Pith Number

pith:UPPBQMP7

pith:2002:UPPBQMP7RRFTRDA2AD4UTZF3KG

not attested not anchored not stored refs pending

The Laplacian and $\bar\partial$ operators on critical planar graphs

Richard Kenyon

arxiv:math-ph/0202018 v1 · 2002-02-13 · math-ph · math.MP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UPPBQMP7RRFTRDA2AD4UTZF3KG}

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	2026-05-18T01:38:34.293281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3de1831ff8c4b388c1a00f949e4bb51b6ca659147b1b0c8c33d518a7cee6f80

Aliases

arxiv: math-ph/0202018 · arxiv_version: math-ph/0202018v1 · doi: 10.48550/arxiv.math-ph/0202018 · pith_short_12: UPPBQMP7RRFT · pith_short_16: UPPBQMP7RRFTRDA2 · pith_short_8: UPPBQMP7

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/UPPBQMP7RRFTRDA2AD4UTZF3KG \
  | 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: a3de1831ff8c4b388c1a00f949e4bb51b6ca659147b1b0c8c33d518a7cee6f80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b2a1dd759440b12e9b5f06c6db920a88f009060bbd4ad710573890d275af2d0",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2002-02-13T15:47:29Z",
    "title_canon_sha256": "1ed150c085c4d932b5d1193a98ba7f98a8bed85c88b6fa4ac26ca4d696c7b73a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0202018",
    "kind": "arxiv",
    "version": 1
  }
}