plurigrid Nashator
Open games DSL → PyTorch Nash equilibrium. GF(3) conservation enforced.
Trit: 0 (ERGODIC - Coordinator) Color: #26D826
Architecture
┌─────────────────┐
Game DSL ─│ Nashator TS │── nashator_solve (OpenClaw tool)
│ (index.ts) │── nashator_compose
│ seq/par/game │── nashator_gf3_check
└────────┬────────┘── nashator_games
│
┌──────▼──────┐
│ Solver │
│ Local: JS │── fictitious play (2-player normal form)
│ Remote: Py │── PyTorch gradient Nash (continuous)
└──────┬───────┘
│
┌──────▼──────────┐
│ pytorch_backend │── HTTP :8001 on dgx-spark
│ torch.autograd │── Adam optimizer on deviation loss
│ CUDA if avail │── GPU-accelerated for large games
└─────────────────┘
Standard Games
| Game | Players | Type | GF(3) | Category |
|---|---|---|---|---|
| prisoners_dilemma | 2 | normal_form | 0 | classic |
| matching_pennies | 2 | zero_sum | 0 | classic |
| coordination | 2 | normal_form | 0 | classic |
| eip1559 | 3 | mechanism_design | 0 | defi |
| cybernetic_loop | 3 | sequential | 0 | cybernetic |
| market | 2 | parallel | 0 | defi |
Phyllotaxis Games (Succulents)
| Game | Players | Type | GF(3) | Category |
|---|---|---|---|---|
| leafLightCompetition | 2 (leaf, neighbor) | zero_sum | 0 | phyllotaxis |
| auxinCompetition | 2 (primordium, inhibitor) | mechanism_design | 0 | phyllotaxis |
| rosetteLifecycle | 2 per phase | sequential | 0 | phyllotaxis |
MAC Address / Network Forensics Games (NEW 2026-02-13)
| Game | Players | Type | GF(3) | Category |
|---|---|---|---|---|
| device_classification | N OUI classes | mechanism_design | 0 | forensics |
| arp_spoofing_detection | 2 (spoofer, monitor) | stackelberg | 0 | forensics |
| network_coloring | N devices | coordination | 0 | forensics |
MAC → Color pipeline: Gay.jl SplitMix64 seed from MAC address → Nashator solves optimal gamut region per OUI class → basin-hedges ParaLens evaluates perceptual distance → Goblins CapTP distributes color identity as capability reference.
Example: 50:BB:B5:4D:BD:04 (AzureWave/gaym) → seed 88767130877188 → #DD794F
burnt orange, GF(3) PLUS (+1). The 9-color palette is 3/3/3 GF(3) balanced.
Wire: RPC server :9999 (JSON-RPC 2.0, 4-byte BE framing) is wire-compatible with
zig-syrup message_frame.zig and Goblins rosette-captp-bridge.scm.
Botnet Attack/Defense Games
| Game | Players | Type | GF(3) | Category |
|---|---|---|---|---|
| botnet_propagation | 2 (Attacker 4-strat, Defender 4-strat) | stackelberg | 0 | botnet |
| dga_cat_and_mouse | 2 (DGA Operator 3-strat, DNS Defender 4-strat) | zero_sum | 0 | botnet |
| blockchain_c2_defense | 2 (C2 Operator 3-strat, Chain Defender 3-strat) | mechanism_design | 0 | botnet |
| botnet_lifecycle | 2 | sequential_composition | 0 | botnet |
| operation_endgame | 2 | sequential_composition | 0 | disruption |
Computed Equilibria (Fictitious Play, 5000 iterations)
Botnet Propagation: Attacker → scan 41% / exploit 19% / persist 22% / exfil 18%. Defender → detect 30% / patch 18% / sinkhole 21% / isolate 31%.
DGA Cat-and-Mouse: Attacker → high-entropy 17% / dict-DGA 17% / hybrid 66%. Defender → entropy 5% / ML 11% / LLM 73% / blocklist 11%. LLM detection dominates.
Blockchain C2: Operator → update 42% / mix-fund 29% / alt-RPC 29%. Defender → monitor 43% / trace 30% / block-RPC 27%.
Operation Endgame Phase 1: LEA → sinkhole 43% / seize 27% / BGP-null 30%. Operator → migrate 49% / rebuild 28% / fragment 23%. Defender payoff +0.56.
Operation Endgame Phase 2: Prosecutors → charge 44% / defer 56%. Customers → cooperate 35% / deny 65%.
Operation Endgame Phase 3: LEA → charge 39% / defer 61%. Operators → cooperate 31% / deny 69%.
