Pith Number

pith:N4R4JYHS

pith:2003:N4R4JYHSJKZUZD24TKR2PMLZOO

not attested not anchored not stored refs pending

Grothendieck polynomials and quiver formulas

Alexander Yong, Anders Skovsted Buch, Andrew Kresch, Harry Tamvakis

arxiv:math/0306389 v1 · 2003-06-27 · 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{N4R4JYHSJKZUZD24TKR2PMLZOO}

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

Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials

Receipt and verification

First computed	2026-05-18T01:05:28.787089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f23c4e0f24ab34c8f5c9aa3a7b179738724de708f9d41b059a1ef5f7cb2b170

Aliases

arxiv: math/0306389 · arxiv_version: math/0306389v1 · doi: 10.48550/arxiv.math/0306389 · pith_short_12: N4R4JYHSJKZU · pith_short_16: N4R4JYHSJKZUZD24 · pith_short_8: N4R4JYHS

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/N4R4JYHSJKZUZD24TKR2PMLZOO \
  | 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: 6f23c4e0f24ab34c8f5c9aa3a7b179738724de708f9d41b059a1ef5f7cb2b170

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74687da09648463fa13cc2373e88c13ace6528dd20431be2a41672739bc48d24",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2003-06-27T08:32:12Z",
    "title_canon_sha256": "d1b460dce14202f4fff776c70f8001e87406b9bd49fe2b48eaf71cb3333eb5a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0306389",
    "kind": "arxiv",
    "version": 1
  }
}