Complete native Chan–He preprocessing

One finite 128-register program per fixed exponent computes every parameter, sorts and counts the initialized signed input, constructs the exact distinct-position frontend, builds its prime bitmap, executes both modulus searches and every heavy/light recursion, and returns a table of exact packed convolution instances. Counts, pointers and the common length are unsigned; packed payloads use the existing signed encoding. Runtime code does not read physical width.

Main definitions

This umbrella re-exports these definitions and results from its imported modules.

• program, flatProgram: structured and flat native code from PreprocessingProgram.
• width: the positive threshold (1300κ+7865) clog₂(n+2) from PreprocessingWidth derives fits.
• cost: all native instructions, including the final halt, from PreprocessingInput.

Main results

• runs_input: complete State.init execution and exact existing ChanHe.instances readback.
• cost_bound: at most Kκ (n+2)(sqrt(n+2)+1)(log₂(n+2)+1)^13 charged instructions.
• intermediates_polynomial, space_polynomial: every prefix at every admitted width uses only polynomial words and a polynomial initial address range.

The initialized-input controller, layout, native execution and resource composition are original. The reused finite Chan–He mathematics credits Anthropic, PBC and [CH20]. No solver or source machine simulation is assumed. This preprocessing endpoint leaves the Exact Triangle solver and complete subquadratic 3SUM composition, including the final 1.9992 exponent, separate.