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