Pith Number

pith:MCTYV772

pith:2012:MCTYV772PJUHR26CZ32BHRBCG7

not attested not anchored not stored refs pending

The Structure of Chromatic Polynomials of Planar Triangulation Graphs and Implications for Chromatic Zeros and Asymptotic Limiting Quantities

Robert Shrock, Yan Xu

arxiv:1201.4200 v1 · 2012-01-20 · 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{MCTYV772PJUHR26CZ32BHRBCG7}

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	2026-05-18T03:55:35.373733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60a78afffa7a6878ebc2cef413c42237c6af6c106d57c8b749ddb24ff149ae89

Aliases

arxiv: 1201.4200 · arxiv_version: 1201.4200v1 · doi: 10.48550/arxiv.1201.4200 · pith_short_12: MCTYV772PJUH · pith_short_16: MCTYV772PJUHR26C · pith_short_8: MCTYV772

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/MCTYV772PJUHR26CZ32BHRBCG7 \
  | 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: 60a78afffa7a6878ebc2cef413c42237c6af6c106d57c8b749ddb24ff149ae89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfd0d3f4034bb54d38f07493f363e5eb78a150dfcab14a1389d8e217b7bc2bfd",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-01-20T02:52:48Z",
    "title_canon_sha256": "53005181af460e724a3822ca15ba0d89df25f993f63999d08f3346e5f745957b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.4200",
    "kind": "arxiv",
    "version": 1
  }
}