Pith Number

pith:DELJ4F55

pith:2010:DELJ4F557ZAEFFS3NWY7S5SUNP

not attested not anchored not stored refs pending

On the nodal sets of toral eigenfunctions

Jean Bourgain, Zeev Rudnick

arxiv:1003.1743 v2 · 2010-03-08 · math-ph · math.AP · 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{DELJ4F557ZAEFFS3NWY7S5SUNP}

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	2026-05-18T02:08:36.350421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19169e17bdfe4042965b6db1f976546bd9440e8a43fb38a1d24a994c7fec6b29

Aliases

arxiv: 1003.1743 · arxiv_version: 1003.1743v2 · doi: 10.48550/arxiv.1003.1743 · pith_short_12: DELJ4F557ZAE · pith_short_16: DELJ4F557ZAEFFS3 · pith_short_8: DELJ4F55

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/DELJ4F557ZAEFFS3NWY7S5SUNP \
  | 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: 19169e17bdfe4042965b6db1f976546bd9440e8a43fb38a1d24a994c7fec6b29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05b9f512a1019776fe795f38cc8840f3fdb4a80b15bff3381678b3f9fc7fa5ec",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-03-08T22:26:49Z",
    "title_canon_sha256": "20a81fb59150bfc809a0aba44d82d0f9569a70990f197c7a1a3d48e9b75e4f2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.1743",
    "kind": "arxiv",
    "version": 2
  }
}