Pith Number

pith:WTZDKK56

pith:2010:WTZDKK56YBQWASIUHPMV7B6EMT

not attested not anchored not stored refs pending

From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction

B\'eatrice de Tili\`ere

arxiv:1012.4836 v3 · 2010-12-21 · math-ph · math.CO · 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{WTZDKK56YBQWASIUHPMV7B6EMT}

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	2026-05-18T02:04:18.885881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4f2352bbec0616049143bd95f87c464f34cfd088f8cfcb8f365b8e2ab89d56c

Aliases

arxiv: 1012.4836 · arxiv_version: 1012.4836v3 · doi: 10.48550/arxiv.1012.4836 · pith_short_12: WTZDKK56YBQW · pith_short_16: WTZDKK56YBQWASIU · pith_short_8: WTZDKK56

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/WTZDKK56YBQWASIUHPMV7B6EMT \
  | 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: b4f2352bbec0616049143bd95f87c464f34cfd088f8cfcb8f365b8e2ab89d56c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc4cb99cff552aaed0d4e40b72fdc6efa1c5c7767979ea63d345a9a2dc24b514",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-12-21T23:00:47Z",
    "title_canon_sha256": "fe590679f1b0b776eb0b846588e0f60488f853463862067b216d7399a83904c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4836",
    "kind": "arxiv",
    "version": 3
  }
}