Pith Number

pith:ZWDNUEAG

pith:2010:ZWDNUEAGKL6ZAQFN7K73F2YV6V

not attested not anchored not stored refs pending

Normal Forms of Hypersurface Singularities in Positive Characteristic

Gert-Martin Greuel, Thomas Markwig, Yousra Boubakri

arxiv:1007.0170 v2 · 2010-07-01 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZWDNUEAGKL6ZAQFN7K73F2YV6V}

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	2026-05-18T04:35:47.671499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd86da100652fd9040adfabfb2eb15f56f3852430c28d04564815680148e33cc

Aliases

arxiv: 1007.0170 · arxiv_version: 1007.0170v2 · doi: 10.48550/arxiv.1007.0170 · pith_short_12: ZWDNUEAGKL6Z · pith_short_16: ZWDNUEAGKL6ZAQFN · pith_short_8: ZWDNUEAG

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/ZWDNUEAGKL6ZAQFN7K73F2YV6V \
  | 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: cd86da100652fd9040adfabfb2eb15f56f3852430c28d04564815680148e33cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "115d094f7b001cb7ed6f9a734cb74587f7fe5ee40fead12ed68c48fa37f4356e",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-07-01T14:00:15Z",
    "title_canon_sha256": "0fcb29238929ab01b25095a2be724588c389ce57aa9e2b4e2df93be8be5ea989"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0170",
    "kind": "arxiv",
    "version": 2
  }
}