Pith Number

pith:ZJA5R454

pith:2007:ZJA5R454G76M4PXNZA2BUV6GCN

not attested not anchored not stored refs pending

Schubert Polynomials for the affine Grassmannian of the symplectic group

Anne Schilling, Mark Shimozono, Thomas Lam

arxiv:0710.2720 v2 · 2007-10-15 · 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{ZJA5R454G76M4PXNZA2BUV6GCN}

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	2026-05-18T04:30:04.071481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca41d8f3bc37fcce3eedc8341a57c613728f0b0f2213a75ec18d233c3148c707

Aliases

arxiv: 0710.2720 · arxiv_version: 0710.2720v2 · doi: 10.48550/arxiv.0710.2720 · pith_short_12: ZJA5R454G76M · pith_short_16: ZJA5R454G76M4PXN · pith_short_8: ZJA5R454

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/ZJA5R454G76M4PXNZA2BUV6GCN \
  | 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: ca41d8f3bc37fcce3eedc8341a57c613728f0b0f2213a75ec18d233c3148c707

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7723212afb6ea000dd1f65ff9da8390ea2562320b5b17fcf84584e3481cb3be",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2007-10-15T05:57:36Z",
    "title_canon_sha256": "6a90880d0c55fa20a307a87b0f0752ad0aed70a7adc93ebb1e681c52b3313370"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.2720",
    "kind": "arxiv",
    "version": 2
  }
}