Pith Number

pith:4QCXAM57

pith:2012:4QCXAM57BIRUNCOKUKGUIPG4X5

not attested not anchored not stored refs pending

Sums of squares of the Littlewood-Richardson coefficients and GL(n)-harmonic polynomials

Jeb F. Willenbring, Pamela E. Harris

arxiv:1206.0404 v2 · 2012-06-02 · math.RT · 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{4QCXAM57BIRUNCOKUKGUIPG4X5}

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	2026-05-18T03:27:23.169646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4057033bf0a234689caa28d443cdcbf605198a499588edfdabbf1b742266ef2

Aliases

arxiv: 1206.0404 · arxiv_version: 1206.0404v2 · doi: 10.48550/arxiv.1206.0404 · pith_short_12: 4QCXAM57BIRU · pith_short_16: 4QCXAM57BIRUNCOK · pith_short_8: 4QCXAM57

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/4QCXAM57BIRUNCOKUKGUIPG4X5 \
  | 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: e4057033bf0a234689caa28d443cdcbf605198a499588edfdabbf1b742266ef2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe2c065923fcaf1958e082ba605e81e88166cfec14504a70697f48e5a6d9480f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-06-02T21:45:55Z",
    "title_canon_sha256": "4de609faacc2e394b466a5995dd7a72dc321429eb03b1f9fd5784fe1f9885ee7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0404",
    "kind": "arxiv",
    "version": 2
  }
}