Pith Number

pith:TA2TKDHV

pith:2018:TA2TKDHVA4KCUEOL4HABG5HZHJ

not attested not anchored not stored refs pending

The chromatic number of the plane is at least 5 - a new proof

Dan Ismailescu, Geoffrey Exoo

arxiv:1805.00157 v1 · 2018-05-01 · 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{TA2TKDHVA4KCUEOL4HABG5HZHJ}

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	2026-05-18T00:17:10.426429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9835350cf507142a11cbe1c01374f93a47bded229eb1fdfd32ca37ea15284134

Aliases

arxiv: 1805.00157 · arxiv_version: 1805.00157v1 · doi: 10.48550/arxiv.1805.00157 · pith_short_12: TA2TKDHVA4KC · pith_short_16: TA2TKDHVA4KCUEOL · pith_short_8: TA2TKDHV

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/TA2TKDHVA4KCUEOL4HABG5HZHJ \
  | 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: 9835350cf507142a11cbe1c01374f93a47bded229eb1fdfd32ca37ea15284134

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d2c7411a1dd913446630f063649b8a91182c8eb2b5cf932c00b2f1bfd00200f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-05-01T02:30:54Z",
    "title_canon_sha256": "f7ba30e23229c2de95d016360ec40082b9647270dfe138091a075caa65659a48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.00157",
    "kind": "arxiv",
    "version": 1
  }
}