Pith Number

pith:73Z2VAC4

pith:2005:73Z2VAC4B5634ZJWKDDSOB7UZJ

not attested not anchored not stored refs pending

Stochastic domination: the contact process, Ising models and FKG measures

Jeffrey E. Steif, Thomas Liggett

arxiv:math/0504530 v1 · 2005-04-26 · 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{73Z2VAC4B5634ZJWKDDSOB7UZJ}

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	2026-05-18T01:38:25.036225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fef3aa805c0f7dbe653650c72707f4ca756134f1a2df22efb89ad17fa96d0e41

Aliases

arxiv: math/0504530 · arxiv_version: math/0504530v1 · doi: 10.48550/arxiv.math/0504530 · pith_short_12: 73Z2VAC4B563 · pith_short_16: 73Z2VAC4B5634ZJW · pith_short_8: 73Z2VAC4

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/73Z2VAC4B5634ZJWKDDSOB7UZJ \
  | 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: fef3aa805c0f7dbe653650c72707f4ca756134f1a2df22efb89ad17fa96d0e41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "127daf6266c97c41854c58769c1f8065e9006162a3de8c52cf7f8b334adbead0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-04-26T11:28:54Z",
    "title_canon_sha256": "c4f10ec5bd5ca7e3fe1c81c1307e6f1090330562830898e00ffd561054a62dc0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0504530",
    "kind": "arxiv",
    "version": 1
  }
}