Pith Number

pith:ASHQNCLA

pith:2010:ASHQNCLAPHSBCPKCDTO55LMI7I

not attested not anchored not stored refs pending

On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus

Jean Bourgain, Zeev Rudnick

arxiv:1012.3843 v2 · 2010-12-17 · 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{ASHQNCLAPHSBCPKCDTO55LMI7I}

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	2026-05-18T02:04:23.211856Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

048f06896079e4113d421cdddead88fa007f60db44203a132ab0c2775e975d86

Aliases

arxiv: 1012.3843 · arxiv_version: 1012.3843v2 · doi: 10.48550/arxiv.1012.3843 · pith_short_12: ASHQNCLAPHSB · pith_short_16: ASHQNCLAPHSBCPKC · pith_short_8: ASHQNCLA

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/ASHQNCLAPHSBCPKCDTO55LMI7I \
  | 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: 048f06896079e4113d421cdddead88fa007f60db44203a132ab0c2775e975d86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8334db0e67a3b861c00ce15407a6f4fd9678e18a338f83456cb8ea5eda1ecef",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-17T10:21:15Z",
    "title_canon_sha256": "cffd58796d1ed6e167c6f650c97dbeb139e7995887d1a956e2520c585f857726"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3843",
    "kind": "arxiv",
    "version": 2
  }
}