Research-Stack/6-Documentation/docs/specs/GENSIS_COMPILER_SPEC.md
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# 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<u64> = vec!{:?};",
block.compressed.iter().map(|q| q.val).collect::<Vec<_>>())
}
```
### §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.*