Pith Number

pith:XCB5WRNG

pith:2010:XCB5WRNGKVHSYR4HZH7AMP2I6H

not attested not anchored not stored refs pending

From quantum Schubert polynomials to k-Schur functions via the Toda lattice

Mark Shimozono, Thomas Lam

arxiv:1010.4047 v2 · 2010-10-19 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XCB5WRNGKVHSYR4HZH7AMP2I6H}

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	2026-05-18T04:38:39.267292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b883db45a6554f2c4787c9fe063f48f1eabc9f952b71f89ff68c5c7e01449ba6

Aliases

arxiv: 1010.4047 · arxiv_version: 1010.4047v2 · doi: 10.48550/arxiv.1010.4047 · pith_short_12: XCB5WRNGKVHS · pith_short_16: XCB5WRNGKVHSYR4H · pith_short_8: XCB5WRNG

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/XCB5WRNGKVHSYR4HZH7AMP2I6H \
  | 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: b883db45a6554f2c4787c9fe063f48f1eabc9f952b71f89ff68c5c7e01449ba6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd877b76ffa2cf74c47178ff104e55093e815a23a62aee1fc8db6fd6dad6273e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-10-19T20:45:06Z",
    "title_canon_sha256": "b074c1236e9fbdbc2899f39a94619663cbcd68aef2df0b9e5a96fb5824fbd016"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4047",
    "kind": "arxiv",
    "version": 2
  }
}