Pith Number

pith:4XMBWHYC

pith:2008:4XMBWHYCCCDUU7BN67WAGNSERJ

not attested not anchored not stored refs pending

Schubert presentation of the integral cohomology ring of the flag manifolds G/T

Haibao Duan, Xuezhi Zhao

arxiv:0801.2444 v12 · 2008-01-16 · 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{4XMBWHYCCCDUU7BN67WAGNSERJ}

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	2026-05-18T01:33:32.953359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5d81b1f0210874a7c2df7ec0336448a51bdd1c686056c3fd8c9293f9c85624e

Aliases

arxiv: 0801.2444 · arxiv_version: 0801.2444v12 · doi: 10.48550/arxiv.0801.2444 · pith_short_12: 4XMBWHYCCCDU · pith_short_16: 4XMBWHYCCCDUU7BN · pith_short_8: 4XMBWHYC

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/4XMBWHYCCCDUU7BN67WAGNSERJ \
  | 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: e5d81b1f0210874a7c2df7ec0336448a51bdd1c686056c3fd8c9293f9c85624e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33056dcbfa584c6f1677bca2477ebbdd2f19189ef6902318c3286fcf9110e47a",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-01-16T07:35:46Z",
    "title_canon_sha256": "79c658c8df2a714f818a153e247e710066e6175ada994d43de6c9766146619cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.2444",
    "kind": "arxiv",
    "version": 12
  }
}