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    "result": "## Preconditions\n\n1. Every emitted program is a single top-level `module { ... }` whose body contains only the optional host `func.func` and one or more `dataflow.thread` definitions.\n2. Every program contains at least one `dataflow.thread` definition at module scope.\n3. Every `dataflow.thread` is declared `private`, carries a symbol name, a `domain(#dataflow.thread_domain<dense>)` clause, the operand list `(%target: memref<1xi32>, %value: i32, %enabled: i1)`, and a `ctrl (%ctrl: none)` clause.\n4. Every thread body is terminated by exactly one `dataflow.thread.yield`.\n5. Every thread body contains exactly one `\"loom.spatial_region\"` operation; no thread has zero regions and none has two or more.\n6. Every `\"loom.spatial_region\"` is written in generic (quoted) form with an inherent-attribute dictionary `<{operandSegmentSizes = array<i32: ...>, resultSegmentSizes = array<i32: ...>}>` present, i.e. operand and result segmentation is always explicit and normalized.\n7. `operandSegmentSizes` on a region always has exactly four entries (a four-way value / stream / memory / fourth operand partition) and `resultSegmentSizes` always has exactly two entries.\n8. The declared segment sizes always sum to, and agree in order with, the actual operand list and result list of the region operation and with its trailing function type.\n9. Every region has exactly one entry block `^bb0` whose block-argument list matches, in order and in type, the region's operands (no arguments when there are no operands).\n10. Every region body ends with a `\"loom.spatial_yield\"` in generic form carrying its own two-entry `operandSegmentSizes`, and the yield's operand count/type matches the region's result count/type.\n11. Every `\"loom.spatial_region\"` carries a discardable attribute dictionary containing both `graph_name` (a string) and `source_maps = []`.\n12. Values consumed by a region are values already in scope in the enclosing thread: the payload operand is the thread's `%value : i32` and the memory operand is the thread's `%target : memref<1xi32>`.\n13. Values defined inside a region body (`%payload`, `%memory`, `%zero`, `%doubled`) are used only within that region body and never escape it except through the `loom.spatial_yield`.\n14. When a region occurs inside control flow, it is nested in structured control flow only: an `scf.for` loop, or an `scf.if` nested inside an `scf.for`; the region is never placed under `scf.parallel` or `scf.forall`.\n15. Every `scf.for` enclosing a region has index-typed lower bound, upper bound and step operands defined by `arith.constant ... : index` operations that dominate the loop.\n16. Every `scf.if` enclosing a region is predicated on an `i1` value in scope \u2014 the thread's `%enabled` argument \u2014 and has a `then` region only (no `else` region).\n17. `scf.if` and `scf.for` bodies containing a region carry no explicit yielded results, consistent with the region being the sole payload of the branch/loop body.\n18. When a region produces a result, that result is bound to an SSA name inside the enclosing thread/loop/branch scope and is not further consumed.\n19. The optional host container, when present, is a module-scope `func.func` with an explicit `return`, whose loop is a plain `scf.for` containing only a `memref.store`; a host function never contains a `loom.spatial_region`.\n20. All memref accesses are in-bounds and type-consistent: stores into `memref<1xi32>` use index `0`, and host stores into `memref<4xi32>` use the loop induction variable of a loop running over `[0, 4)`.\n21. Symbol names of threads are distinct within the module, and each thread's `graph_name` is distinct across threads.\n\n## Sampling conventions\n\n1. The number of threads per module is drawn from 1 to 3 inclusive; larger modules are never emitted.\n2. The host `func.func` is either present exactly once, immediately after `module {` and before all threads, or entirely absent; it is never emitted more than once and never placed after a thread.\n3. The host function has the fixed signature `@host_container(%target: memref<4xi32>, %value: i32)`, fixed constants `0`, `4`, `1` named `%hz`, `%hf`, `%ho`, and a fixed single-store loop body over induction variable `%hi`.\n4. Threads are named by a monotonically increasing zero-based counter, `@thread_0`, `@thread_1`, \u2026, and the corresponding region is tagged `graph_name = \"graph_<same index>\"`, so symbol and graph name always share their numeric suffix.\n5. Each thread independently samples one of exactly three body shapes: the region directly in the thread body, the region inside one `scf.for`, or the region inside an `scf.if` inside one `scf.for`; loop nesting deeper than one `scf.for` plus one `scf.if` is never emitted.\n6. Each thread independently samples one of exactly three region flavors: a no-operand/no-result region, a two-operand store region, or a one-operand/one-result value region; no other operand/result combination is emitted.\n7. Shape and flavor are chosen independently per thread, so all nine combinations are reachable and the same module may mix them.\n8. The generated `scf.for` schedule is always the fixed trip range `0` to `4` step `1`, with constants named `%c_zero`, `%c_one`, `%c_trip` and induction variable `%iv`; the induction variable is never used inside the region.\n9. The `scf.if` site always uses the thread's `%enabled` operand as its condition rather than a freshly computed predicate.\n10. The empty-region flavor fixes `operandSegmentSizes = array<i32: 0, 0, 0, 0>`, `resultSegmentSizes = array<i32: 0, 0>`, type `() -> ()`, and an argument-less `^bb0`.\n11. The store flavor fixes `operandSegmentSizes = array<i32: 1, 0, 1, 0>` (one value operand, no stream operands, one memory operand), `resultSegmentSizes = array<i32: 0, 0>`, type `(i32, memref<1xi32>) -> ()`, and a body of exactly one `arith.constant 0 : index` plus one `memref.store`.\n12. The value flavor fixes `operandSegmentSizes = array<i32: 1, 0, 0, 0>`, `resultSegmentSizes = array<i32: 1, 0>`, type `(i32) -> i32`, and a body of exactly one `arith.addi %payload, %payload` feeding the yield; no other arithmetic op is ever generated.\n13. Region operands are always drawn from the thread's own block arguments in the fixed order `(%value)` or `(%value, %target)`; the `%ctrl` and `%enabled` arguments are never passed into a region.\n14. Internal SSA names are fixed strings (`%payload`, `%memory`, `%zero`, `%doubled`, `%region_out`) and are reused verbatim across threads rather than uniquified.\n15. `source_maps` is always the empty list; no populated source-map attribute is ever emitted.\n16. The stream operand segment of every region is always zero and the second result segment is always zero, so stream-typed publication operands and secondary results are never exercised.\n17. All memref types are fixed to `memref<1xi32>` inside threads and `memref<4xi32>` in the host; element types are always `i32`.\n18. Indentation, blank-line separation between threads, and the trailing newline after the closing `}` of the module are fixed formatting choices.\n19. No thread declares results, attributes beyond those shown, or additional operations before or after its region site other than the constants required by the sampled loop shape.",
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