Pith Number

pith:VCCS4DRD

pith:2015:VCCS4DRDZEAGTB34YRLNMUCTGD

not attested not anchored not stored refs pending

Annealed central limit theorems for the Ising model on random graphs

Claudio Giberti, Cristian Giardin\`a, Maria Luisa Prioriello, Remco van der Hofstad

arxiv:1509.02695 v2 · 2015-09-09 · math.PR · math-ph · 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{VCCS4DRDZEAGTB34YRLNMUCTGD}

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	2026-05-18T01:21:00.949617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8852e0e23c90069877cc456d6505330e5006dda288f39ff61482bef5c386197

Aliases

arxiv: 1509.02695 · arxiv_version: 1509.02695v2 · doi: 10.48550/arxiv.1509.02695 · pith_short_12: VCCS4DRDZEAG · pith_short_16: VCCS4DRDZEAGTB34 · pith_short_8: VCCS4DRD

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/VCCS4DRDZEAGTB34YRLNMUCTGD \
  | 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: a8852e0e23c90069877cc456d6505330e5006dda288f39ff61482bef5c386197

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d2066d99fa735255ecba62b267f4db6ee3b7288826f2fabafa404f7cd903645",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-09-09T09:45:52Z",
    "title_canon_sha256": "a4b4e8aa72dcdb76f094cafb3af855e01232c2d7b641225183618736a3f8cc8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02695",
    "kind": "arxiv",
    "version": 2
  }
}