Pith Number

pith:FWBGFFMQ

pith:2026:FWBGFFMQAGXMOOGNADHLWW3NVJ

not attested not anchored not stored refs pending

Sharp bounds for the fractional chromatic number of high-girth $d$-degenerate graphs

Abhishek Dhawan, Jonathan A. Noel, Peter Allen

arxiv:2607.26271 v1 · 2026-07-28 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FWBGFFMQAGXMOOGNADHLWW3NVJ}

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	2026-07-30T01:17:53.156973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

2d8262959001aec738cd00cebb5b6daa5796b42e4f5be15467d26d9e130ec892

Aliases

arxiv: 2607.26271 · arxiv_version: 2607.26271v1 · doi: 10.48550/arxiv.2607.26271 · pith_short_12: FWBGFFMQAGXM · pith_short_16: FWBGFFMQAGXMOOGN · pith_short_8: FWBGFFMQ

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/FWBGFFMQAGXMOOGNADHLWW3NVJ \
  | 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: 2d8262959001aec738cd00cebb5b6daa5796b42e4f5be15467d26d9e130ec892

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a42d4f6836868c89d36c1c7a0c1adc3983af391fc9c846f87e88503ecae1be9c",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-28T21:02:45Z",
    "title_canon_sha256": "2f70d37eca3d389d38a2282cb34b1da27b06091143f7a6fc1157906b1aade37d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26271",
    "kind": "arxiv",
    "version": 1
  }
}