Pith Number

pith:4GZCY4XM

pith:2024:4GZCY4XMBBP3TGNN77GFAGQDU5

not attested not anchored not stored refs pending

A shorter proof of the Four Colour Theorem

Carl Feghali

arxiv:2412.00172 v2 · 2024-11-29 · 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{4GZCY4XMBBP3TGNN77GFAGQDU5}

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	2026-07-05T10:04:20.191942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1b22c72ec085fb999adffcc501a03a769bc148ebd319e0f92eaec8e58fe8312

Aliases

arxiv: 2412.00172 · arxiv_version: 2412.00172v2 · doi: 10.48550/arxiv.2412.00172 · pith_short_12: 4GZCY4XMBBP3 · pith_short_16: 4GZCY4XMBBP3TGNN · pith_short_8: 4GZCY4XM

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/4GZCY4XMBBP3TGNN77GFAGQDU5 \
  | 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: e1b22c72ec085fb999adffcc501a03a769bc148ebd319e0f92eaec8e58fe8312

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e0628acac7ee3eaf7037cf6e61b9272a8ff4972be76d9085a80314f7ff1d4b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-11-29T17:40:24Z",
    "title_canon_sha256": "0419cdb92234bb2531105efdb755dd934298cbc119f8303dffb86d91bb6a1689"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.00172",
    "kind": "arxiv",
    "version": 2
  }
}