Pith Number

pith:ER4XFYZ2

pith:2013:ER4XFYZ2HD6EU4WJWFJM27Y2NK

not attested not anchored not stored refs pending

On Pleijel's nodal domain theorem

Jean Bourgain

arxiv:1308.4422 v1 · 2013-08-20 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ER4XFYZ2HD6EU4WJWFJM27Y2NK}

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	2026-05-18T03:15:31.886568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

247972e33a38fc4a72c9b152cd7f1a6a9c5f169521ebd7f735337a34034fce63

Aliases

arxiv: 1308.4422 · arxiv_version: 1308.4422v1 · doi: 10.48550/arxiv.1308.4422 · pith_short_12: ER4XFYZ2HD6E · pith_short_16: ER4XFYZ2HD6EU4WJ · pith_short_8: ER4XFYZ2

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/ER4XFYZ2HD6EU4WJWFJM27Y2NK \
  | 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: 247972e33a38fc4a72c9b152cd7f1a6a9c5f169521ebd7f735337a34034fce63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1cedc85d855a82a1d5101dee9bf56d321c1c5d7cfb33a48b758bb3970634827",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-08-20T20:05:45Z",
    "title_canon_sha256": "8105215aadbcbc43ff46f66e6e16319f9c4cad070a5a886c18675f6967352fa1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4422",
    "kind": "arxiv",
    "version": 1
  }
}