Pith Number

pith:2XMQNOEH

pith:2011:2XMQNOEHGHCBS4P26PK4YWZO6G

not attested not anchored not stored refs pending

Quantum double Schubert polynomials represent Schubert classes

Mark Shimozono, Thomas Lam

arxiv:1108.4958 v1 · 2011-08-24 · 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{2XMQNOEHGHCBS4P26PK4YWZO6G}

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

2 papers in Pith

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

Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials

Receipt and verification

First computed	2026-05-18T04:14:45.716278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5d906b88731c41971faf3d5cc5b2ef1b3470d10ddfb4cd4434803c43b896be9

Aliases

arxiv: 1108.4958 · arxiv_version: 1108.4958v1 · doi: 10.48550/arxiv.1108.4958 · pith_short_12: 2XMQNOEHGHCB · pith_short_16: 2XMQNOEHGHCBS4P2 · pith_short_8: 2XMQNOEH

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/2XMQNOEHGHCBS4P26PK4YWZO6G \
  | 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: d5d906b88731c41971faf3d5cc5b2ef1b3470d10ddfb4cd4434803c43b896be9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8acdc915f2dcab9f1a2b24a2509f8c580d5e6a5c64618880c5db66b29211071",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-24T21:48:18Z",
    "title_canon_sha256": "92329a2e3b3d4e4cb1e2bf421270742e17f9376eac34e9dfc52df040109fa36b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4958",
    "kind": "arxiv",
    "version": 1
  }
}