Pith Number

pith:WIY3WIQQ

pith:2010:WIY3WIQQLB7CP5JGUEWPPIUFKK

not attested not anchored not stored refs pending

Improved bounds on coloring of graphs

Aldo Procacci, Benedetto Scoppola, Sokol Ndreca

arxiv:1005.1875 v2 · 2010-05-11 · 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{WIY3WIQQLB7CP5JGUEWPPIUFKK}

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	2026-05-18T04:06:56.896998Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b231bb2210587e27f526a12cf7a285529fe0bf65fdb557b1591a396de6db690a

Aliases

arxiv: 1005.1875 · arxiv_version: 1005.1875v2 · doi: 10.48550/arxiv.1005.1875 · pith_short_12: WIY3WIQQLB7C · pith_short_16: WIY3WIQQLB7CP5JG · pith_short_8: WIY3WIQQ

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/WIY3WIQQLB7CP5JGUEWPPIUFKK \
  | 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: b231bb2210587e27f526a12cf7a285529fe0bf65fdb557b1591a396de6db690a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48b74eded966e7b8421a0af5aa829f5c333d737d73a6740fb4bea2942cc6d519",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-05-11T16:05:46Z",
    "title_canon_sha256": "caaa94b66ac90050cb49af246357e4f7d70bb0da52d520c7c1a1bbb2c7f1af59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.1875",
    "kind": "arxiv",
    "version": 2
  }
}