Pith Number

pith:JYDS7L2W

pith:2011:JYDS7L2WYKEVRFSQRD6XJTZQAV

not attested not anchored not stored refs pending

Level Sets of Differentiable Functions of Two Variables with Non-vanishing Gradient

M\'arton Elekes

arxiv:1109.4959 v1 · 2011-09-22 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JYDS7L2WYKEVRFSQRD6XJTZQAV}

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	2026-05-18T04:12:31.808493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e072faf56c28958965088fd74cf3005585960665885cda2eda1599f1f9630a0

Aliases

arxiv: 1109.4959 · arxiv_version: 1109.4959v1 · doi: 10.48550/arxiv.1109.4959 · pith_short_12: JYDS7L2WYKEV · pith_short_16: JYDS7L2WYKEVRFSQ · pith_short_8: JYDS7L2W

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/JYDS7L2WYKEVRFSQRD6XJTZQAV \
  | 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: 4e072faf56c28958965088fd74cf3005585960665885cda2eda1599f1f9630a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42c8e07dcda351242d892a61c0d3bf1725ad4f45b519b07f14c06a640246f1be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-09-22T21:46:51Z",
    "title_canon_sha256": "2022dcdecbbe40e8242278fe14241e4ea76038652c4bf7332f9a38a8baf310ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4959",
    "kind": "arxiv",
    "version": 1
  }
}