Pith Number

pith:TAA3QU2B

pith:2015:TAA3QU2BEVW3OANNRS4GGYEDX7

not attested not anchored not stored refs pending

The packing chromatic number of the infinite square lattice is between 13 and 15

Barnaby Martin, Franco Raimondi, Jos Martin, Taolue Chen

arxiv:1510.02374 v3 · 2015-10-08 · cs.DM · 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{TAA3QU2BEVW3OANNRS4GGYEDX7}

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	2026-05-18T00:52:08.596266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9801b85341256db701ad8cb8636083bfda7852fb20f846869fd74e05c23f1200

Aliases

arxiv: 1510.02374 · arxiv_version: 1510.02374v3 · doi: 10.48550/arxiv.1510.02374 · pith_short_12: TAA3QU2BEVW3 · pith_short_16: TAA3QU2BEVW3OANN · pith_short_8: TAA3QU2B

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/TAA3QU2BEVW3OANNRS4GGYEDX7 \
  | 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: 9801b85341256db701ad8cb8636083bfda7852fb20f846869fd74e05c23f1200

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29c095750909f5cf6400542b4e88288e7fb6b3852ccb090adc072f9d2d7e649f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2015-10-08T15:55:02Z",
    "title_canon_sha256": "33142145f2ea8b1f5fc6e3e58a95e9a86fdfdc21aabbb29defb40de61e90f92f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02374",
    "kind": "arxiv",
    "version": 3
  }
}