Pith Number

pith:34EKX3ZA

pith:2010:34EKX3ZA64ZR3NMUCGX3YNLVES

not attested not anchored not stored refs pending

A first order phase transition in the threshold-$\theta\ge 2$ contact process on random $r$-regular graphs and $r$-trees

Rick Durrett, Shirshendu Chatterjee

arxiv:1011.1567 v4 · 2010-11-06 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{34EKX3ZA64ZR3NMUCGX3YNLVES}

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	2026-05-18T03:10:14.796431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df08abef20f7331db59411afbc357524a4be8e8241e272662489b51409cf3b7b

Aliases

arxiv: 1011.1567 · arxiv_version: 1011.1567v4 · doi: 10.48550/arxiv.1011.1567 · pith_short_12: 34EKX3ZA64ZR · pith_short_16: 34EKX3ZA64ZR3NMU · pith_short_8: 34EKX3ZA

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/34EKX3ZA64ZR3NMUCGX3YNLVES \
  | 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: df08abef20f7331db59411afbc357524a4be8e8241e272662489b51409cf3b7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "755ab1bcbd135b9f1d91abc18a3f23982ab58bab9e2c68986a62304a32cd7a60",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-11-06T16:07:26Z",
    "title_canon_sha256": "403227be97bd85a69085b180348aff7c16ce81b624c88e989b919f2ae812c912"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1567",
    "kind": "arxiv",
    "version": 4
  }
}