Pith Number

pith:77ONRQFK

pith:2006:77ONRQFKRCP5NCPSQPV5K2HJIJ

not attested not anchored not stored refs pending

On the Critical Behavior at the Lower Phase Transition of the Contact Process

Michael Aizenman, Paul Jung

arxiv:math/0603227 v2 · 2006-03-09 · math.PR · cond-mat.stat-mech · 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{77ONRQFKRCP5NCPSQPV5K2HJIJ}

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	2026-07-04T15:14:40.280069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffdcd8c0aa889fd689f283ebd568e94253c46f8340027f4ecb9e24e6399dbe83

Aliases

arxiv: math/0603227 · arxiv_version: math/0603227v2 · doi: 10.48550/arxiv.math/0603227 · pith_short_12: 77ONRQFKRCP5 · pith_short_16: 77ONRQFKRCP5NCPS · pith_short_8: 77ONRQFK

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/77ONRQFKRCP5NCPSQPV5K2HJIJ \
  | 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: ffdcd8c0aa889fd689f283ebd568e94253c46f8340027f4ecb9e24e6399dbe83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "286d9972bcddc4536827707054bce88972cd92105f883105d5bad77fb128f48f",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2006-03-09T17:37:45Z",
    "title_canon_sha256": "944f110518f2ef348de8a329e1bf42ce1b9f853bf348f3c248e7e867d6f903d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0603227",
    "kind": "arxiv",
    "version": 2
  }
}