Pith Number

pith:DKVRJLAW

pith:2026:DKVRJLAWRHFMBYX6APQIDSMSEQ

not attested not anchored not stored refs pending

Breaking the $2^n$ barrier for graph $k$-coloring

Kevin Pratt

arxiv:2607.27159 v1 · 2026-07-29 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DKVRJLAWRHFMBYX6APQIDSMSEQ}

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	2026-07-30T01:23:54.741427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

1aab14ac1689cac0e2fe03e081c99224086eed1c45d7318902cbf8a46c2a63ce

Aliases

arxiv: 2607.27159 · arxiv_version: 2607.27159v1 · doi: 10.48550/arxiv.2607.27159 · pith_short_12: DKVRJLAWRHFM · pith_short_16: DKVRJLAWRHFMBYX6 · pith_short_8: DKVRJLAW

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/DKVRJLAWRHFMBYX6APQIDSMSEQ \
  | 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: 1aab14ac1689cac0e2fe03e081c99224086eed1c45d7318902cbf8a46c2a63ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0347c6e4a95b57821b1359fee49426fde83356e743d2b11ecd93ac7cc484ca5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-07-29T17:36:11Z",
    "title_canon_sha256": "f3c40e1529734a56ab599e58c95fba10e7dae3049ddd96d9254969ae774b77b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27159",
    "kind": "arxiv",
    "version": 1
  }
}