Pith Number

pith:72FOPNGD

pith:2011:72FOPNGDGFA72Z6P44K5UNC3RN

not attested not anchored not stored refs pending

Chromatic Polynomials of Planar Triangulations, the Tutte Upper Bound, and Chromatic Zeros

Robert Shrock, Yan Xu

arxiv:1110.5883 v1 · 2011-10-26 · 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{72FOPNGDGFA72Z6P44K5UNC3RN}

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	2026-05-18T04:04:15.030038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe8ae7b4c33141fd67cfe715da345b8b6ec403a1cac20a99a29ede14385c58e9

Aliases

arxiv: 1110.5883 · arxiv_version: 1110.5883v1 · doi: 10.48550/arxiv.1110.5883 · pith_short_12: 72FOPNGDGFA7 · pith_short_16: 72FOPNGDGFA72Z6P · pith_short_8: 72FOPNGD

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/72FOPNGDGFA72Z6P44K5UNC3RN \
  | 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: fe8ae7b4c33141fd67cfe715da345b8b6ec403a1cac20a99a29ede14385c58e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3328bac9d45ccac00fbb6ddbfe34f822edefd56f861c0ae16e182e676810b1c1",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-10-26T19:14:42Z",
    "title_canon_sha256": "935a29103c96580158f36889d51e3655aa71206ecbc253a9f105daf6fb431940"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5883",
    "kind": "arxiv",
    "version": 1
  }
}