Pith Number

pith:WK6NJCD5

pith:2014:WK6NJCD5ZRJ7WABELYOOX4OY3V

not attested not anchored not stored refs pending

Horizontal gradient of polynomial functions for the standard Engel structure on $\mathbb R^4$

Krzysztof Kurdyka, Si Tiep Dinh

arxiv:1401.5399 v1 · 2014-01-21 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WK6NJCD5ZRJ7WABELYOOX4OY3V}

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	2026-05-18T01:19:00.639598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2bcd4887dcc53fb00245e1cebf1d8dd70d378d52765615eade6167bec2511f6

Aliases

arxiv: 1401.5399 · arxiv_version: 1401.5399v1 · doi: 10.48550/arxiv.1401.5399 · pith_short_12: WK6NJCD5ZRJ7 · pith_short_16: WK6NJCD5ZRJ7WABE · pith_short_8: WK6NJCD5

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/WK6NJCD5ZRJ7WABELYOOX4OY3V \
  | 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: b2bcd4887dcc53fb00245e1cebf1d8dd70d378d52765615eade6167bec2511f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ea5b0baacb243ed1cf55b835c5324befeaf32dc664ae7fb6b3fba9fcbad1ee2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-01-21T17:37:54Z",
    "title_canon_sha256": "95917925242d5007a32fd0c907b8a578098ffdd42c0c197b3def17e552ef93dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.5399",
    "kind": "arxiv",
    "version": 1
  }
}