Pith Number

pith:O276HN73

pith:2012:O276HN7335GRCZNUPVK4BXSBOO

not attested not anchored not stored refs pending

Benjamini-Schramm convergence and the distribution of chromatic roots for sparse graphs

Mikl\'os Ab\'ert, Tam\'as Hubai

arxiv:1201.3861 v3 · 2012-01-18 · math.CO · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O276HN7335GRCZNUPVK4BXSBOO}

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	2026-05-18T03:25:33.511659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76bfe3b7fbdf4d1165b47d55c0de4173b71aad2606f9c2c63e487cdfb844b139

Aliases

arxiv: 1201.3861 · arxiv_version: 1201.3861v3 · doi: 10.48550/arxiv.1201.3861 · pith_short_12: O276HN7335GR · pith_short_16: O276HN7335GRCZNU · pith_short_8: O276HN73

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/O276HN7335GRCZNUPVK4BXSBOO \
  | 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: 76bfe3b7fbdf4d1165b47d55c0de4173b71aad2606f9c2c63e487cdfb844b139

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa75ec45d083de23898001f3106e3a90e72a32a1dad2fd14f4852ca9537f3539",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-01-18T17:23:05Z",
    "title_canon_sha256": "2ff3d662d901475057d01c6317fd289d47e2c6b2f8332c63c6c3919173d49ecd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3861",
    "kind": "arxiv",
    "version": 3
  }
}