Pith Number

pith:B7GCETTW

pith:2018:B7GCETTW7FPI5CPRIUYSIYVEDO

not attested not anchored not stored refs pending

Effective {\L}ojasiewicz gradient inequality and finite determinacy of non-isolated Nash function singularities

Beata Osi\'nska-Ulrych, Grzegorz Skalski, Stanis{\l}aw Spodzieja

arxiv:1812.04883 v1 · 2018-12-12 · 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{B7GCETTW7FPI5CPRIUYSIYVEDO}

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	2026-05-17T23:58:27.072901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fcc224e76f95e8e89f145312462a41b933ffcf32ab2f7d4ade07eb6678f5512

Aliases

arxiv: 1812.04883 · arxiv_version: 1812.04883v1 · doi: 10.48550/arxiv.1812.04883 · pith_short_12: B7GCETTW7FPI · pith_short_16: B7GCETTW7FPI5CPR · pith_short_8: B7GCETTW

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/B7GCETTW7FPI5CPRIUYSIYVEDO \
  | 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: 0fcc224e76f95e8e89f145312462a41b933ffcf32ab2f7d4ade07eb6678f5512

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "581b20b10d6a8243bed00f6a56607ebbc3dc248e2768b73af6776f71c94eed2d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-12-12T10:27:27Z",
    "title_canon_sha256": "4e1544d5c750055e863745b49e4650d3e7b78a5e8053c984c5c0dde5bc8b9ee0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.04883",
    "kind": "arxiv",
    "version": 1
  }
}