🌈💀👑 Rainbow Array Machine — v1

An array machine whose source language is UTF-8 emoji and whose execution target is WebAssembly. Every program compiles to its own standalone WASM module — parser, typed FLAT stages, and code generator are C11; Clang's wasm32 target produces the module; the operations and the assertions execute inside it. 🕸️

🌀 BQN · 🔺 APL · ⚡ K · 🐺 Wolfram subset · 📐 geometry (namespace tags for a bounded, explicitly defined subset — not full implementations of those languages)

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▶️ A program, executing

One program, five instructions — vectors, matmul, geometry, an inverse, and the affine — compiled into a single module:

🌀 📏 ➕ 3 1 2 3 4 5 6 >>>>>>>€ 5 7 9
🌀 🟦 🧲 2 3 2 1 2 3 4 5 6 7 8 9 10 11 12 >>>>>>>€ 58 64 139 154
🌀 📐 @@ ROTATE_Z 2 1 1 0 0 0 1 0 >>>>>>>€ 0 1 0 -1 0 0
↶ 🌀 📐 @@ ROTATE_Z 1 1 0 1 0 >>>>>>>€ 1 0 0
🐺 🔹 📜 2 3 7 4 >>>>>>>€ 27

make -C core modules        # ramc → flat_check → flat_lower
                            # → ram_codegen → clang wasm32

$ run showcase.wasm
PASS standalone WASM: 17 outputs
[5,7,9, 58,64,139,154, 0,1,0,-1,0,0, 1,0,0, 27]

run() returns 0 only when every operation and every assertion inside the module passes. A false assertion returns a nonzero code from the WASM itself — the host computes nothing. 🛡️

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🏗️ Pipeline

🌈 emoji source (.ram)
  → ramc        C11 strict parser            → RAMIR1
  → flat_check  C11 shape/op validation      → FLAT1 metadata
  → flat_lower  C11 metadata + payload       → FLAT2
  → ram_codegen C11 standalone lowering      → C source
  → clang       wasm32                       → 📦 program.wasm
  → run()       operations + assertions execute in-module
💀👑 .skull      reversible serialization of the .wasm bytes

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📊 Benchmarks

Measured by execution (2026-11-05, AMD EPYC 9D25 VM, Clang 23, Node 24; medians of 5 runs). Reproduce with make test and the timing method in STATUS.

Compile pipeline — the showcase program, source → module:

Stage	Median
ramc (parse → RAMIR1)	1.08 ms
flat_check (→ FLAT1)	1.43 ms
flat_lower (→ FLAT2)	1.43 ms
ram_codegen (FLAT2 → C)	2.87 ms
clang (C → wasm32)	234.26 ms
Total	≈ 241 ms

Modules and execution:

Module	Size	Instantiate	run() median	Throughput
array.wasm (5 instr)	3,093 B	0.94 ms	0.094 µs	≈ 10.6 M runs/s
geometry.wasm (5 instr)	2,984 B	—	—	—
symbolic.wasm (1 instr)	2,298 B	0.38 ms	0.027 µs	≈ 37.0 M runs/s
showcase.wasm (5 instr)	2,975 B	2.29 ms	0.170 µs	≈ 5.9 M runs/s

Serialization: a 3,093-byte module encodes to a 98,976-byte .skull — exactly 32× (8 symbols per byte × 4 UTF-8 bytes per symbol), byte-for-byte reversible. 💀👑

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🔒 Invariants

These hold by construction and are exercised by the test suites:

1. Per-program modules. Each program compiles to its own standalone .wasm. There is no instruction interpreter and no shared dispatcher in the execution path.
2. Assertions execute in WASM. >>>>>>>€ expectations are compiled into the module and checked by the kernel's assert_equal (tolerance 1e-10) inside run(); failure returns a nonzero code identifying the instruction.
3. The host computes nothing. A harness instantiates the module, calls run(), and reads exported linear memory.
4. Division by zero is refused — the elementwise kernel returns an error code, never an infinity.
5. Kernel bounds are enforced in-module: elementwise n ≤ 4096, matmul dimensions ≤ 64, geometry points ≤ 1024. Violations return an error code; nothing is clamped silently.
6. FLAT2 integrity. Every executable payload line travels paired with its validated FLAT1 metadata line. A missing payload or a count mismatch is refused before code generation.
7. The frontend fails closed. Unknown namespaces or opcodes, missing operands, non-finite numbers, and trailing input are rejected with a nonzero exit — no partial program is ever lowered.
8. ↶ is exact for geometry. Inverses are the parse-time negation of quarter turns and translation deltas; a transform followed by its inverse returns the declared points exactly.
9. 💀👑 is serialization, never execution. A .skull is decoded to bytes before any runtime loads the module.
10. No scripting languages in the build path. Parser, FLAT stages, and code generator are C11; the compiler target is Clang wasm32.

