Pith Number

pith:JOBV43YZ

pith:2019:JOBV43YZCT4AA55ZXYHF5G4RWY

not attested not anchored not stored refs pending

Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula

Allen Knutson

arxiv:1909.13777 v2 · 2019-09-30 · 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{JOBV43YZCT4AA55ZXYHF5G4RWY}

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.

Cited by

1 paper in Pith

A Littlewood-Richardson Rule for Forest Polynomials via the Schubert Bialgebra

Receipt and verification

First computed	2026-07-05T03:54:16.568295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b835e6f1914f80077b9be0e5e9b91b62d2f29e8fd874e4b7bea418929a3a3b1

Aliases

arxiv: 1909.13777 · arxiv_version: 1909.13777v2 · doi: 10.48550/arxiv.1909.13777 · pith_short_12: JOBV43YZCT4A · pith_short_16: JOBV43YZCT4AA55Z · pith_short_8: JOBV43YZ

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/JOBV43YZCT4AA55ZXYHF5G4RWY \
  | 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: 4b835e6f1914f80077b9be0e5e9b91b62d2f29e8fd874e4b7bea418929a3a3b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20b80bcf147e8fc6612ea9a80d6805710219eed6d9af82dc80c373e5bec1929b",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-09-30T15:17:01Z",
    "title_canon_sha256": "686f9e64dacefba6bc30031a11746358a2e33734c38fd14b2bfa358dc01f2a16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.13777",
    "kind": "arxiv",
    "version": 2
  }
}