Pith Number

pith:DJ6XYWVF

pith:2016:DJ6XYWVF4A7YYTEQT5BBT3VF32

not attested not anchored not stored refs pending

Littlewood-Richardson coefficients for Grothendieck polynomials from integrability

Michael Wheeler, Paul Zinn-Justin

arxiv:1607.02396 v1 · 2016-07-08 · math.CO · math-ph · math.AG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DJ6XYWVF4A7YYTEQT5BBT3VF32}

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	2026-05-18T01:11:20.478257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a7d7c5aa5e03f8c4c909f4219eea5de992688a49c608b43b8514fb293a1f449

Aliases

arxiv: 1607.02396 · arxiv_version: 1607.02396v1 · doi: 10.48550/arxiv.1607.02396 · pith_short_12: DJ6XYWVF4A7Y · pith_short_16: DJ6XYWVF4A7YYTEQ · pith_short_8: DJ6XYWVF

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/DJ6XYWVF4A7YYTEQT5BBT3VF32 \
  | 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: 1a7d7c5aa5e03f8c4c909f4219eea5de992688a49c608b43b8514fb293a1f449

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82707d8975839d6867ed63cd668ea9e0995dcdb5fbddc56a7dcc5073ce748938",
    "cross_cats_sorted": [
      "math-ph",
      "math.AG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-07-08T14:57:59Z",
    "title_canon_sha256": "33f0f9033a510937b6a7e2ab7d03a2e6cc2cc1122f4abcda8380a26314e99e0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.02396",
    "kind": "arxiv",
    "version": 1
  }
}