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📜 Theorems

proofs/Arithmetic.lean — mathematical specifications of the kernels, kernel-checked with lake build (Lean v4.9.0, Mathlib v4.9.0; build exit 0, no sorry):

def affineSpec (a b c x : ℤ) : ℤ := (a + b) * x + c

theorem affine_expand (a b c x : ℤ) :
    affineSpec a b c x = a * x + b * x + c

theorem inverse_translation (x delta : ℤ) :
    (x + delta) - delta = x

theorem transpose_index_roundtrip (m n i j : ℕ)
    (hi : i < m) (hj : j < n) :
    (j * m + i) / m = j ∧ (j * m + i) % m = i

Scope, stated plainly: these theorems specify the mathematics the kernels implement — the affine law, translation inversion, and the row-major transpose index decode (both axes recovered). They do not claim instruction-level equivalence between the specification and the emitted WASM; that requires a formal WASM semantics and a simulation proof, and it is not claimed here. 🧾

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🧩 Components

Piece	Role
core/src/ramc.c	🌐 Strict UTF-8 emoji parser → RAMIR1 (↶ geometry inverses at parse)
core/src/flat_check.c	🏷️ RAMIR1 validation → FLAT1 typed metadata (rank, shape, elements, assert flag)
core/src/flat_lower.c	📐 FLAT1 + payload → FLAT2, count-checked pairing
core/src/ram_codegen.c	⚙️ FLAT2 → standalone C module source
core/src/kernel.c	🕸️ The WASM kernel — elementwise (➕➖✖️➗), matmul, transpose, reduce_sum, affine, rotate, translate, assert_equal — compiled by Clang to wasm32
src/skull.c	💀👑 Skull/Crown encode/decode/invert — the repo codec; it frames the same MSB-first symbol stream with a newline per byte
core/proofs/Arithmetic.lean	📜 The theorems above

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🔐 V3 — the ASTRA-VAULT layer (crypto/)

Hand-rolled cryptography and the mathematics it seals with — owner-authored, carried verbatim, verified by execution; findings are recorded in STATUS.md, never silently patched.

Artifact	What it is	Verification status
crypto/astra-vault-unlambda.unl	🌌 Madhava's π/sine series + Qin Jiushao's Dayan (CRT) closure in pure Unlambda combinators	Numerals execute with exact iteration counts (variant encoding); 21 of 28 definitions are open fragments completed textually at use sites; mod is referenced but undefined; odd is textually the numeral 3 — conversion to standard Unlambda is the open step
crypto/astra_math_vault.m	🧮 Recursive mathematical vault — layered bases, entropy statistics, deviation analysis, invariants, compression over a synthetic trillion-parameter field	Runs end to end (Octave record in STATUS); construction-consistent figures verified (RMS ≈ 1, mean |z| ≈ √(2/π)); two entropy-semantics findings recorded (hash-pooled bins; discrete-vs-differential delta)
crypto/seal_recursion.hc	🔏 The seal — 2070 descending by 10s to 0 as a 12-bit 💀👑 grid, with inversion-carry detection	Executes via the C11 port: 208 rows, carry at row 1 col 7 (bit 4), 2070 → 2060
crypto/seal_recursion.c	The C11 port of the seal — the form that enters the CompCert pipeline	Output identical to the verified reference run

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⚙️ CompCert lowering (compcert/)

The host-side C — the seal, the four core pipeline tools, and the v0.1-line tools — lowers to assembly through CompCert, the verified C compiler whose Coq-checked theorem guarantees the assembly preserves the C semantics. compcert/lower.sh performs the lowering and the differential re-verification of the CompCert-built binaries against the reference suites.

Scope: CompCert proves C → assembly preservation; it does not prove the C itself, and it has no wasm32 target — the per-program WASM modules stay clang-built, and CompCert lowers the host toolchain that produces them. Toolchain status and lowering results are recorded in STATUS.md.

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🛣️ Open frontier

• FLAT2 carries validated metadata with the payload; it is not yet an SSA IR with buffer allocation or a type-soundness proof
• Full BQN/APL/KCL/Wolfram semantics are not implemented; the namespaces tag a bounded subset
• Runtime-input ABI (programs that take external data at run time) is future work; v1 programs carry their constants
• WASM↔specification equivalence proofs are not claimed

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🏷️ Topics

rainbow-array-machine, webassembly, wasm, emoji-programming,
array-programming, bqn, apl, k, wolfram, compiler, typed-ir,
flat-ir, skull-crown, cold-boot, provenance, reversible-computing,
lean, mathlib, c11, clang

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⚖️ License

SNAPKITTY OPAQUE SOURCE LICENSE v1.0 — LicenseRef-Sovereign-Leviathan-SL-AGPL3-001 © 2026 SnapKitty West. Owners: Nova Parr, Ahmad Ali Parr, and Team HoloTwinKitty. Publication is not commercial authorization; commercial use requires separate written authorization from the owners. 📜