Pith Number

pith:MZTI3PSH

pith:2008:MZTI3PSHGA3LHVXZDVMRAQG2H7

not attested not anchored not stored refs pending

Combinatorial Hopf algebras, noncommutative Hall-Littlewood functions, and permutation tableaux

Jean-Christophe Novelli, Jean-Yves Thibon, Lauren K. Williams

arxiv:0804.0995 v3 · 2008-04-07 · 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{MZTI3PSHGA3LHVXZDVMRAQG2H7}

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	2026-05-18T03:34:12.542853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66668dbe473036b3d6f91d591040da3ff2e3d16110b3983f8d717441743db975

Aliases

arxiv: 0804.0995 · arxiv_version: 0804.0995v3 · doi: 10.48550/arxiv.0804.0995 · pith_short_12: MZTI3PSHGA3L · pith_short_16: MZTI3PSHGA3LHVXZ · pith_short_8: MZTI3PSH

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/MZTI3PSHGA3LHVXZDVMRAQG2H7 \
  | 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: 66668dbe473036b3d6f91d591040da3ff2e3d16110b3983f8d717441743db975

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af567d6410b4071ccf3f9256aeceecdd9c4e69274c6e80dcbf3c65a92a5d19af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-04-07T09:35:15Z",
    "title_canon_sha256": "0a1c13ce741bdd2f0e331f4fc0850cb8c9b4d5992545e5c7992a2ed2e8af9a7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.0995",
    "kind": "arxiv",
    "version": 3
  }
}