Pith Number

pith:6N2F7GOQ

pith:2024:6N2F7GOQMBPATGQCK6ICSUCX7V

not attested not anchored not stored refs pending

Counterexamples to two conjectures on mean color numbers of graphs

Wushuang Zhai, Yan Yang

arxiv:2405.01890 v2 · 2024-05-03 · 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{6N2F7GOQMBPATGQCK6ICSUCX7V}

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	2026-07-05T08:30:12.079106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3745f99d0605e099a025790295057fd670012731b9c7e1051086db2cecccc3a

Aliases

arxiv: 2405.01890 · arxiv_version: 2405.01890v2 · doi: 10.48550/arxiv.2405.01890 · pith_short_12: 6N2F7GOQMBPA · pith_short_16: 6N2F7GOQMBPATGQC · pith_short_8: 6N2F7GOQ

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/6N2F7GOQMBPATGQCK6ICSUCX7V \
  | 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: f3745f99d0605e099a025790295057fd670012731b9c7e1051086db2cecccc3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44f73c4936b2a0d43822400064dcac789c4ad6b45d072a0e908568db7be3950c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-05-03T07:26:50Z",
    "title_canon_sha256": "9e4c1cea46daf954592573491f13a9355849a8d423feffceb7d9de0f47c614d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.01890",
    "kind": "arxiv",
    "version": 2
  }
}