Pith Number

pith:NN5AFNLL

pith:2025:NN5AFNLLJOXKL2MDGOS3LNP3OC

not attested not anchored not stored refs pending

A Constructive Proof of the Four-Color Theorem

Dagong Ding

Any planar graph can be four-colored by sequentially adding regions while preserving Property A on the outer boundary.

arxiv:2602.16996 v6 · 2025-11-19 · math.GM

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\usepackage{pith}
\pithnumber{NN5AFNLLJOXKL2MDGOS3LNP3OC}

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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.

Claims

C1strongest claim

After sequentially adding specific regions on an outer boundary satisfying Property A, the new outer boundary still satisfies Property A, ultimately allowing the entire given graph to be colored with four colors.

C2weakest assumption

That the newly introduced concepts such as primitive set, knot, valid pair group, and the three theorems correctly cover every possible planar graph configuration without gaps or unhandled cases.

C3one line summary

A constructive framework using new graph concepts and three theorems claims to prove any planar graph is four-colorable without computer checks.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:04:26.064115Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b7a02b56b4baea5e98333a5b5b5fb70aedc372b01cb9d3a20d46a0cb27b5a89

Aliases

arxiv: 2602.16996 · arxiv_version: 2602.16996v6 · doi: 10.48550/arxiv.2602.16996 · pith_short_12: NN5AFNLLJOXK · pith_short_16: NN5AFNLLJOXKL2MD · pith_short_8: NN5AFNLL

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/NN5AFNLLJOXKL2MDGOS3LNP3OC \
  | 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: 6b7a02b56b4baea5e98333a5b5b5fb70aedc372b01cb9d3a20d46a0cb27b5a89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c55564043e3162a46ac220889dcddcc4005dd4be2ceef6b55be568bcfeb2366a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2025-11-19T12:49:07Z",
    "title_canon_sha256": "33a7510feabb3d4fb6f993f05dca7ad39e35f2188c4d5f18ad7e06e822e198f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.16996",
    "kind": "arxiv",
    "version": 6
  }
}