Pith Number

pith:A6IQPH4M

pith:2014:A6IQPH4MJFUZXXINYL2ET2I2XH

not attested not anchored not stored refs pending

The Sum and Product of Chromatic Numbers of Graphs and their Line Graphs

Sunny Joseph Kalayathankal, Susanth C

arxiv:1404.1698 v2 · 2014-04-07 · 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{A6IQPH4MJFUZXXINYL2ET2I2XH}

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	2026-05-18T02:42:25.823157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0791079f8c49699bdd0dc2f449e91ab9c6744b5c3f08dd5f8af7f9ec5d47416c

Aliases

arxiv: 1404.1698 · arxiv_version: 1404.1698v2 · doi: 10.48550/arxiv.1404.1698 · pith_short_12: A6IQPH4MJFUZ · pith_short_16: A6IQPH4MJFUZXXIN · pith_short_8: A6IQPH4M

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/A6IQPH4MJFUZXXINYL2ET2I2XH \
  | 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: 0791079f8c49699bdd0dc2f449e91ab9c6744b5c3f08dd5f8af7f9ec5d47416c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ba032f16a916943bc983da540fc544837097279e52f60ee4b22d426722cd627",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-04-07T08:59:57Z",
    "title_canon_sha256": "054daf099f1f38f1b62764b35bdde316f2300f73e2b04fc3f90e4ff3838bf43b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.1698",
    "kind": "arxiv",
    "version": 2
  }
}