Pith Number

pith:7WLSAFQR

pith:2013:7WLSAFQRP553PW7RPYSRAZYZDS

not attested not anchored not stored refs pending

Sch\"utzenberger's factorization on the (completed) Hopf algebra of $q-$stuffle product

Chen Bui, G\'erard Henry Edmond Duchamp (LIPN), Vincel Hoang Ngoc Minh (LIPN)

arxiv:1305.4450 v1 · 2013-05-20 · math.CO · cs.SC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7WLSAFQRP553PW7RPYSRAZYZDS}

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	2026-05-18T03:12:34.825591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd972016117f7bb7dbf17e251067191cb324107acb6a0907e26b3c4f41c22af4

Aliases

arxiv: 1305.4450 · arxiv_version: 1305.4450v1 · doi: 10.48550/arxiv.1305.4450 · pith_short_12: 7WLSAFQRP553 · pith_short_16: 7WLSAFQRP553PW7R · pith_short_8: 7WLSAFQR

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/7WLSAFQRP553PW7RPYSRAZYZDS \
  | 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: fd972016117f7bb7dbf17e251067191cb324107acb6a0907e26b3c4f41c22af4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f1779572bae5a8810362f8a55e0fe52b66ea96c6b17d57a17ab09d8634850ca",
    "cross_cats_sorted": [
      "cs.SC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-05-20T07:25:06Z",
    "title_canon_sha256": "0b20ce152b8cca43d8f7a52852b5aa448ee8d5d6bf636277198806552e45caaf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4450",
    "kind": "arxiv",
    "version": 1
  }
}