Pith Number

pith:WHFIT2N6

pith:2012:WHFIT2N6K5Z6A42TXZVSWEJ7JM

not attested not anchored not stored refs pending

Macdonald polynomials, Laumon spaces and perverse coherent sheaves

Alexander Braverman, Jun'ichi Shiraishi, Michael Finkelberg

arxiv:1206.3131 v2 · 2012-06-14 · math.AG · math.CO · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WHFIT2N6K5Z6A42TXZVSWEJ7JM}

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	2026-05-18T03:08:14.589013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1ca89e9be5773e07353be6b2b113f4b142e6b34abb1d11dd2efd1cec88d2bff

Aliases

arxiv: 1206.3131 · arxiv_version: 1206.3131v2 · doi: 10.48550/arxiv.1206.3131 · pith_short_12: WHFIT2N6K5Z6 · pith_short_16: WHFIT2N6K5Z6A42T · pith_short_8: WHFIT2N6

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/WHFIT2N6K5Z6A42TXZVSWEJ7JM \
  | 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: b1ca89e9be5773e07353be6b2b113f4b142e6b34abb1d11dd2efd1cec88d2bff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee771e6e19cf2772fa0c375ab1934ccfcf1cc95a088b3d5ae2c5d34b7e2a2160",
    "cross_cats_sorted": [
      "math.CO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-06-14T15:11:00Z",
    "title_canon_sha256": "0a20b1bd60771eacbf43ce3f697ffe391c496e0199e385eed8e81c2cd494aff5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3131",
    "kind": "arxiv",
    "version": 2
  }
}