Pith Number

pith:P7FD5AFA

pith:2011:P7FD5AFAHRPCYN4DW42D6PSPBH

not attested not anchored not stored refs pending

Restriction of toral eigenfunctions to hypersurfaces and nodal sets

Jean Bourgain, Zeev Rudnick

arxiv:1105.0018 v2 · 2011-04-29 · 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{P7FD5AFAHRPCYN4DW42D6PSPBH}

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	2026-05-18T04:12:33.732169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fca3e80a03c5e2c3783b7343f3e4f09e95635edf8e31dd18bf230f68673191e

Aliases

arxiv: 1105.0018 · arxiv_version: 1105.0018v2 · doi: 10.48550/arxiv.1105.0018 · pith_short_12: P7FD5AFAHRPC · pith_short_16: P7FD5AFAHRPCYN4D · pith_short_8: P7FD5AFA

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/P7FD5AFAHRPCYN4DW42D6PSPBH \
  | 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: 7fca3e80a03c5e2c3783b7343f3e4f09e95635edf8e31dd18bf230f68673191e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8c5b54a8a4759bf5be89ed0aafcff10cbd0bd79cc821e9bbb3b346723511f03",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-04-29T20:26:07Z",
    "title_canon_sha256": "3c2bb39a86941543744136b343e14b80ab6f4e9c8a427c802bc08cf7d27ed6ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.0018",
    "kind": "arxiv",
    "version": 2
  }
}