HvdH machine lemma CR.twR_spec (The twiddle program for the chirp table (namespace `NLogN.CR`))

The following holds (Lean statement, in the scope of module NLogN.HCrTw):

theorem NLogN.CR.twR_spec (M : MulSpec) (p R : ℕ) : TwSpec M twR p R (twCost p R)

Context. The lemma belongs to the part The twiddle program for the chirp table (namespace NLogN.CR): twR instantiates the abstract hypothesis TwSpec of chirpP_spec/chirpP_cost with the numerics program twDP (HNumTwD.lean): a wrapper copies p (hPp), R (hM2), c (hC) onto 28, 29, 53, runs twDP and restores; the whole is relocated by the swap 10 ↔ 54 so that it does not write the loop counter hQ = 10.

Formalization Note. This is a lemma of the Lean development NLogN, a multitape-Turing-machine implementation of the Harvey–van der Hoeven $O(n\log n)$ integer multiplication algorithm, used in the proof of NLogN.FIN.theorem_1_1_nlogn : IntMul.MulTimeBound fun n => n * Real.log n. All names refer to the definition bundles IntMul_HvdH_M_Defs1–IntMul_HvdH_M_Defs8 (namespace NLogN), built on the platform model Def_IntMul_MultitapeModel and the published reference Def_IntMul_HvdH_MachineRef. The machine layer: IState HS is a state of 64 item stacks; RM programs have a semantics p.run s, a definedness predicate p.ok M s and a cost p.cost M s relative to a multiplication spec M : MulSpec; zsz z is the bit length of $|z|$.