Pith Number

pith:IE3ISIBP

pith:2012:IE3ISIBPSZU56BOW4W3BGHM6EX

not attested not anchored not stored refs pending

The graph cohomology ring of the GKM graph of a flag manifold of type $G_2$

Yukiko Fukukawa

arxiv:1207.5229 v1 · 2012-07-22 · math.AT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IE3ISIBPSZU56BOW4W3BGHM6EX}

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	2026-05-18T03:50:24.121564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

413689202f9669df05d6e5b6131d9e25cbddb10f47743aa3684d1194ad09c4c1

Aliases

arxiv: 1207.5229 · arxiv_version: 1207.5229v1 · doi: 10.48550/arxiv.1207.5229 · pith_short_12: IE3ISIBPSZU5 · pith_short_16: IE3ISIBPSZU56BOW · pith_short_8: IE3ISIBP

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/IE3ISIBPSZU56BOW4W3BGHM6EX \
  | 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: 413689202f9669df05d6e5b6131d9e25cbddb10f47743aa3684d1194ad09c4c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2547d5e3dcdc3c5c0c076ce7a1577d999b450ebc2b4a2ad908113a6827af1b57",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-07-22T13:21:11Z",
    "title_canon_sha256": "355eedd0390158aaab308691046587e4db825b3dcf941ff697949ba2e0107a9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5229",
    "kind": "arxiv",
    "version": 1
  }
}