Pith Number

pith:LHWMUJK7

pith:2010:LHWMUJK7GPXW73CZRXZP4UPE4G

not attested not anchored not stored refs pending

On some upper bounds on the fractional chromatic number of weighted graphs

Ashwin Ganesan

arxiv:1001.3053 v4 · 2010-01-18 · cs.IT · math.CO · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LHWMUJK7GPXW73CZRXZP4UPE4G}

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	2026-05-18T04:01:26.629058Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59ecca255f33ef6fec598df2fe51e4e1b3939cf436517fd932c7289ebb38f785

Aliases

arxiv: 1001.3053 · arxiv_version: 1001.3053v4 · doi: 10.48550/arxiv.1001.3053 · pith_short_12: LHWMUJK7GPXW · pith_short_16: LHWMUJK7GPXW73CZ · pith_short_8: LHWMUJK7

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/LHWMUJK7GPXW73CZRXZP4UPE4G \
  | 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: 59ecca255f33ef6fec598df2fe51e4e1b3939cf436517fd932c7289ebb38f785

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67e5f9ffba6f29606ed66a6b8c277b23a318af3a4469f45510edbbd24e6de6a5",
    "cross_cats_sorted": [
      "math.CO",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2010-01-18T13:21:04Z",
    "title_canon_sha256": "9ac3c4aac2d4746cf09c8ddc74150df1230ac14d358bf429be355092a694748b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.3053",
    "kind": "arxiv",
    "version": 4
  }
}