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Library / First Principles Framework (FPF) - Core Conceptual Specification
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C.29.2:4.3 - Obtain the computational construction

If a known construction answers the question, recover its inputs, operative rules or steps and assumptions from its explanation and use it. B.5 supports that recovery. Check that the available operations can perform those steps and that their result has the required interpretation. A library or solver can supply the construction, but its accepted input class, result guarantee and failure behavior must fit the present use.

When the connection is not yet known, work on the missing operation rather than rewriting the output condition:

  1. Calculate a small instance with enough detail to see what is being produced.
  2. Identify what remains to be obtained after one available operation. Try to express that remainder using the same kind of problem or a known subproblem.
  3. Retain the intermediate information needed to join the contributions. If an operation overwrites a value still needed later, save it or change the ordering.
  4. State how the joined result satisfies the original answer condition, then try a case that changes a material assumption.

This is a way to expose and develop a construction, not a universal algorithm-discovery guarantee. Recurrence construction, search, optimization, numerical discretization and other techniques have their own subject methods. Use C.39 to find or develop a missing way; use C.40 when a workable change-and-test operation is already available and branching search is the live difficulty.

For a still-missing contribution, return a substantive task: the available inputs and operations, the result or intermediate relation needed, the conditions it must preserve, and what would count as a useful solution. “Find a better algorithm” is usually too weak. After a dense-state rejection, for example: “Given this circuit family and this requested observable, provide a representation and update/readout procedure with a justified error bound and a peak-memory estimate below the stated budget; do not materialize the full amplitude array in a hidden conversion.”