Pith Number

pith:QG6ZRH7L

pith:2011:QG6ZRH7LKRIL7KENV5OPAGDZUA

not attested not anchored not stored refs pending

k-Double Schur functions and equivariant (co)homology of the affine Grassmannian

Mark Shimozono, Thomas Lam

arxiv:1105.2170 v1 · 2011-05-11 · 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{QG6ZRH7LKRIL7KENV5OPAGDZUA}

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	2026-05-18T04:22:21.368433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81bd989feb5450bfa88daf5cf01879a011a2c8b350ce70d6fa571042ff060cc3

Aliases

arxiv: 1105.2170 · arxiv_version: 1105.2170v1 · doi: 10.48550/arxiv.1105.2170 · pith_short_12: QG6ZRH7LKRIL · pith_short_16: QG6ZRH7LKRIL7KEN · pith_short_8: QG6ZRH7L

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/QG6ZRH7LKRIL7KENV5OPAGDZUA \
  | 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: 81bd989feb5450bfa88daf5cf01879a011a2c8b350ce70d6fa571042ff060cc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e50288b29c567b528674c0776cc783bcdae376331234161a4d68aac5bce116a2",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-11T12:18:39Z",
    "title_canon_sha256": "b5a15e958516ff8089a9194243f10335c9f76f97a11a2629afa5057529ba0d40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2170",
    "kind": "arxiv",
    "version": 1
  }
}