Pith Number

pith:CL2JWUZK

pith:2016:CL2JWUZK7ZPY5LYM273XEAFEZA

not attested not anchored not stored refs pending

Plactic monoids: a braided approach

Victoria Lebed

arxiv:1612.05768 v1 · 2016-12-17 · math.CO · math.KT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CL2JWUZK7ZPY5LYM273XEAFEZA}

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	2026-05-18T00:54:46.760444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12f49b532afe5f8eaf0cd7f77200a4c83556a0efcd6ee514f991a6688305900f

Aliases

arxiv: 1612.05768 · arxiv_version: 1612.05768v1 · doi: 10.48550/arxiv.1612.05768 · pith_short_12: CL2JWUZK7ZPY · pith_short_16: CL2JWUZK7ZPY5LYM · pith_short_8: CL2JWUZK

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/CL2JWUZK7ZPY5LYM273XEAFEZA \
  | 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: 12f49b532afe5f8eaf0cd7f77200a4c83556a0efcd6ee514f991a6688305900f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ec53daa40ac377ac32bc10284fb64f7394d8ff64bd54a8c45c0cd0c91de6883",
    "cross_cats_sorted": [
      "math.KT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-17T13:58:07Z",
    "title_canon_sha256": "4109eefca2702606a866a2e27ff83ad548c30ce8986e50d77f19913480088ada"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.05768",
    "kind": "arxiv",
    "version": 1
  }
}