Pith Number

pith:JBD6HNOP

pith:2013:JBD6HNOPC3EYGWSKNWR5NVZPN3

not attested not anchored not stored refs pending

Deformations of shuffles and quasi-shuffles

Fr\'ed\'eric Patras (JAD), Jean-Yves Thibon (LIGM), Lo\"ic Foissy (LMPA)

arxiv:1311.1464 v1 · 2013-11-06 · math.RA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JBD6HNOPC3EYGWSKNWR5NVZPN3}

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	2026-05-18T03:07:53.249794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4847e3b5cf16c9835a4a6da3d6d72f6eca47db31639cdaa57142be64de4ffd43

Aliases

arxiv: 1311.1464 · arxiv_version: 1311.1464v1 · doi: 10.48550/arxiv.1311.1464 · pith_short_12: JBD6HNOPC3EY · pith_short_16: JBD6HNOPC3EYGWSK · pith_short_8: JBD6HNOP

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/JBD6HNOPC3EYGWSKNWR5NVZPN3 \
  | 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: 4847e3b5cf16c9835a4a6da3d6d72f6eca47db31639cdaa57142be64de4ffd43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95805bad549eda1779fffb7625e9e39cf653229d6b871a13a6a6b177d6c1b40f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-11-06T17:55:07Z",
    "title_canon_sha256": "f049ec293bb4c3a4b2fe358fbdc1ae07649e6f4e6abe19854b24364deab89a58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1464",
    "kind": "arxiv",
    "version": 1
  }
}