Pith Number

pith:RAL2CJDK

pith:2012:RAL2CJDKR73KKINUG5BLATWQ6H

not attested not anchored not stored refs pending

Finite Gr\"obner--Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids

Alan J. Cain, Ant\'onio Malheiro, Robert D. Gray

arxiv:1205.4885 v3 · 2012-05-22 · math.RA · 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{RAL2CJDKR73KKINUG5BLATWQ6H}

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	2026-05-18T01:29:51.729396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8817a1246a8ff6a521b43742b04ed0f1f8f487ef71ea3bcc35473b8fa0ccc05d

Aliases

arxiv: 1205.4885 · arxiv_version: 1205.4885v3 · doi: 10.48550/arxiv.1205.4885 · pith_short_12: RAL2CJDKR73K · pith_short_16: RAL2CJDKR73KKINU · pith_short_8: RAL2CJDK

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/RAL2CJDKR73KKINUG5BLATWQ6H \
  | 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: 8817a1246a8ff6a521b43742b04ed0f1f8f487ef71ea3bcc35473b8fa0ccc05d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13c634ac9586094b4eff251f4058435e97732878bcc8ef02fdc9482f7630479e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-05-22T11:34:51Z",
    "title_canon_sha256": "149d6a9f2f125ee510c838406d15c0e32e4de90619aa8af074677f68b4f16c00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.4885",
    "kind": "arxiv",
    "version": 3
  }
}