Congressional Trading Games ("Mother")
| Game | Players | Type | GF(3) | Category |
|---|---|---|---|---|
| mother_congress_trading | 3 (Mother 4-strat, Retail 3-strat, MM 3-strat) | information_asymmetry | 0 | congress |
| congress_trading_lifecycle | 2 per phase | sequential_composition | 0 | congress |
Mother(-1) + Retail(0) + MarketMaker(+1) = 0
Lifecycle: InformedTrading ; Disclosure ; CopyTradeCascade
Latest trades (Jan 16 2026): AB $1-5M, GOOGL $500K-1M, AMZN $500K-1M, NVDA $250-500K, TEM $50-100K
Proof Exploratorium
SvelteKit app at nashator/exploratorium/:
- 24 proofs from 13 Lean files (39 proved / 83 sorry of 122 total)
- Triad ranking: show 3, assign gold/silver/bronze, Elo update
- Leaderboard: cumulative proof quality rankings
- All Proofs: filterable/sortable catalog
Top compact proofs (compactness = proof_lines / statement_lines):
unworld_balanced: 0.33 —exact ⟨rfl, rfl, rfl⟩coalgebra_hom_compose: 0.33 —exact ⟨comp g f, fun _ => rfl⟩causality_transitive: 0.50 —unfold; intro; omega
HEVM Bridge (NEW 2026-02-13)
OGE×HEVM integration inspired by 20squares blog (Videla & Zahn, 2025-05-21).
Nashator TS DSL ─→ Solidity contracts ─→ Foundry (--ast) ─→ OGE×HEVM
│ │ │
fictitious play BotnetGame.sol $(loadFoundry ".") + hevmDecision
propagator net EIP1559Game.sol real EVM payoffs via balance reads
GF(3) check foundry.toml compareModelVsContract
Two directions:
- Model → Contract: validate implementation matches intended game
- Contract → Model: extract payoff matrix from unknown contracts
Key files: hevm-bridge/NashatorHEVM.hs, hevm-bridge/contracts/{BotnetGame,EIP1559Game}.sol
CapTP oracle: ^hevm-oracle-actor serves HEVM payoff evaluations to Goblins propagator network
Files
nashator/
├── package.json @plurigrid/nashator v0.1.0
├── openclaw.plugin.json OpenClaw extension config
├── index.ts 4 tools: solve, compose, gf3_check, games
├── launch_pytorch.sh Deploy to dgx-spark
├── nashator-captp.zig Zig SIMD solver + C ABI (botnet games included)
├── nashator-goblins.scm Goblins actors: games/solver/gf3/compose
├── src/
│ ├── types.ts OpenGame, GameExpr, NashResult, Trit
│ ├── gf3.ts GF(3) arithmetic + conservation
│ ├── dsl.ts game(), seq(), par(), standard library + botnet + phyllotaxis
│ ├── solver.ts 3-tier: PyTorch → Propagator → Fictitious play
│ ├── propagator.ts SDF Ch7 cells+propagators, temperature annealing (33/33 tests)
│ ├── propagator.test.ts Comprehensive test suite
│ ├── stress-games.ts Phyllotaxis: leafLight, auxin, rosette games
│ ├── stress-games.test.ts 4 phyllotaxis tests passing
│ ├── rpc-server.ts ✅ TCP :9999, JSON-RPC 2.0, 4-byte BE framing
│ └── pytorch_backend.py HTTP :8001, gradient Nash via autograd
├── hevm-bridge/
│ ├── NashatorHEVM.hs Haskell bridge: Nashator types → OGE + HEVM
│ ├── foundry.toml Foundry config (ast=true, solc 0.8.26)
│ └── contracts/
│ ├── BotnetGame.sol 4×4 attacker/defender on-chain payoffs
│ └── EIP1559Game.sol 3-player base fee mechanism game
├── zig-core/ 9 Zig modules (solver, game types, SIMD)
├── hs-bridge/ 8 Haskell bridge files
├── cybercat-oge/ 24 files (CyberCat open games)
├── botnet-solver 13.3 MB compiled Haskell executable
└── exploratorium/
└── src/routes/ SvelteKit proof ranking app
GF(3) Triads
open-games (0) ⊗ nashator (0) ⊗ cybernetic-open-game (0) — all coordinators
aptos-agent (-1) ⊗ nashator (0) ⊗ eip1559-game (+1) = 0 ✓
cats-for-ai (0) ⊗ nashator (0) ⊗ cognitive-category (0) — ergodic triple
botnet-studies (-1) ⊗ nashator (0) ⊗ botnet-disruption (+1) = 0 ✓ [security triad]
reverse-engineering (-1) ⊗ nashator (0) ⊗ agent-o-rama (+1) = 0 ✓ [analysis→equilibrium→action]
References
- Ghani, Hedges et al. "Compositional Game Theory" (2018)
- Capucci & Gavranović, "Actegories for Open Games"
- CyberCat Institute, open-game-engine
- plurigrid/act — cognitive category theory building blocks