Pith Number

pith:QX445TIF

pith:2015:QX445TIF7E65OLKOXLUWVB5QUU

not attested not anchored not stored refs pending

Central limit theorems for the spectra of classes of random fractals

Ben M. Hambly, David A. Croydon, Philippe H. A. Charmoy

arxiv:1503.06028 v2 · 2015-03-20 · 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{QX445TIF7E65OLKOXLUWVB5QUU}

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	2026-05-18T00:55:39.578222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85f9cecd05f93dd72d4ebae96a87b0a5204ce8666b1a6800ef2aabf979c8ab81

Aliases

arxiv: 1503.06028 · arxiv_version: 1503.06028v2 · doi: 10.48550/arxiv.1503.06028 · pith_short_12: QX445TIF7E65 · pith_short_16: QX445TIF7E65OLKO · pith_short_8: QX445TIF

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/QX445TIF7E65OLKOXLUWVB5QUU \
  | 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: 85f9cecd05f93dd72d4ebae96a87b0a5204ce8666b1a6800ef2aabf979c8ab81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d58ff4744f59b64e40d6f09ab80aaa5bf1cde92547a2889d66da34fdaac37cb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-03-20T09:57:09Z",
    "title_canon_sha256": "d5590ee11633c1a39a71614837e469ec649534aae05cf1279df88e00e35badc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06028",
    "kind": "arxiv",
    "version": 2
  }
}