Pith Number

pith:APUNC4SN

pith:2010:APUNC4SNG6SJLMLNEMHWE37SHB

not attested not anchored not stored refs pending

The Fractional Chromatic Number of Triangle-free Graphs with $\Delta\leq 3$

Linyuan Lu, Xing Peng

arxiv:1011.2500 v2 · 2010-11-10 · 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{APUNC4SNG6SJLMLNEMHWE37SHB}

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	2026-05-18T03:50:11.083442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03e8d1724d37a495b16d230f626ff238436ab62e53045258243d8fa6816e47d1

Aliases

arxiv: 1011.2500 · arxiv_version: 1011.2500v2 · doi: 10.48550/arxiv.1011.2500 · pith_short_12: APUNC4SNG6SJ · pith_short_16: APUNC4SNG6SJLMLN · pith_short_8: APUNC4SN

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/APUNC4SNG6SJLMLNEMHWE37SHB \
  | 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: 03e8d1724d37a495b16d230f626ff238436ab62e53045258243d8fa6816e47d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f10035d5636f4d09f07b966e2769cfa2e1e589adcc2a198e19ebeea090cb6257",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-10T21:02:26Z",
    "title_canon_sha256": "c32fa3efefc47e7bccefe66653e354c58b1a8d84a754e53d82ad695776c7fe68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2500",
    "kind": "arxiv",
    "version": 2
  }
}