migration D (C2 wave 1): reversible VM opcodes (4 kernels, 4-gate green)

[hyperpolymath]

Phase D / cluster C2 wave 1 of the ReScript → AffineScript → wasm migration of hyperpolymath/idaptik. Continues #535 (Phase B + C1, merged). Staged under proposals/idaptik/migrated/ — verified + applyable, not applied (idaptik write-access gate).

What landed — the reversible VM value-transform opcodes

The VM stores state in a dict<int> keyed by register name, each instruction a pair of execute/invert closures. Re-decomposition: names + dict stay host-side (senses); the brain is the reversible scalar-int value transform per opcode.

Kernel	Brain	Reversibility
VmArith	ADD/SUB, NEGATE, NOOP, SWAP	inverse-pair + self-inverse
VmBitwise	FLIP, XOR, ROL, ROR (32-bit)	self-inverse + rotation pair
VmAncilla	AND, OR (Bennett ancilla)	conditional (iff ancilla c==0)
VmInstruction	23-opcode encoding + tier classifier	LOSSLESS taxonomy

The defining VM invariant — invert ∘ execute = id — is pinned as explicit *_roundtrip exports (oracle = identity) and swept over i32 extremes.

Four gates green (migrated/EVIDENCE-C2.adoc)

• G1 compile — 4/4 → wasm
• G2 parity — 2100/2100 oracle-vs-wasm inputs, including every reversibility round-trip over i32 extremes (incl. 0x55555555/0xAAAAAAAA and overflow)
• G3 echo-boundary — VmInstruction 23-opcode encoding Agda-certified LOSSLESS (agda exit 0)
• G4 assail — 4/4 clean

Compiler findings (worked around; recorded as findings)

Migrating the bitwise opcodes surfaced three AffineScript backend facts:

1. Unary ~ mis-compiles — emits i32.xor with a missing operand (the wasm won't instantiate). Isolated to unary ~; &/|/^ are sound. → FLIP uses ~a == -a-1 (verified equal + self-inverse). Candidate Phase-F compiler fix.
2. >> is arithmetic and >>> doesn't exist, but ROL/ROR need a logical shift-right → emulated lsr(a,n) = (a>>n) & ((1<<(32-n))-1); rotations then match JS ((a<<n)|(a>>>(32-n)))|0 and round-trip over the full i32 range.
3. << and i32 wrap are correct (the VM's word model).

AND/OR are the honest outlier — reversible only via Bennett's ancilla trick under a declared precondition (ancilla starts at 0); every other opcode here is unconditionally reversible.

Ledger

Phase D (C2 wave 1) DONE; migration-map.json C2 → IN_PROGRESS with the wave-1 detail. NEXT: C2 wave 2 — Mul/Div, stack/memory (Push/Pop/Load/Store), control flow (Call/Loop/IfPos/IfZero), I/O (Send/Recv/CoprocessorCall) and the structural VM files; these need an array/linear-memory ABI.

On top of current main (d706d52, post-#535).

https://claude.ai/code/session_01WoKhFQePiRsAj7aqnxbG8s

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