Dimensional Chess: what a lift is worth once it must carry a proof

Can lifting chess into the right state coordinates (symmetry, history, relations) give exact, independently checkable results, and can it narrow the value of the initial position?

C1 applies the theory's computational rules to a closed chess universe, where success and failure can be checked exactly; revisions 1.30–1.38 carry the series into the manuscript.

1. Independently checked

   Step 1

   What was built. C1–C2 (15 September): exact KRK and KQK solutions with a proved D4 symmetry quotient, a frozen full-chess target (FCS-2023) and an interval-dominance pruning theorem.

   What was found. Exact endgame values with independent verifiers, but the quotient by complete future laws barely compresses, and the ideal pruning numbers come from the answer itself.

   What it opens. The gap is named: cheap relational bounds that certify move deletions before a position is solved.

   • Dimensional Chess Experiment C1 Public
   • Dimensional Chess C2: Full-Chess Gate Public

2. Independently checked

   Step 2

   What was built. C3–C4: a full-move state engine (castling, en passant, promotion, repetition and move-count draws; dead-position predicate partial) passing perft, then table-hidden constraint waves on KRK and KQK.

   What was found. An exact depth-four probe leaves the root at [−1,+1]. Constraint waves prove every endgame value but keep almost one signature per state: a compressed tablebase.

   What it opens. C5 moves from compressing state to ordering search.

   • Dimensional Chess C3: Full-State and Initial-Position Probe Public
   • Dimensional Chess C4: Constraint Waves and Human-Style Search Public

3. Independently checked

   Step 3

   What was built. C5–C6: a tension heat map, then a legal exchange-dependency graph for move ordering; run R1 applies C6 to the real initial position to seven plies.

   What was found. Both cut nodes on tactical sets, though heat is no evaluation; at the initial position C6 used about 18% more nodes than lexical order. Neither side forces mate within seven plies.

   What it opens. R1's conclusion: ordering is not the wallbreaker; a sound bound on unexpanded continuations is needed.

   • Dimensional Chess C5: Tension Fields and Tactical Entry Ordering Public
   • Dimensional Chess C6: Legal Exchange Dependencies Public
   • Dimensional Chess: Initial-Position Mate Frontier R1 Public

4. Independently checked

   Step 4

   What was built. C7–C8: a horizon-safe projection dropping history coordinates that cannot matter in time, then learned movement-frequency classes to order defender moves.

   What was found. Neither side forces mate within nine plies, verified independently. Frequency ordering cut White's proof time by about 29% but failed for Black; richer variants failed outright.

   What it opens. The open problem: a learned relation that carries a sound interval or proof obligation.

   • Dimensional Chess C7: Horizon-Safe State Projection Public
   • Dimensional Chess C8: Movement-Frequency Relations Public

The next question. Can a compact, transferable abstraction carry proof-checked lower and upper bounds over many continuations, narrowing the root interval rather than reordering an exponential search?

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