Pith Number

pith:7XFCJWUE

pith:2012:7XFCJWUE43BM2JQQCGD5ADEEUE

not attested not anchored not stored refs pending

Cohomology for Frobenius kernels of $SL_2$

Nham V. Ngo

arxiv:1209.1662 v3 · 2012-09-07 · math.RT · math.AC · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7XFCJWUE43BM2JQQCGD5ADEEUE}

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	2026-05-18T03:10:46.011698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdca24da84e6c2cd26101187d00c84a1170494e324e0382a480bf25b7377124f

Aliases

arxiv: 1209.1662 · arxiv_version: 1209.1662v3 · doi: 10.48550/arxiv.1209.1662 · pith_short_12: 7XFCJWUE43BM · pith_short_16: 7XFCJWUE43BM2JQQ · pith_short_8: 7XFCJWUE

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/7XFCJWUE43BM2JQQCGD5ADEEUE \
  | 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: fdca24da84e6c2cd26101187d00c84a1170494e324e0382a480bf25b7377124f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c55b4c958ce3bb084c909c1066aa6fe2222ecdd675b46f90bb706d3b680dfda",
    "cross_cats_sorted": [
      "math.AC",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-09-07T22:20:44Z",
    "title_canon_sha256": "a082b2ce34693b9dc0f84e747e351600f2fd4369f3cefea8b3d9159195b5ade1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1662",
    "kind": "arxiv",
    "version": 3
  }
}