Pith Number

pith:3O67DO5N

pith:2015:3O67DO5NS4ZEEPJ67DP764XP5P

not attested not anchored not stored refs pending

Critical exponents on Fortuin--Kasteleyn weighted planar maps

Beno\^it Laslier, Gourab Ray, Nathana\"el Berestycki

arxiv:1502.00450 v2 · 2015-02-02 · math.PR · math-ph · 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{3O67DO5NS4ZEEPJ67DP764XP5P}

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	2026-05-18T01:11:18.390158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbbdf1bbad9732423d3ef8dfff72efebd0dde46e1aa044f6225648866db58792

Aliases

arxiv: 1502.00450 · arxiv_version: 1502.00450v2 · doi: 10.48550/arxiv.1502.00450 · pith_short_12: 3O67DO5NS4ZE · pith_short_16: 3O67DO5NS4ZEEPJ6 · pith_short_8: 3O67DO5N

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/3O67DO5NS4ZEEPJ67DP764XP5P \
  | 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: dbbdf1bbad9732423d3ef8dfff72efebd0dde46e1aa044f6225648866db58792

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c59ad46cbf53c1edc7d095fd39f91b8ecc8d3dd7ddfd69adc388ab3b07a9a090",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-02-02T12:24:47Z",
    "title_canon_sha256": "82ffdc5463530f7037c5a83a9b27d54e7ce1a1ec53979942ee7f5bfb2c4a5b9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.00450",
    "kind": "arxiv",
    "version": 2
  }
}