": "c80840109d83e35d5d74589e56f6c85efb5a835e8d47235b3875fbc27a23a9f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3087",
    "kind": "arxiv",
    "version": 1
  }
}