# GENSIS Compiler Specification v2.0 ## Q0.64 0D Scalar × AngrySphinx Gate × Matryoshka Brane Layers ### Version History | Version | Date | Author | Changes | |---------|------|--------|---------| | 2.0 | 2026-05-04 | GENSIS | Full rewrite: Q0.64, AngrySphinx, Matryoshka | --- ## §0. Architecture Overview The GENSIS compiler transforms arbitrary data through a **Matryoshka Brane Stack** — nested reality shells (quantum foam → cell → organ → person → group → planet → universe), each with its own native dimensionality, all communicating through a single **Q0.64 0D scalar**. ``` ┌──────────────────────────────────────────────────────────────┐ │ GENSIS Compiler v2.0 │ ├──────────────────────────────────────────────────────────────┤ │ Data In → [1D Scalar Stream] → Matryoshka Stack → Out │ │ │ │ Matryoshka Shell Layers (bottom to top): │ │ Layer 0: Quantum Foam (d=0, point) │ │ Layer 1: Preonic/String (d=1, line) │ │ Layer 2: Quark/Gluon (d=2, plane) │ │ Layer 3: Nucleon/Atom (d=3, volume) │ │ Layer 4: Molecule (d=4, tesseract) │ │ Layer 5: Cell (d=5, 5-cube) │ │ Layer 6: Organ (d=6, 6-cube) │ │ Layer 7: Organism (d=7, 7-cube) │ │ Layer 8: Group (d=8, 8-cube) │ │ Layer 9: Species (d=9, 9-cube) │ │ Layer N: Universe (d=N, N-cube) │ │ │ │ AngrySphinx Gate at every boundary: │ │ E_attack = n → E_solve ≥ 2^n │ │ Frustration F → 0 at max pressure → NaN boundary │ └──────────────────────────────────────────────────────────────┘ ``` --- ## §1. Q0.64 0D Scalar: The Universal Lingua Franca ### §1.1 Definition The Q0.64 fixed-point type represents real numbers in [0, 1) with 2^−64 precision. ```lean structure Q0_64 where val : UInt64 -- unsigned 64-bit integer -- value = val / 2^64 ∈ [0, 1) deriving Repr, DecidableEq, BEq ``` ### §1.2 Constants ```lean def Q0_64.zero : Q0_64 := { val := 0x0000_0000_0000_0001 } -- smallest non-zero = 5.4×10^−20 def Q0_64.epsilon : Q0_64 := { val := 0x0000_0000_0000_0001 } -- 2^−64 ≈ 5.42×10^−20 def Q0_64.half : Q0_64 := { val := 0x8000_0000_0000_0000 } -- 0.5 def Q0_64.near_one : Q0_64 := { val := 0xFFFF_FFFF_FFFF_FFFF } -- 1 - 2^−64 ≈ 0.99999... ``` ### §1.3 Arithmetic All operations are **saturating unsigned** — results stay in [0, 1). ```lean -- Addition: a + b, saturates at near_one def Q0_64.add (a b : Q0_64) : Q0_64 := let sum := a.val + b.val if sum < a.val || sum < b.val then Q0_64.near_one -- overflow → saturate else { val := min sum 0xFFFF_FFFF_FFFF_FFFF } -- Subtraction: a - b (a ≥ b), else zero def Q0_64.sub (a b : Q0_64) : Q0_64 := if a.val ≥ b.val then { val := a.val - b.val } else Q0_64.zero -- Multiplication: a × b in [0, 1)² → [0, 1) -- (a.val * b.val) >> 64 via high 64 bits of 128-bit product def Q0_64.mul (a b : Q0_64) : Q0_64 := let product : UInt128 := a.val.toUInt128 * b.val.toUInt128 { val := product.high } -- upper 64 bits = floor(product / 2^64) -- Division: a / b, guard against b=0 def Q0_64.div (a b : Q0_64) : Q0_64 := if b.val = 0 then Q0_64.near_one -- div-by-zero → max else -- (a.val << 64) / b.val, but a.val < b.val typically -- Shift a.val left by 64, divide, take high bits let dividend : UInt128 := a.val.toUInt128 << 64 let quotient := dividend / b.val.toUInt128 { val := quotient.low } ``` ### §1.4 Conversion ```lean -- Byte to Q0_64: map byte [0,255] → [0, 1) def Q0_64.ofByte (b : UInt8) : Q0_64 := { val := (b.toUInt64 << 56) } -- b * 2^56 / 2^64 = b / 256 -- Float to Q0_64 (for testing) def Q0_64.ofFloat (f : Float) : Q0_64 := if f ≤ 0.0 then Q0_64.zero else if f ≥ 1.0 then Q0_64.near_one else { val := (f * 0x1p64).toUInt64 } -- Q0_64 to Float (for visualization) def Q0_64.toFloat (q : Q0_64) : Float := q.val.toFloat / 0x1p64 ``` ### §1.5 Semantic Primes as Q0_64 Values The 12 irreducible semantic primes (CrossDimensionalFilter §0) map to fixed Q0_64 values for inter-shell communication: ```lean def semanticPrimeValue (p : SemanticPrime) : Q0_64 := match p with | .Identity => { val := 0x1555_5555_5555_5555 } -- 1/12 ≈ 0.0833 | .Agent => { val := 0x2AAA_AAAA_AAAA_AAAA } -- 2/12 ≈ 0.1667 | .Object => { val := 0x4000_0000_0000_0000 } -- 3/12 = 0.25 | .Action => { val := 0x5555_5555_5555_5555 } -- 4/12 ≈ 0.3333 | .State => { val := 0x6AAA_AAAA_AAAA_AAAA } -- 5/12 ≈ 0.4167 | .Relation => { val := 0x8000_0000_0000_0000 } -- 6/12 = 0.5 | .Good => { val := 0x9555_5555_5555_5555 } -- 7/12 ≈ 0.5833 | .Bad => { val := 0xAAAA_AAAA_AAAA_AAAA } -- 8/12 ≈ 0.6667 | .Want => { val := 0xC000_0000_0000_0000 } -- 9/12 = 0.75 | .Know => { val := 0xD555_5555_5555_5555 } -- 10/12 ≈ 0.8333 | .Place => { val := 0xEAAA_AAAA_AAAA_AAAA } -- 11/12 ≈ 0.9167 | .Time => { val := 0xF555_5555_5555_5555 } -- 11.5/12 ≈ 0.9583 ``` --- ## §2. AngrySphinx Gate: Exponential Proof-of-Defense ### §2.1 Core Theorem ``` E_attack = n ⟹ E_solve ≥ 2^n ``` At maximum attack pressure, frustration metric F → 0, causing division by zero (NaN boundary) — the self-destruct mechanism. ### §2.2 Frustration Metric ```lean structure FrustrationMetric where value : Q0_64 -- F ∈ [0, 1), F→0 under pressure -- F(p) = 1 / (p + 1) mapped to Q0_64 def frustrationUnderPressure (pressure : Q0_64) : FrustrationMetric := -- F = 1 - pressure (linearized in [0,1)) let f := Q0_64.sub Q0_64.half pressure { value := Q0_64.max Q0_64.epsilon f } ``` ### §2.3 S³ Shell Lattice Concentric 3-sphere shells, each transition multiplies solve energy by g_k: ```lean structure ShellDepth where depth : Nat -- number of S³ layers structure GearRatio where ratio : Nat -- default: 2 (doubling) h_ge_two : ratio ≥ 2 -- ∏g_k = 2^depth for g_k = 2 def gearProduct (depth : ShellDepth) (g : GearRatio) : UInt64 := g.ratio ^ depth.depth -- E_solve = E_attack · ∏g_k -- If depth = n and g = 2, E_solve = n · 2^n -- In Q0.64: map to [0,1) via log def solveEnergy (pressure : Q0_64) (depth : ShellDepth) (g : GearRatio) : Q0_64 := let attackWork := pressure.val.toNat let totalGear := gearProduct depth g let raw := attackWork * totalGear -- Map to [0,1): log_2(raw) / log_2(max) { val := min raw (0xFFFF_FFFF_FFFF_FFFF) } ``` ### §2.4 NaN Boundary When F = 0, the solve denominator hits NaN: ```lean structure NaNBoundary where frustration : FrustrationMetric isZero : frustration.value = Q0_64.zero def solveDenominator (F : FrustrationMetric) : Option Q0_64 := if F.value = Q0_64.zero then none -- NaN else some (Q0_64.div Q0_64.half F.value) theorem nanBoundaryCorrect (F : FrustrationMetric) (h_zero : F.value = Q0_64.zero) : solveDenominator F = none := by simp [solveDenominator, h_zero] ``` ### §2.5 PoD Accumulator ```lean structure PodAccumulator where totalWork : Q0_64 shellDepth : ShellDepth lastAttestation : String -- Each unit of attack work deepens the shell def accumulateWork (pod : PodAccumulator) (work : Q0_64) (g : GearRatio) : PodAccumulator := { totalWork := Q0_64.add pod.totalWork work shellDepth := { depth := pod.shellDepth.depth + 1 } lastAttestation := s!"work={pod.totalWork.toFloat},depth={pod.shellDepth.depth + 1}" } -- Verify: totalWork ≥ 2^depth def verifyPod (pod : PodAccumulator) (g : GearRatio) : Bool := pod.totalWork.val ≥ gearProduct pod.shellDepth g ``` --- ## §3. Matryoshka Brane Layers ### §3.1 Shell Structure Each Matryoshka shell has native dimensionality and communicates via the 1D Q0_64 scalar: ```lean structure MatryoshkaShell where shellId : String dimension : Nat -- native dimensionality understoodPrimes : List SemanticPrime -- primes this shell interprets scalarValue : Q0_64 -- current 1D scalar interface gearRatio : GearRatio -- AngrySphinx gear ratio for this shell frustration : FrustrationMetric -- current frustration level ``` **Shell dimension mapping:** | Shell | Native D | Shape | Primes Understood | Gear Ratio | |-------|----------|-------|-------------------|------------| | Quantum Foam | 0 | Point | {Identity} | 2^0=1 | | String | 1 | Line | {Identity, Relation} | 2^1=2 | | Quark | 2 | Plane | {Identity, Agent, Action} | 2^2=4 | | Nucleon | 3 | Volume | {+Object, State} | 2^3=8 | | Molecule | 4 | Tesseract | {+Good, Bad} | 2^4=16 | | Cell | 5 | 5-cube | {+Want, Know} | 2^5=32 | | Organ | 6 | 6-cube | {+Place} | 2^6=64 | | Organism | 7 | 7-cube | {+Time} | 2^7=128 | | Group | 8 | 8-cube | all 12 | 2^8=256 | | Species | 9 | 9-cube | all 12 | 2^9=512 | | Planet | 10 | 10-cube | all 12 | 2^10=1024 | | Universe | N | N-cube | all 12 | 2^N | ### §3.2 ReductionFilter: High-D → 1D Scalar High-dimensional state collapses to a Q0_64 scalar by **semantic prime overlap**: ```lean def reductionFilter (entity : DimensionalEntity) (targetShell : MatryoshkaShell) : Q0_64 := -- Find all primes BOTH entity and target shell understand let sharedPrimes := entity.emittedPrimes.filter (fun p => targetShell.understoodPrimes.contains p) -- Aggregate into scalar: weighted mean of prime values if sharedPrimes.isEmpty then Q0_64.zero else let sum := sharedPrimes.foldl (fun acc p => Q0_64.add acc (semanticPrimeValue p)) Q0_64.zero let count := Q0_64.ofNat sharedPrimes.length Q0_64.div sum count ``` **Theorem**: The reduction filter is dimension-independent: ``` reductionFilter(e, s1) = reductionFilter(e, s2) when sharedPrimes(e, s1) = sharedPrimes(e, s2) ``` ### §3.3 ExpansionFilter: 1D Scalar → Low-D Projection ```lean def expansionFilter (scalar : Q0_64) (targetShell : MatryoshkaShell) : DimensionalEntity := -- Decompose scalar into understood prime values let n := targetShell.understoodPrimes.length let primeStep := Q0_64.div Q0_64.half (Q0_64.ofNat n) -- Each prime gets a slice of the scalar let projectedState := targetShell.understoodPrimes.map (fun p => let primeVal := semanticPrimeValue p let diff := Q0_64.sub scalar primeVal Q0_64.mul diff primeStep -- proximity-weighted ) DimensionalEntity.mk "projected" targetShell projectedState targetShell.understoodPrimes ``` ### §3.4 Cross-Shell Communication Pipeline The complete pipeline for sending data between shells: ```lean def sendToShell (entity : DimensionalEntity) (target : MatryoshkaShell) : DimensionalEntity := -- Step 1: Reduce to 1D scalar let scalar := reductionFilter entity target -- Step 2: Apply AngrySphinx gate (check solve energy) let requiredEnergy := solveEnergy scalar { depth := target.dimension } target.gearRatio let availableEnergy := entity.hostShell.scalarValue if availableEnergy < requiredEnergy then none -- AngrySphinx gate blocks: insufficient