Pith Number

pith:WGML7H7F

pith:2014:WGML7H7F6UP7EC6YTSLKHHOLHR

not attested not anchored not stored refs pending

The shifted Poirier-Reutenauer algebra

Naihuan Jing, Yunnan Li

arxiv:1411.2131 v1 · 2014-11-08 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WGML7H7F6UP7EC6YTSLKHHOLHR}

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	2026-05-18T01:27:08.090152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b198bf9fe5f51ff20bd89c96a39dcb3c4f14cbd14e62d6713c7be72403ce18dc

Aliases

arxiv: 1411.2131 · arxiv_version: 1411.2131v1 · doi: 10.48550/arxiv.1411.2131 · pith_short_12: WGML7H7F6UP7 · pith_short_16: WGML7H7F6UP7EC6Y · pith_short_8: WGML7H7F

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/WGML7H7F6UP7EC6YTSLKHHOLHR \
  | 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: b198bf9fe5f51ff20bd89c96a39dcb3c4f14cbd14e62d6713c7be72403ce18dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db50e1952b748ee486d97bad74e45c8feda0dd783bdcc6583ee62e432d35b112",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-11-08T15:54:06Z",
    "title_canon_sha256": "41bcd586bdc30bdc041dc6207e05328ed9ce09bed149102580238bab3eba5573"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.2131",
    "kind": "arxiv",
    "version": 1
  }
}