Pith Number

pith:MQRNLH52

pith:2016:MQRNLH52PVYYKTIOSA6PPXTNBZ

not attested not anchored not stored refs pending

Gradient Gibbs measures and fuzzy transformations on trees

Christof Kuelske, Philipp Schriever

arxiv:1609.00159 v2 · 2016-09-01 · 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{MQRNLH52PVYYKTIOSA6PPXTNBZ}

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	2026-05-18T00:56:45.545253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6422d59fba7d71854d0e903cf7de6d0e795c3b2baee4ec696e647234536b41ef

Aliases

arxiv: 1609.00159 · arxiv_version: 1609.00159v2 · doi: 10.48550/arxiv.1609.00159 · pith_short_12: MQRNLH52PVYY · pith_short_16: MQRNLH52PVYYKTIO · pith_short_8: MQRNLH52

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/MQRNLH52PVYYKTIOSA6PPXTNBZ \
  | 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: 6422d59fba7d71854d0e903cf7de6d0e795c3b2baee4ec696e647234536b41ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a2197361f13988b502ba36bb431aa1dbecddbfed46fcba7aba9e527a02d52fbc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-01T09:40:48Z",
    "title_canon_sha256": "dc63edc1f161f1f47c332e2cf67f385b48985f3a2b62e6d8d06936fb97305e6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.00159",
    "kind": "arxiv",
    "version": 2
  }
}