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Generate the selected rank-one recursion on fixed tapes with paid cutoff comparison and two-sided remainder hooks - #7349
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…d remainder control
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Result
Emit a literal finite four-tape controller for rank-one children of width floor(e/N), stopping below max(N,L), with paid pre/post e mod N hooks and exact descriptor/ancestor restoration.
Novelty and predecessors
Separates the raw mixed-rank law r*floor(e/m) from the final rank-one specialization. Proves complete control time <= 200(P+1)*sum_v e_v and historical backing K0+(4+N/(N-1))*e_root+8.
Verification
Independent dense CPU (125 cases), source/cost proof review and remainder negative controls. Run python3 -B research/selected-rank-control/verify_all.py.
Limits and kappa
L is supplied; row grants, payload consumers and final selected native word remain. No new kappa; 0.00363005817 remains conditional.
Credit
Prepared for @CubeJerry with substantial OpenAI assistance; credit predecessor authors and PRs as detailed in the package.
Full proof, reproducibility, negative controls and provenance: https://github.com/CubeJerry/integer-mult-bounds/tree/9dfe6747b8553fd11b408f2b045c5954ef1e6eaa/research/selected-rank-control