Pith Number

pith:JBGL7AHT

pith:2011:JBGL7AHT3F26IBRVJICB32RAZJ

not attested not anchored not stored refs pending

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

Mark Shimozono, Thomas Lam

arxiv:1109.2193 v1 · 2011-09-10 · 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{JBGL7AHT3F26IBRVJICB32RAZJ}

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	2026-05-18T04:13:38.335544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

484cbf80f3d975e406354a041dea20ca7422a2fbb528a22d3cf013d6ef28b3b5

Aliases

arxiv: 1109.2193 · arxiv_version: 1109.2193v1 · doi: 10.48550/arxiv.1109.2193 · pith_short_12: JBGL7AHT3F26 · pith_short_16: JBGL7AHT3F26IBRV · pith_short_8: JBGL7AHT

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/JBGL7AHT3F26IBRVJICB32RAZJ \
  | 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: 484cbf80f3d975e406354a041dea20ca7422a2fbb528a22d3cf013d6ef28b3b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df3a88087179ea6eda4bdb9fe23695d2277b8404cf330e7c0fdd4d55484b0f21",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-09-10T04:44:16Z",
    "title_canon_sha256": "5b7f1ab7e6bebfd78379b445c325cc7f12d668d387e474ebe5b8ab3bb46e7e36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2193",
    "kind": "arxiv",
    "version": 1
  }
}