Pith Number

pith:7RYMUMK6

pith:2013:7RYMUMK6JUUKLJAIMCWAKD3K67

not attested not anchored not stored refs pending

Critical points of multidimensional random Fourier series: variance estimates

Liviu I. Nicolaescu

arxiv:1310.5571 v2 · 2013-10-21 · math.PR · math-ph · math.AP · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7RYMUMK6JUUKLJAIMCWAKD3K67}

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	2026-05-18T01:57:23.689798Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc70ca315e4d28a5a40860ac050f6af7d2e5b07b260a45da93b5ba766c38f9c4

Aliases

arxiv: 1310.5571 · arxiv_version: 1310.5571v2 · doi: 10.48550/arxiv.1310.5571 · pith_short_12: 7RYMUMK6JUUK · pith_short_16: 7RYMUMK6JUUKLJAI · pith_short_8: 7RYMUMK6

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/7RYMUMK6JUUKLJAIMCWAKD3K67 \
  | 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: fc70ca315e4d28a5a40860ac050f6af7d2e5b07b260a45da93b5ba766c38f9c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f91f40414b0e8a8e157fa8ba0a913e0633240c204b0a9e5b18268e61f416436",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.DG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-21T14:38:59Z",
    "title_canon_sha256": "cb87d6f101ca51eb8d5d0b098afebc5214c07f3aa39bf7f0704a3b59b1fd0b26"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.5571",
    "kind": "arxiv",
    "version": 2
  }
}