Pith Number

pith:W6DCJAFN

pith:2010:W6DCJAFNFZ6GYRINZOPT4UGKGS

not attested not anchored not stored refs pending

Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras

Aaron Lauve, Amy Pang, Anders Hendrickson, Andrea Jedwab, Carlos Andre, Carolina Benedetti, C. Ryan Vinroot, Eric Marberg, Franco Saliola, Gizem Karaali, Huilan Li, I. Martin Isaacs, Jean-Christophe Novelli, Jean-Yves Thibon, Kay Magaard, Kenneth Johnson, Lenny Tevlin, Marcelo Aguiar, Mike Zabrocki, Nantel Bergeron, Nathaniel Thiem, Ning Yan, Persi Diaconis, Samuel Hsiao, Stephen Lewis, Tung Le, Vidya Venkateswaran, Zhi Chen

arxiv:1009.4134 v2 · 2010-09-21 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W6DCJAFNFZ6GYRINZOPT4UGKGS}

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	2026-05-18T04:04:06.914216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7862480ad2e7c6c450dcb9f3e50ca34bace782c8d63316c2737f2fb2dd96364

Aliases

arxiv: 1009.4134 · arxiv_version: 1009.4134v2 · doi: 10.48550/arxiv.1009.4134 · pith_short_12: W6DCJAFNFZ6G · pith_short_16: W6DCJAFNFZ6GYRIN · pith_short_8: W6DCJAFN

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/W6DCJAFNFZ6GYRINZOPT4UGKGS \
  | 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: b7862480ad2e7c6c450dcb9f3e50ca34bace782c8d63316c2737f2fb2dd96364

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a260a7148726464b48794bd608c3762ac3042dbc53925b7633d13f7d956cdbf",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-09-21T16:29:24Z",
    "title_canon_sha256": "6db6ae35a44d2a17676b0393e9f35c7ff2b800bfd6d5f88b345422adedd8d4ff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4134",
    "kind": "arxiv",
    "version": 2
  }
}