Pith Number

pith:F46TKG3F

pith:2026:F46TKG3FLQ2QXSA4QLXPVZUN64

not attested not anchored not stored refs pending

Graph k-Coloring in Average Sublinear Time

Asaf Shapira, Cassandra Marcussen, Edward Pyne, Ronitt Rubinfeld, Shlomo Tauber

arxiv:2607.26592 v1 · 2026-07-29 · cs.DS · cs.CC · 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{F46TKG3FLQ2QXSA4QLXPVZUN64}

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	2026-07-30T01:21:26.128893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

2f3d351b655c350bc81c82eefae68df7265ebf50ea3d95db39827124021c201e

Aliases

arxiv: 2607.26592 · arxiv_version: 2607.26592v1 · doi: 10.48550/arxiv.2607.26592 · pith_short_12: F46TKG3FLQ2Q · pith_short_16: F46TKG3FLQ2QXSA4 · pith_short_8: F46TKG3F

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/F46TKG3FLQ2QXSA4QLXPVZUN64 \
  | 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: 2f3d351b655c350bc81c82eefae68df7265ebf50ea3d95db39827124021c201e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "912441f60887544559b02200bdbc6784908b5a6e8ec1b08f2d51370b9d5fc718",
    "cross_cats_sorted": [
      "cs.CC",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-07-29T08:13:43Z",
    "title_canon_sha256": "fa93970403c82b9b4885b330480812d107ae5dc2c28940bfc4bff2e10bfe7c22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26592",
    "kind": "arxiv",
    "version": 1
  }
}