Pith Number

pith:2WL6FSOX

pith:2015:2WL6FSOX3WY3VC6F5RNENKPMU3

not attested not anchored not stored refs pending

The mechanics of shuffle products and their siblings

Christophe Tollu (LIPN), G\'erard H. E. Duchamp (LIPN), Jean-Yves Enjalbert (LIPN), Vincel Hoang (LIPN)

arxiv:1512.01637 v1 · 2015-12-05 · 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{2WL6FSOX3WY3VC6F5RNENKPMU3}

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	2026-05-18T01:25:10.754532Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d597e2c9d7ddb1ba8bc5ec5a46a9eca6c536d030b888dbd77028ca410752bff9

Aliases

arxiv: 1512.01637 · arxiv_version: 1512.01637v1 · doi: 10.48550/arxiv.1512.01637 · pith_short_12: 2WL6FSOX3WY3 · pith_short_16: 2WL6FSOX3WY3VC6F · pith_short_8: 2WL6FSOX

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/2WL6FSOX3WY3VC6F5RNENKPMU3 \
  | 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: d597e2c9d7ddb1ba8bc5ec5a46a9eca6c536d030b888dbd77028ca410752bff9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0ff2c0a387dbf579f28594a17374f36a983b50530b746a972a16ebd3edcd5df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-05T08:15:07Z",
    "title_canon_sha256": "1742a0705620709ca17d460476b8b48da594ce6aff9d95b90f10eaf88bec65f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01637",
    "kind": "arxiv",
    "version": 1
  }
}