Pith Number

pith:JXTPSUDC

pith:2012:JXTPSUDCJLQZAAL4ZWF53RE4UH

not attested not anchored not stored refs pending

The Laplacian on planar graphs and graphs on surfaces

Richard Kenyon

arxiv:1203.1256 v1 · 2012-03-06 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JXTPSUDCJLQZAAL4ZWF53RE4UH}

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	2026-05-18T04:00:39.956386Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4de6f950624ae190017ccd8bddc49ca1d084716c1af8ca7af36b796f4619afa1

Aliases

arxiv: 1203.1256 · arxiv_version: 1203.1256v1 · doi: 10.48550/arxiv.1203.1256 · pith_short_12: JXTPSUDCJLQZ · pith_short_16: JXTPSUDCJLQZAAL4 · pith_short_8: JXTPSUDC

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/JXTPSUDCJLQZAAL4ZWF53RE4UH \
  | 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: 4de6f950624ae190017ccd8bddc49ca1d084716c1af8ca7af36b796f4619afa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9e5a4ff9e9298e3400cd5909c2e8325a939a48802eeae6fbf8c9aa336fd1f81",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-03-06T17:10:19Z",
    "title_canon_sha256": "70dac5821ca6cf27b82c1318b46c18a7cee8ba0b127033818fd8c00f49f17d83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1256",
    "kind": "arxiv",
    "version": 1
  }
}