Pith Number

pith:LTWIV64J

pith:2013:LTWIV64JCAVAEV2NRYNHJKGTQ5

not attested not anchored not stored refs pending

Nodal intersections and Lp restriction theorems on the torus

Jean Bourgain, Zeev Rudnick

arxiv:1308.4247 v3 · 2013-08-20 · math.AP · math-ph · math.MP · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LTWIV64JCAVAEV2NRYNHJKGTQ5}

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	2026-05-18T03:00:12.652876Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cec8afb89102a02574d8e1a74a8d3875b093d92fd06c35a6578d4715d0b65df

Aliases

arxiv: 1308.4247 · arxiv_version: 1308.4247v3 · doi: 10.48550/arxiv.1308.4247 · pith_short_12: LTWIV64JCAVA · pith_short_16: LTWIV64JCAVAEV2N · pith_short_8: LTWIV64J

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/LTWIV64JCAVAEV2NRYNHJKGTQ5 \
  | 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: 5cec8afb89102a02574d8e1a74a8d3875b093d92fd06c35a6578d4715d0b65df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb71a95d1a3588f88d8f338a2c600aa2f857e721caec2788badbb7dfa9afa069",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-08-20T07:51:34Z",
    "title_canon_sha256": "5dc5ed02c54bd1794e0df2311ce11f1380de0d478ba1a425b739107b74742945"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4247",
    "kind": "arxiv",
    "version": 3
  }
}