Pith Number

pith:OPW5JEMD

pith:2009:OPW5JEMDTDFCLGKNB7BVOMSU7Z

not attested not anchored not stored refs pending

Schubert calculus and the Hopf algebra structures of exceptional Lie groups

Haibao Duan, Xuezhi Zhao

arxiv:0903.4501 v4 · 2009-03-26 · math.AT · 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{OPW5JEMDTDFCLGKNB7BVOMSU7Z}

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	2026-05-18T03:02:44.692268Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73edd4918398ca25994d0fc3573254fe52e95c8f6564e91fc06ecb29b3ed8d5b

Aliases

arxiv: 0903.4501 · arxiv_version: 0903.4501v4 · doi: 10.48550/arxiv.0903.4501 · pith_short_12: OPW5JEMDTDFC · pith_short_16: OPW5JEMDTDFCLGKN · pith_short_8: OPW5JEMD

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/OPW5JEMDTDFCLGKNB7BVOMSU7Z \
  | 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: 73edd4918398ca25994d0fc3573254fe52e95c8f6564e91fc06ecb29b3ed8d5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19b469eae02079b4ac70749f633ddaf73b7d8f4225989bf5632a159fc2058a21",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-03-26T09:14:48Z",
    "title_canon_sha256": "33cfded00797eb38f4c03127b84f4a75f1f768c62431b3535b63f245b37c459d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.4501",
    "kind": "arxiv",
    "version": 4
  }
}