Pith Number

pith:2VN7TCE2

pith:2011:2VN7TCE2UJT44G43DVZD76BVPR

not attested not anchored not stored refs pending

The {\L}ojasiewicz exponent of nondegenerate surface singularities

Grzegorz Oleksik

arxiv:1110.4273 v1 · 2011-10-19 · math.CV · 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{2VN7TCE2UJT44G43DVZD76BVPR}

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	2026-05-18T04:10:37.793226Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d55bf9889aa267ce1b9b1d723ff8357c45b7a751a59337c43971bc6af92db0c8

Aliases

arxiv: 1110.4273 · arxiv_version: 1110.4273v1 · doi: 10.48550/arxiv.1110.4273 · pith_short_12: 2VN7TCE2UJT4 · pith_short_16: 2VN7TCE2UJT44G43 · pith_short_8: 2VN7TCE2

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/2VN7TCE2UJT44G43DVZD76BVPR \
  | 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: d55bf9889aa267ce1b9b1d723ff8357c45b7a751a59337c43971bc6af92db0c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0916bcbf845e8d2dae3d8f09c0a21af2186e6466f9fe8ba1f16acdf0a11ca6cc",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-10-19T13:14:37Z",
    "title_canon_sha256": "24c9771099a4d3be736057ddd2914e43a18214f000a2d465fd366a4b7771c952"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4273",
    "kind": "arxiv",
    "version": 1
  }
}