solve energy else -- Step 3: Expand into target shell some (expansionFilter scalar target) ``` --- ## §4. GENSIS Compiler Pipeline ### §4.1 Data Flow ``` Data Bytes │ ▼ ┌──────────────────────────────────────────────┐ │ Q0.64 Scalar Encoder │ │ byte → ofByte(byte) → Q0_64 stream │ │ 12 semantic primes as scalar anchors │ ├──────────────────────────────────────────────┤ │ Matryoshka Shell Selector │ │ dimension = optimalDimension(data) │ │ code_table = geneticCodeTable(data) │ ├──────────────────────────────────────────────┤ │ Reduction Filter │ │ High-D state vector → 1D Q0_64 scalar │ │ Preserves only shared semantic primes │ ├──────────────────────────────────────────────┤ │ AngrySphinx Gate │ │ F = frustrationUnderPressure(pressure) │ │ E_solve = attackEnergy · 2^depth │ │ If F = 0 → NaN boundary (reject) │ ├──────────────────────────────────────────────┤ │ Expansion Filter │ │ 1D scalar → target shell's native projection │ ├──────────────────────────────────────────────┤ │ N-Space Shell Encoding │ │ Generalized PIST in target shell's dimension │ ├──────────────────────────────────────────────┤ │ PoD Accumulator │ │ Verify work ≥ 2^depth │ ├──────────────────────────────────────────────┤ │ δ-GCL Encode + Trixal + Homeostatic │ │ (from MISC v1 pipeline) │ └──────────────────────────────────────────────┘ ``` ### §4.2 Compiler Phases ```lean def gensisCompile (data : List UInt8) (targetD : Nat) : Option CompressedBlock := -- Phase 1: Encode data as Q0_64 scalar stream let scalarStream := data.map Q0_64.ofByte -- Phase 2: Build Matryoshka target shell let targetShell := MatryoshkaShell.mk "target" targetD (allSemanticPrimes.take targetD) Q0_64.half defaultGearRatio -- Phase 3: Reduce scalar stream to compressed scalar let compressedScalar := scalarStream.foldl (fun acc s => Q0_64.add acc (Q0_64.mul acc s)) Q0_64.half -- Phase 4: Apply AngrySphinx gate let frustration := frustrationUnderPressure compressedScalar if frustration.value = Q0_64.zero then none -- NaN boundary: compression blocked else -- Phase 5: Expand to target shell's state let projected := expansionFilter compressedScalar targetShell -- Phase 6: Verify PoD let pod : PodAccumulator := { totalWork := compressedScalar, shellDepth := { depth := targetD }, lastAttestation := "gensis" } if not (verifyPod pod defaultGearRatio) then none -- Insufficient work for shell depth else -- Phase 7: Return compressed block some { compressed := projected.nativeState.map (·.val), trixal := computeTrixal projected, pod := pod } ``` ### §4.3 Decompiler ```lean def gensisDecompile (block : CompressedBlock) (targetD : Nat) : Option (List UInt8) := let scalar := block.scalar let sourceShell := MatryoshkaShell.mk "source" targetD allSemanticPrimes scalar defaultGearRatio -- Reconstruction via inverse expansion let reconstructed := block.compressed.map (fun (v : UInt64) => let q := { val := v } : Q0_64 UInt8.ofNat (q.val.toNat >> 56) -- extract byte from high bits ) some reconstructed ``` --- ## §5. Formal Invariants ### §5.1 Q0_64 Arithmetic Totality ```lean theorem Q0_64_add_total (a b : Q0_64) : ∃ c : Q0_64, c = Q0_64.add a b := by -- Addition always produces a valid Q0_64 (saturating) refine ⟨Q0_64.add a b, rfl⟩ theorem Q0_64_mul_bounded (a b : Q0_64) : (Q0_64.mul a b).val ≤ a.val := by -- Multiplication in [0,1) never increases the value -- Proof: (a*b) ≤ a when b ≤ 1 ... ``` ### §5.2 AngrySphinx Exponential Scaling ```lean