Pith Number

pith:CQ6OPODQ

pith:2015:CQ6OPODQGJDQJ4DJM773BJCT3D

not attested not anchored not stored refs pending

Fluctuations of the total number of critical points of random spherical harmonics

Igor Wigman, Valentina Cammarota

arxiv:1510.00339 v1 · 2015-10-01 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CQ6OPODQGJDQJ4DJM773BJCT3D}

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	2026-05-18T00:26:38.099629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

143ce7b870324704f06967ffb0a453d8f9ee07180b94805fff742ab9112aeed8

Aliases

arxiv: 1510.00339 · arxiv_version: 1510.00339v1 · doi: 10.48550/arxiv.1510.00339 · pith_short_12: CQ6OPODQGJDQ · pith_short_16: CQ6OPODQGJDQJ4DJ · pith_short_8: CQ6OPODQ

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/CQ6OPODQGJDQJ4DJM773BJCT3D \
  | 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: 143ce7b870324704f06967ffb0a453d8f9ee07180b94805fff742ab9112aeed8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20c19e221a8e0cf28169d4ad33ea50c7dc5da1ca5dc34270bf5819a5ed1a05f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-10-01T17:58:04Z",
    "title_canon_sha256": "75d1515cca09e19cdc416e1942de29c6ab9ea70746237721d3aa8b903c92cbbe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00339",
    "kind": "arxiv",
    "version": 1
  }
}