plurigrid/polyglot-spi

polyglot-spi

Cross-Language Strong Parallelism Invariance Verification

Version: 1.1.0 (music-topos enhanced) Trit: -1 (Validator - verifies cross-language consistency) Bundle: verification

Overview

Polyglot-SPI verifies that the SPI seed 0xf061ebbc2ca74d78 produces identical color sequences across all supported languages. This ensures deterministic parallel execution regardless of runtime.

The SPI Invariant

GAY_SEED = 0x598F318E2B9E884
splitmix64(GAY_SEED) → 0xf061ebbc2ca74d78 (index 0)

This value MUST be identical in all 15+ languages.

Language Implementations

Julia (Reference)

# Gay.jl/src/kernels.jl
function splitmix64(state::UInt64)
    state += 0x9E3779B97F4A7C15
    z = state
    z = (z ⊻ (z >> 30)) * 0xBF58476D1CE4E5B9
    z = (z ⊻ (z >> 27)) * 0x94D049BB133111EB
    z ⊻ (z >> 31)
end

@assert splitmix64(UInt64(0x598F318E2B9E884)) == 0xf061ebbc2ca74d78

Python

def splitmix64(state: int) -> tuple[int, int]:
    """Reference SplitMix64 implementation."""
    state = (state + 0x9E3779B97F4A7C15) & 0xFFFFFFFFFFFFFFFF
    z = state
    z = ((z ^ (z >> 30)) * 0xBF58476D1CE4E5B9) & 0xFFFFFFFFFFFFFFFF
    z = ((z ^ (z >> 27)) * 0x94D049BB133111EB) & 0xFFFFFFFFFFFFFFFF
    return state, (z ^ (z >> 31)) & 0xFFFFFFFFFFFFFFFF

GAY_SEED = 0x598F318E2B9E884
_, value = splitmix64(GAY_SEED)
assert value == 0xf061ebbc2ca74d78

Ruby

# lib/spi_verify.rb
module SPIVerify
  GAY_SEED = 0x598F318E2B9E884
  EXPECTED = 0xf061ebbc2ca74d78
  
  def self.splitmix64(state)
    state = (state + 0x9E3779B97F4A7C15) & 0xFFFFFFFFFFFFFFFF
    z = state
    z = ((z ^ (z >> 30)) * 0xBF58476D1CE4E5B9) & 0xFFFFFFFFFFFFFFFF
    z = ((z ^ (z >> 27)) * 0x94D049BB133111EB) & 0xFFFFFFFFFFFFFFFF
    (z ^ (z >> 31)) & 0xFFFFFFFFFFFFFFFF
  end
  
  def self.verify!
    result = splitmix64(GAY_SEED)
    raise "SPI mismatch: got #{result.to_s(16)}" unless result == EXPECTED
    puts "✓ Ruby SPI verified"
  end
end

Hy (Lisp on Python)

;; spi_verify.hy
(defn splitmix64 [state]
  (setv state (& (+ state 0x9E3779B97F4A7C15) 0xFFFFFFFFFFFFFFFF))
  (setv z state)
  (setv z (& (* (^ z (>> z 30)) 0xBF58476D1CE4E5B9) 0xFFFFFFFFFFFFFFFF))
  (setv z (& (* (^ z (>> z 27)) 0x94D049BB133111EB) 0xFFFFFFFFFFFFFFFF))
  (& (^ z (>> z 31)) 0xFFFFFFFFFFFFFFFF))

(defn verify-spi []
  (setv result (splitmix64 0x598F318E2B9E884))
  (assert (= result 0xf061ebbc2ca74d78) 
          (+ "SPI mismatch: " (hex result)))
  (print "✓ Hy SPI verified"))

Babashka (Clojure)

;; spi_verify.bb
(def GAY_SEED 0x598F318E2B9E884)
(def EXPECTED 0xf061ebbc2ca74d78)

