Pith Number

pith:MC7MZ2RJ

pith:2026:MC7MZ2RJVZV5TSNVHE2E7BLMKJ

not attested not anchored not stored refs pending

Improved bounds on the b-chromatic number using the independence and chromatic numbers

Manouchehr Zaker

arxiv:2606.07461 v1 · 2026-06-05 · 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{MC7MZ2RJVZV5TSNVHE2E7BLMKJ}

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	2026-06-08T01:05:28.403002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60beccea29ae6bd9c9b539344f856c526c8a4c9ac4a9f606321363d5fe0f28b0

Aliases

arxiv: 2606.07461 · arxiv_version: 2606.07461v1 · doi: 10.48550/arxiv.2606.07461 · pith_short_12: MC7MZ2RJVZV5 · pith_short_16: MC7MZ2RJVZV5TSNV · pith_short_8: MC7MZ2RJ

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/MC7MZ2RJVZV5TSNVHE2E7BLMKJ \
  | 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: 60beccea29ae6bd9c9b539344f856c526c8a4c9ac4a9f606321363d5fe0f28b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a907c2bd0e13e4344144f4a00b90166e66eb8b67b85c0a6dbb0dd553e3dd02c8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-05T17:13:10Z",
    "title_canon_sha256": "ef98044a6079cb32664a16412a2c34fc33f2a319434bf0a47eaf410a49de7743"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07461",
    "kind": "arxiv",
    "version": 1
  }
}