Pith Number

pith:4P7HX64W

pith:2011:4P7HX64WUEABYCEG3YM2AKDISJ

not attested not anchored not stored refs pending

Metastates in mean-field models with random external fields generated by Markov chains

A. Reichenbachs, C. Kuelske, M. Formentin

arxiv:1109.4246 v2 · 2011-09-20 · math-ph · cond-mat.dis-nn · math.MP · 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{4P7HX64WUEABYCEG3YM2AKDISJ}

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	2026-05-18T02:00:28.857575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3fe7bfb96a1001c0886de19a0286892673bc3b90028daae2ae6f09eda360548

Aliases

arxiv: 1109.4246 · arxiv_version: 1109.4246v2 · doi: 10.48550/arxiv.1109.4246 · pith_short_12: 4P7HX64WUEAB · pith_short_16: 4P7HX64WUEABYCEG · pith_short_8: 4P7HX64W

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/4P7HX64WUEABYCEG3YM2AKDISJ \
  | 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: e3fe7bfb96a1001c0886de19a0286892673bc3b90028daae2ae6f09eda360548

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f65aae7b089856a181969774133aee3208feabc241d8a8720d6fbb82da1979c",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-09-20T09:14:04Z",
    "title_canon_sha256": "b4247b6f1a749134aa594b1e05a645d4e38f46fc32f0b681e6f786427995e181"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4246",
    "kind": "arxiv",
    "version": 2
  }
}