Preview: arena knowledge distilled into the browser · September 2026
Proof Coach now keeps a verified candidate state separate from player notes and can expose P0–P3 deductions: naked/hidden singles, pointing/claiming, naked pairs, X-Wing and XY-Wing. Elimination hints change only the coach state; they never silently alter the player grid.
Game Review evaluates each entered value from the state before the move. A correct move is only called logically verified when a proof is actually found; otherwise it remains UNKNOWN_REASONING. Wrong-answer checking is kept separate and uses the certified unique puzzle solution.
This is a product preview at /S/new/. The current /S/ game remains untouched until manual review.
New: R6 HF3 HF1 research arena · September 2026
The Python arena now combines multiple Sudoku representations, independently checked proofs,
Proof Atlas memory and resumable experiments. Its new causal study separates MDL prediction,
DCC allocation and learned transfer, with seeded MRV and Luby restarts as strong comparisons.
This browser game continues to use Logic/Trace v1.2 RC7. The R6 arena is a separate research program;
its specialists are being evaluated before browser integration. The current experiment has not yet established an MDL- or DCC-specific advantage.
Explore the new arena, solving logic and evidence ↗
Phase 1 — Founding Hypothesis Confirmed · ρ = 0.85
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March 25, 2026 · AIM³ Lab · 200 puzzles × 5 strategies = 1000 solve logs
ρ = 0.85
Smarter algorithm → more compressible solving process. Same kernel, different domain. TSP ρ = 0.80 on geometry. Sudoku ρ = 0.85 on constraint satisfaction. The kernel is domain-independent — because it works on a different alphabet.
Per-strategy averages (seed99, 200 puzzles):
| Strategy | Steps | BT | Guesses | LZproc | Gini | Casc.Wt |
|---|
| random | 6419 | 3200 | 3218 | 1.020 | 0.000 | low |
| mrv | 282 | 116 | 166 | 0.957 | 0.000 | low |
| naked | 339 | 19 | 23 | 0.455 | 0.971 | high |
| full | 59 | 0.6 | 1.3 | 0.411 | 0.975 | high |
| human | 62 | 0.5 | 1.1 | 0.388 | 0.976 | high |
Top sensors by |ρ|(strategy_rank, sensor):
| # | Sensor | |ρ| |
|---|
| 1 | n_guesses | 0.853 |
| 2 | cascade_weighted | 0.839 |
| 3 | gini_cascade | 0.829 |
| 4 | LZ_multi |Σ|=4 | 0.805 |
| 5 | LZ_process | 0.786 |
| 6 | density_flow | 0.762 |
| 7 | LZ_cascade | 0.741 |
| 8 | n_backtracks | 0.716 |
12 of 14 sensors |ρ| > 0.3. Eight above |ρ| > 0.7. LZ_process flipped from ρ = +0.09 (Phase 0, measuring problem difficulty) to ρ = −0.786 (Phase 1, measuring algorithm quality). Exactly as predicted: the real test is different algorithms on the same problem.
Origin Story — one afternoon, one question, one answer
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March 23, 2026 · AIM³ Lab · Ljubljana
310
lines of code. That's the entire engine — puzzle generator, backtracking solver with snapshot-based state restoration, live metrics, AI animation, keyboard shortcuts, notes mode, undo history, and the ADSR measurement system. Not 310 lines for the game loop. 310 lines for everything.
The question that started it: does the same MDL kernel that finds optimal TSP tours — the one that navigates 3,496 cities in Nicaragua — also work on constraint satisfaction? In TSP, the founding insight was simple: the shortest route has the most structured search process (Spearman ρ = +0.80, verified on official Waterloo benchmarks). In Sudoku, the question becomes: do easier puzzles have more structured solving processes?
We built a backtracking solver with full process logging. Ran it on 1,000 puzzles across four difficulty levels. Measured ADSR bimodality — whether the solving process cleanly separates into cascading chain-reactions and isolated single-placements.
Result: ρ = −0.50 (p < 10⁻⁶⁴). Easier puzzles score higher. Evil puzzles drop below 0.95. The same principle that guides the TSP solver through a combinatorial space of 101783 possible tours also predicts how hard a Sudoku puzzle is. One kernel. One afternoon. Third domain confirmed.
What the sensors are actually measuring
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Phase 1 winning sensors · live metrics
Every Sudoku app solves puzzles. This is the only one that watches itself solve and shows you the structure of what it sees.
LZ Complexity (ρ = −0.79) — Lempel-Ziv compression of the entropy-delta sequence. Each step changes the grid's uncertainty by some amount. We encode these changes as a binary string (above/below median) and compress it. Lower = the process is more structured. A smart solver produces highly compressible patterns — it finds the same lever and pulls it repeatedly.
Gini Cascade (ρ = +0.83) — Inequality of cascade depths. When a smart solver places a digit, it triggers chain reactions — one move resolves 5, 10, 15 more cells. The Gini coefficient measures how unequal these cascades are: a few deep ones + many zeros = high Gini = structured solving. Random has Gini = 0 (no cascades at all).
Cascade Power (ρ = +0.84) — Weighted cascade strength: depth × entropy-delta for each step. Higher = the steps that trigger cascades are more informative. The best solvers make moves that ripple far and reduce a lot of uncertainty each time.
Density Flow (ρ = −0.76) — Smoothness of candidate-count reduction over the solving process. A structured solver drains candidates steadily. A random solver has a jagged, chaotic descent. We measure this with LZ compression on the candidate flow — lower = smoother = better.
ADSR (ρ = −0.12 on Phase 1) — Attack-Decay-Sustain-Release bimodality. This was the Phase 0 winner (ρ = −0.50 for problem difficulty) but is weak for algorithm quality. It measures problem structure, not solver intelligence. Kept as context.
How to play
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Quick guide
Select a cell by clicking or tapping. Highlighted cells share a row, column, or box with your selection.
Place a number using the numpad below the grid, or press 1–9 on your keyboard. Click the same number again to clear it. Arrow keys move the selection.
Notes mode — toggle with the Notes button or press N. Numbers become small pencil marks — candidates you're considering.
Undo with the button or Ctrl+Z. Erase with button or Backspace.
💡 Hint — first checks whether your entered values contradict the unique solution. If so, it highlights all wrong entries and jumps to the most recently changed one. Otherwise it highlights the next logical cell and explains why. It never places the number.
AI Solve — select a strategy, watch the solving process animated. Green = naked single. Blue = hidden single. Violet = pointing pair. Orange = guess. Red = backtrack. Step through one move at a time.
⚡ Compare All — runs all 5 strategies on the current puzzle and shows a comparison table with steps, backtracks, and sensor readings.
Difficulty: Easy has 36–42 given digits and solves with pure logic. Evil has only 20–23 — watch the sensors diverge.
Investor Snapshot — why this is more than commodity Sudoku
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Companion page · monetization lens
This is not just a Sudoku skin. The real asset is the engine that shows how a puzzle is solved: path of play, strategy choice, cascade structure, stability, and low-entropy decision flow. The teaching effect is part of the product, not decoration.
The monetization logic is therefore broader than ads alone: free reach, premium coaching and explainable hints, advanced compare/replay features, subscription as reasoning training, and possible licensing into education, brain-training, or explainable decision products.
Open the investor brief ↗
Less describes more.