Pith Number

pith:HAG75B3P

pith:2012:HAG75B3P5MJID46HVRCFNMLHML

not attested not anchored not stored refs pending

Nordhaus-Gaddum Theorem for the Distinguishing Chromatic Number

Ann Trenk, Karen L. Collins

arxiv:1203.5765 v1 · 2012-03-26 · math.CO · cs.DM · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HAG75B3P5MJID46HVRCFNMLHML}

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	2026-05-18T03:59:14.302723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

380dfe876feb1281f3c7ac4456b16762f33a4bbd9e4942a397d420047fbd7d38

Aliases

arxiv: 1203.5765 · arxiv_version: 1203.5765v1 · doi: 10.48550/arxiv.1203.5765 · pith_short_12: HAG75B3P5MJI · pith_short_16: HAG75B3P5MJID46H · pith_short_8: HAG75B3P

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/HAG75B3P5MJID46HVRCFNMLHML \
  | 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: 380dfe876feb1281f3c7ac4456b16762f33a4bbd9e4942a397d420047fbd7d38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "792aef2ee5a7aef6668412b67e3e3d0a0a9dcbf01ef5223f80eba55cd1402e8b",
    "cross_cats_sorted": [
      "cs.DM",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-26T19:29:01Z",
    "title_canon_sha256": "fa6196ed7ea8e52f3894ab9294c25ca6cdb4d85f5222e17f38983bb7bec2b21f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5765",
    "kind": "arxiv",
    "version": 1
  }
}