Pith Number

pith:45UNVK4W

pith:2016:45UNVK4WBWX2CM4IRKEGNKNMLK

not attested not anchored not stored refs pending

Color groups of colorings of $N$-planar modules

Lilibeth D. Valdez, Ma. Lailani B. Walo, Manuel Joseph C. Loquias

arxiv:1609.03122 v2 · 2016-09-11 · math.MG · 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{45UNVK4WBWX2CM4IRKEGNKNMLK}

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	2026-05-18T00:46:49.091795Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e768daab960dafa133888a8866a9ac5aa21c2f7e8ea55ba330a645c8e4eb1cb7

Aliases

arxiv: 1609.03122 · arxiv_version: 1609.03122v2 · doi: 10.48550/arxiv.1609.03122 · pith_short_12: 45UNVK4WBWX2 · pith_short_16: 45UNVK4WBWX2CM4I · pith_short_8: 45UNVK4W

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/45UNVK4WBWX2CM4IRKEGNKNMLK \
  | 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: e768daab960dafa133888a8866a9ac5aa21c2f7e8ea55ba330a645c8e4eb1cb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90c0f23fe2b2a2a356ab415e97d9ba4354f5574f063203a3ec41669e7410ecf9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-09-11T06:00:58Z",
    "title_canon_sha256": "5232f46fe057a424fc0053c2de7c28679979ac6758940c4b48b169f2a2a688e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.03122",
    "kind": "arxiv",
    "version": 2
  }
}