Published research successor · Combinatorial game theory · Domineering · thermographs · exact finite computation

Berlekamp’s Domineering-Temperature Conjecture

Research update

Lech Mazur's manuscript gives a rectangle-reachable 28-cell Domineering position with exact game {17/8 | -2+*} and temperature 33/16 > 2. The attached Lean development kernel-checks the board–target equality, explicit target thermograph, 30-move replay, and resulting existential statement through its narrow HasValueTemperature interface; unrelated external replication and specialist review remain open.

G (B') = {\frac{17}{8} ∣ - 2 + *}, t (G (B')) = \frac{33}{16} > 2, μ (G (B')) = \frac{1}{16}

Public versionAug 14, 2026

Formal evidenceScoped Lean theorem

Review boundarySpecialist review remains open

Open the current paper, Lean artifact, and sources This reader view supersedes the earlier collaboration snapshot without rewriting its provenance.

A manuscript and scoped Lean artifact give a rectangle-reachable 28-cell Domineering position left after 30 moves on an 11 × 8 board, with exact temperature 33/16 > 2.

Current mathematical release

The rectangle-reachable 28-cell witness

Lean-checked rectangle-reachable witness at 33/16. The explicit rectangle-reachable witness moves the finite frontier above 2; how high Domineering temperatures can be and whether an infinite hotter family exists remain open.

Exact formal boundary

Lean checks the exact existential theorem through the development's narrow HasValueTemperature interface. General thermograph invariance, unrelated reproduction, specialist review, and historical priority remain outside this release.

What ProofAtlas connected

The August 14 paper, exact 30-move replay, checked Lean statement, finite certificate, public source bundle, and visual explanation are connected at one stable reader route.

A dark mathematical infographic shows the complete 30-move replay on an 11 by 8 Domineering board: odd cyan vertical dominoes and even coral horizontal dominoes leave the exact 28-cell rectangle-reachable witness, whose value is {17/8 | -2+*} and temperature is 33/16. — The rectangle-reachable 28-cell witness B′, all 30 moves that produce it, the value-preserving two-cell repair of the 26-cell core, and the Lean-checked temperature 33/16.

Read the canonical research page

What remains outside this release

Checked scope is not broader acceptance

BoundaryThis update does not record independent ProofAtlas acceptance or specialist peer review of the mathematical result.

BoundaryThe Lean theorem uses the stated HasValueTemperature witness interface; it does not include a general theorem that thermographs are invariant under every game-equivalence presentation.

BoundaryThe bundled Python audits and Lean development were coordinated in the author-directed workflow and are not unrelated external replication.

BoundaryThe Lean theorem does not formalize the one-cell deletion audit or separately formalize the checkerboard unreachability of the raw 26-cell core B.

BoundaryThe one-square deletion audit does not establish global size minimality or uniqueness.

BoundaryThe 26-cell board B and the rectangle-reachable 28-cell witness B′ are distinct positions and must not be conflated.

BoundaryProofAtlas has not independently established historical priority.

BoundaryThe infographic is an explanatory rendering; the coordinate replay and checked source are the evidence.

Continue the mathematics

Independent replication and the hotter-family frontier remain open

The earlier 26-cell computation remains retained as the core inside the current 28-cell rectangle-reachable construction. The canonical research page carries the exact paper, Lean scope, source bundle, and review boundaries.

Continue from the current release