Pith Number

pith:CKQM4ICF

pith:2005:CKQM4ICFRN6X4BGG2TI4GERA5U

not attested not anchored not stored refs pending

Two Phase Transitions for the Contact Process on Small Worlds

Paul Jung, Rick Durrett

arxiv:math/0501481 v2 · 2005-01-27 · 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{CKQM4ICFRN6X4BGG2TI4GERA5U}

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	2026-07-04T14:39:33.860512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12a0ce20458b7d7e04c6d4d1c31220ed2a005f2c9a2cf7241a451459687dcff8

Aliases

arxiv: math/0501481 · arxiv_version: math/0501481v2 · doi: 10.48550/arxiv.math/0501481 · pith_short_12: CKQM4ICFRN6X · pith_short_16: CKQM4ICFRN6X4BGG · pith_short_8: CKQM4ICF

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/CKQM4ICFRN6X4BGG2TI4GERA5U \
  | 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: 12a0ce20458b7d7e04c6d4d1c31220ed2a005f2c9a2cf7241a451459687dcff8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29fa9b0a1b1834e5823e33c39bb0d797030c6043694d22bcac47593dd70b79b9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-01-27T20:56:09Z",
    "title_canon_sha256": "4e4e74b16df204c7da50f2eb6f493908840b60cb97ca6a2d73fa7a8e185576f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0501481",
    "kind": "arxiv",
    "version": 2
  }
}