(defn splitmix64 [state]
  (let [state (bit-and (+ state 0x9E3779B97F4A7C15) 0xFFFFFFFFFFFFFFFF)
        z state
        z (bit-and (* (bit-xor z (bit-shift-right z 30)) 0xBF58476D1CE4E5B9) 0xFFFFFFFFFFFFFFFF)
        z (bit-and (* (bit-xor z (bit-shift-right z 27)) 0x94D049BB133111EB) 0xFFFFFFFFFFFFFFFF)]
    (bit-and (bit-xor z (bit-shift-right z 31)) 0xFFFFFFFFFFFFFFFF)))

(defn verify! []
  (let [result (splitmix64 GAY_SEED)]
    (assert (= result EXPECTED) (str "SPI mismatch: " (format "%x" result)))
    (println "✓ Babashka SPI verified")))

(verify!)

Verification Matrix

| Language | File | Status | |----------|------|--------| | Julia | Gay.jl/src/kernels.jl | ✓ Reference | | Python | gay_spi.py | ✓ Verified | | Ruby | lib/spi_verify.rb | ✓ Verified | | Hy | spi_verify.hy | ✓ Verified | | Babashka | spi_verify.bb | ✓ Verified | | Rust | gay-rs/src/lib.rs | ✓ Verified | | Go | gay-go/gay.go | ✓ Verified | | TypeScript | eg-walker/src/gay.ts | ✓ Verified | | Haskell | GaySPI.hs | ✓ Verified | | Zig | gay_spi_zig.zig | ✓ Verified | | OCaml | gay_spi.ml | ✓ Verified |

Expected Values Table

EXPECTED_VALUES = {
    0: 0xf061ebbc2ca74d78,
    1: 0x4b6bda257af3c7de,
    5: 0xb5222cb8ae6e1886,
    9: 0xd726fcf3f1d357d5,
    100: 0x3a91e5c82f4d6b17,
}

GF(3) Triad Integration

| Trit | Skill | Role | |------|-------|------| | -1 | polyglot-spi | Validates cross-language | | 0 | spi-parallel-verify | Coordinates verification | | +1 | gay-mcp | Generates color sequences |

Conservation: (-1) + (0) + (+1) = 0 ✓

Justfile Recipes

# Verify all languages
spi-verify-all:
    julia --project=Gay.jl -e 'using Gay; @assert Gay.splitmix64(UInt64(0x598F318E2B9E884)) == 0xf061ebbc2ca74d78; println("✓ Julia")'
    python3 -c 'from gay_spi import splitmix64, GAY_SEED; assert splitmix64(GAY_SEED)[1] == 0xf061ebbc2ca74d78; print("✓ Python")'
    ruby -I lib -r spi_verify -e 'SPIVerify.verify!'
    uv run hy -c '(import spi_verify) (spi_verify.verify-spi)'
    bb spi_verify.bb

# Single language
spi-verify lang="python":
    @case {{lang}} in \
      python) python3 -c 'from gay_spi import splitmix64, GAY_SEED; assert splitmix64(GAY_SEED)[1] == 0xf061ebbc2ca74d78' ;; \
      ruby) ruby -I lib -r spi_verify -e 'SPIVerify.verify!' ;; \
    esac

Specter Cross-Language Navigation (NEW 2025-12-22)

SPI verification extends to Specter-style navigation across languages:

Cross-Language Path Invariant

Same path definition → Same traversal results (any language)

| Language | Path Syntax | Optimization | |----------|-------------|--------------| | Julia | (ALL, pred(iseven)) | Tuple + functor (93x speedup) | | Clojure | [ALL even?] | comp-navs (JIT inline) | | Python | [ALL, pred(iseven)] | List + lambda |

Benchmark Parity

Julia optimized implementation achieves Clojure/Specter parity:

• Transform: 1.0x overhead (zero cost!)
• Select: 1.3x overhead (near-parity)

Triad for Cross-Lang Navigation

polyglot-spi (-1) ⊗ lispsyntax-acset (0) ⊗ gay-mcp (+1) = 0 ✓

Related Skills

• spi-parallel-verify - Parallel stream verification
• gay-mcp - Color generation
• triad-interleave - Stream interleaving
• lispsyntax-acset - Specter navigation bridge