Each arena follows the same pattern:
problem → trace → encoding → MDL sensors → null controls → DCC search/governance → invariant target → practical output or proof bridge
Problems where the endpoint is a formal invariant, theorem, or proof bridge. Clay Millennium problems belong here.
Competitions and open benchmarks with clear scoring: ARC, Hutter, SAT/SMT/PACE, CASP, DREAM, MLPerf, Kaggle-like arenas.
Domains where value comes from working solutions now: TSP/trips, routing, compression, trading, drug discovery, protein folding, cyber, logistics.
All seven Clay problems mapped into signal arenas. RH is active through prime-gap compression; Poincare now has a v0.2 positive-control result showing structure-preserving simplification across 550 cases.
Open millennium arena →Prime gaps, wheel/Markov controls, scaling tests, and the search for a formal prime-distribution invariant.
Open RH arena →Not a claim of formal P=NP. The practical question: how much of the real problem universe is structurally compressible enough to become governable?
Future page →Use the solved case as a calibration mirror. v0.2: 550 cases, 0 DCC invariant violations, 0 path breaks, 0 false sphere classifications; DCC-beam beats MDL-only in hard 2D and full-grid regimes.
Open Poincare arena →Program synthesis as shortest explanatory rule. Active private ARC-AGI × MDLxDCC arena with dynamic primitives, category routing, family filters, workers, LOO, and failure mining.
Open ARC arena →Compression as intelligence. Natural home for 8Z/MDL generators and DCC codec switching.
Future page →Solver traces, restarts, clause-learning motifs, hardness signatures, and practical tractability maps.
Future page →Sequence-to-structure traces, contact maps, folding motifs, and the DNA/RNA scanner transfer path.
Future page →Omics, biomarkers, drug response, disease subtypes, and biological predictor governance under strong null controls.
Future page →Wildfire, water, carbon removal, quantum applications, healthspan, and other real-world DCC governance arenas.
Future page →Fast, good-enough JavaScript route optimization in the browser. The practical value is deployment: local, private, cheap, no heavy server.
Portfolio / app context →High-Z biological sequence signals show that MDLxDCC can detect hidden mathematical order in natural sequence data.
DNA paper →Abstract resistance-control simulation. Interim result: all viable complete strategies contain WEAKEN_ESCAPED; current robust winner is combo__weaken_escaped__freeze_dim; DCC basic failure exposes the next selector patch.
Search spaces become steerable when architecture traces reveal compressible structure.
Domain map →Images, audio, FASTA/genomics, and other formats demonstrate MDL as shorter description of real structure.
Domain map →Decision quality, elegance, and constraint satisfaction can be governed through compressibility and DCC scoring.
Sudoku →Market traces, lead-lag structure, and semantic inversion across DCC layers: same sensor, different action depending on governance level.
Domain map →Natural next life-science arenas: sequence-to-structure, contact maps, molecule search, biological null ladders.
Future protein arena →Fleet governance, traffic engineering, scheduling, resource allocation, and regime switching across large infrastructure systems.
Domain map →| Arena | Status | First useful experiment | Canonical page name |
|---|---|---|---|
| Grand Challenge hub | active | Maintain all arenas and statuses | MDLxDCC-Arenas.html |
| Clay Millennium | deep dive | Formal signal maps for all 7 problems | MDLxDCC-Arena-Millennium.html |
| RH / prime gaps | active | LZ76 + wheel/Markov/Cramér + scaling | MDLxDCC-Arena-RH.html |
| P vs NP | designed | SAT/TSP/NAS practical tractability traces | MDLxDCC-arena-p-vs-np.html |
| Poincare | v0.2 positive-control PASS | 550-case structure-preserving simplification calibration; DCC-beam vs MDL-only; 0 false sphere | MDLxDCC-Arena-Poincare.html |
| ARC-AGI × MDLxDCC | active private prototype | Dynamic primitive arena; v0.4 partial: category/family routing signal, natural-law primitives, failure mining | MDLxDCC-Arena-ARC.html |
| Hutter Prize | ready | Compression-intelligence benchmark | MDLxDCC-arena-hutter.html |
| SAT/SMT/PACE | ready | Solver-trace compression / hardness signatures | MDLxDCC-arena-sat-smt-pace.html |
| CASP / protein | designed | DNA scanner → protein sequence / contact map | MDLxDCC-arena-casp-protein.html |
| AMR strategy control | interim active | 64,800-task abstract strategy sweep; current signal: WEAKEN_ESCAPED kernel and DCC selector patch target | MDLxDCC-Arena-AMR.html |
| DREAM / biomedicine | designed | Omics / biomarkers / drug response | MDLxDCC-arena-dream-bio.html |
| XPRIZE | future | Applied DCC governance challenges | MDLxDCC-arena-xprize.html |
Use a single prefix for every problem-specific page:
MDLxDCC-arena-[short-name].html
Keep MDLxDCC.html as the kernel/domain-map page. Use MDLxDCC-Arenas.html as the execution hub. Every deeper page gets the MDLxDCC-arena- prefix.