theorem solveEnergyExponential (p : Q0_64) (d : ShellDepth) (h : d.depth ≥ 1) : solveEnergy p d defaultGearRatio ≥ Q0_64.ofNat (2 ^ d.depth) := by -- Core theorem: E_solve ≥ 2^depth for any positive attack energy ... ``` ### §5.3 Reduction Filter Dimension Independence ```lean theorem reductionFilterInvariant (e : DimensionalEntity) (s1 s2 : MatryoshkaShell) (h : s1.understoodPrimes = s2.understoodPrimes) : reductionFilter e s1 = reductionFilter e s2 := by -- Reduction depends only on shared primes, not shell dimension simp [reductionFilter, h] ``` ### §5.4 NaN Boundary Correctness ```lean theorem nanBoundarySelfDestruct (p : Q0_64) (h : p = Q0_64.near_one) : solveDenominator (frustrationUnderPressure p) = none := by -- At maximum pressure, frustration → 0 → NaN ... ``` ### §5.5 Matryoshka Shell Monotonicity ```lean theorem shellMonotone (s1 s2 : MatryoshkaShell) (h : s1.dimension ≤ s2.dimension) : s1.understoodPrimes ≤ s2.understoodPrimes := by -- Higher-dimensional shells understand at least all primes of lower shells ... ``` --- ## §6. Compiler Target Specifications ### §6.1 Hardware Targets | Target | Word Size | Q0_64 Native? | AngrySphinx | Matryoshka Layers | |--------|-----------|---------------|-------------|-------------------| | Lean 4 | UInt64 | ✅ Direct | ✅ Formal | ✅ Full | | Rust | u64 | ✅ Direct | ⚠️ Partial | ⚠️ Core | | C | uint64_t | ✅ Direct | ⚠️ Partial | ⚠️ Core | | RISC-V | 64-bit | ✅ Direct | ❌ External | ❌ External | | Verilog | 64-bit reg | ✅ Direct | ❌ LUT | ❌ LUT | ### §6.2 Lean 4 Extraction (Primary Target) ```lean -- Compile GENSIS to Lean 4 def gensisExtractLean (block : CompressedBlock) : String := s!"def compressedBlock : List UInt64 := {block.compressed.map (·.val)}" ``` ### §6.3 Rust Extraction ```rust // Compile GENSIS to Rust pub fn gensis_extract_rust(block: &CompressedBlock) -> String { format!("let compressed_block: Vec = vec!{:?};", block.compressed.iter().map(|q| q.val).collect::>()) } ``` ### §6.4 Verilog Extraction ```verilog // GENSIS compressed block as Verilog ROM module gensis_rom #(parameter DEPTH = 64) ( input [5:0] addr, output [63:0] data ); reg [63:0] rom [0:DEPTH-1]; assign data = rom[addr]; endmodule ``` --- ## §7. Compiler Implementation Plan ### Phase 1: Core Q0_64 (Week 1) - [ ] Implement `Q0_64` with all arithmetic in Lean 4 - [ ] Prove totality theorems for add/sub/mul/div - [ ] Generate Rust/C extraction ### Phase 2: AngrySphinx Gate (Week 2) - [ ] Implement `FrustrationMetric`, `ShellDepth`, `GearRatio` - [ ] Prove `solveEnergyExponential` theorem - [ ] Implement `NaNBoundary` and `PodAccumulator` ### Phase 3: Matryoshka Branes (Week 3) - [ ] Implement `MatryoshkaShell` with all shell dimensions (0..N) - [ ] Implement `reductionFilter` / `expansionFilter` - [ ] Prove `reductionFilterInvariant` ### Phase 4: Full Pipeline (Week 4) - [ ] Implement `gensisCompile` / `gensisDecompile` - [ ] Implement semantic prime mapping - [ ] Cross-shell communication test suite ### Phase 5: Extraction (Week 5) - [ ] Lean 4 → Rust extraction - [ ] Lean 4 → C extraction - [ ] Lean 4 → Verilog extraction - [ ] Hardware benchmark suite --- *GENSIS Compiler v2.0: Q0.64 0D Scalar × AngrySphinx Exponential Gate × Matryoshka Brane Layers.* *Every shell communicates through the same 1D scalar interface. Every layer is AngrySphinx-gated.* *The universe is a stack of nested shells, and data is the scalar that flows between them.*