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    "result": "## Preconditions\n\n1. Every emitted program is a single MLIR module written as `module {` \u2026 `}` containing only top-level `llvm.func` definitions and nothing else.\n2. Every function is a definition with a body (never a declaration), written as `llvm.func @NAME(%arg0: T) { \u2026 }` with exactly one block, no block label, and no explicit entry-block argument list beyond the function signature.\n3. Every function takes exactly one parameter, always named `%arg0`, and that parameter's type is a single type `T` fixed per function.\n4. Every function's signature declares no result type, and every function body ends with the terminator `llvm.return` carrying no operand, so the body is void-returning.\n5. The parameter/operand/result type `T` of a function is always an exact, statically shaped standard numeric type: either a signless integer type or a fixed-shape vector of signless integers; no scalable vectors, floats, pointers, index, opaque, or dialect-custom types occur.\n6. Within one function every operation consumes `%arg0` as its only source operand and produces a result whose type is identical to `T`, so all operand and result types inside a function coincide exactly with the function's parameter type.\n7. Zero-count operations are always spelled in generic operation form, `\"llvm.intr.ctlz\"`/`\"llvm.intr.cttz\"` applied to `(%arg0)`, and always carry the property dictionary `<{is_zero_poison = B}>` with a boolean `B`; the attribute is never omitted and never inherited by default.\n8. A zero-count operation's functional type is always written `(T) -> T`, a single operand type mapping to a single result type equal to it.\n9. Binary integer operations are always spelled in custom assembly form as `llvm.add`, `llvm.mul`, or `llvm.and` with both operands being `%arg0` and a single trailing type annotation `: T`.\n10. Every operation in a body defines a fresh SSA result named `%v` followed by its zero-based position index in that body, so result names are unique within a function and defined before the terminator.\n11. No SSA result defined in a body is ever used as an operand by any later operation or by the terminator; all defined values are dead except for their definitions.\n12. Every function body contains at least one operation before `llvm.return`, so no body consists of the terminator alone.\n13. Function bodies contain no control flow, no nested regions, no calls, no constants, no memory operations, and no operations other than the zero-count intrinsics, the three binary integer operations, and the final `llvm.return`.\n14. Function attribute dictionaries, when present, contain only importer-owned entries drawn from `passthrough` and `target_cpu`; no other function attributes (linkage, visibility, argument attributes, result attributes) are ever written.\n15. Function names are unique within the module, all sharing the prefix `@zero_counts_` followed by the function's zero-based index in the module.\n\n## Sampling conventions\n\n1. The module contains between 1 and 3 functions inclusive.\n2. Functions are named `@zero_counts_0`, `@zero_counts_1`, \u2026 using the running zero-based counter, rather than any other unique-name scheme.\n3. The per-function type `T` is drawn from exactly six choices: `i32`, `i8`, `i16`, `i64`, `vector<4xi32>`, and `vector<2xi64>`; other integer widths (e.g. `i1`, `i128`), other vector shapes, and multi-dimensional vectors are never emitted.\n4. The type is chosen once per function and reused verbatim for the parameter and for every operand/result type annotation in that function's body.\n5. Each function body contains between 1 and 4 operations, chosen independently per function.\n6. Each body operation is one of three kinds: a zero-count op with a freely chosen poison flag, a zero-count op with the flag pinned to `true`, or a binary op; the duplicated flagged alternative exists only to bias generation toward `is_zero_poison = true` and produces no syntactic form the first alternative could not.\n7. The intrinsic kind is drawn from exactly `ctlz` and `cttz`; no other LLVM intrinsics (e.g. `ctpop`, `bswap`, `abs`, `fshl`) are emitted.\n8. The `is_zero_poison` attribute value is one of the literals `true` or `false`, written as a bare boolean rather than as a typed or unit attribute.\n9. Binary operations are restricted to exactly `llvm.add`, `llvm.mul`, and `llvm.and`; no subtraction, division, shifts, comparisons, `or`/`xor`, or overflow/exact flags appear.\n10. Binary operations are never given operand flags or attributes, and always use `%arg0, %arg0` rather than distinct or previously defined operands.\n11. The function attribute clause is one of exactly four alternatives: absent, ` attributes {passthrough = [\"nounwind\"]}`, ` attributes {passthrough = [\"strictfp\"]}`, or ` attributes {passthrough = [[\"no-trapping-math\", \"true\"]], target_cpu = \"generic\"}`; these three dictionaries are fixed constants, not assembled from a larger attribute vocabulary.\n12. Result numbering restarts at `%v0` in each function, so the same SSA names recur across functions in the module.\n13. 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