Historical context: `PyMlirContext::liveOperations` was an optimization meant to cut down on the number of Python object allocations and (partially) a mechanism for updating validity of ops after transformation. E.g. during walking/transforming the AST. See original patch [here](https://reviews.llvm.org/D87958). Inspired by a [renewed](https://github.com/llvm/llvm-project/pull/139721#issuecomment-3217131918) interest in https://github.com/llvm/llvm-project/pull/139721 (which has become a little stale...) <p align="center"> <img width="504" height="375" alt="image" src="https://github.com/user-attachments/assets/0daad562-d3d1-4876-8d01-5dba382ab186" /> </p> In the previous go-around (https://github.com/llvm/llvm-project/pull/92631) there were two issues which have been resolved 1. ops that were "fetched" under a root op which has been transformed are no longer reported as invalid. We simply "[formally forbid](https://github.com/llvm/llvm-project/pull/92631#issuecomment-2119397018)" this; 2. `Module._CAPICreate(module_capsule)` must now be followed by a `module._clear_mlir_module()` to prevent double-freeing of the actual `ModuleOp` object (i.e. calling the dtor on the `OwningOpRef<ModuleOp>`): ```python module = ... module_dup = Module._CAPICreate(module._CAPIPtr) module._clear_mlir_module() ``` - **the alternative choice** here is to remove the `Module._CAPICreate` API altogether and replace it with something like `Module._move(module)` which will do both `Module._CAPICreate` and `module._clear_mlir_module`. Note, the other approach I explored last year was a [weakref system](https://github.com/llvm/llvm-project/pull/97340) for `mlir::Operation` which would effectively hoist this `liveOperations` thing into MLIR core. Possibly doable but I now believe it's a bad idea. The other potentially breaking change is `is`, which checks object equality rather than value equality, will now report `False` because we are always allocating `new` Python objects (ie that's the whole point of this change). Users wanting to check equality for `Operation` and `Module` should use `==`.