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Generate exact chronological compiler library tables with product aggregation and explicit binary and tape cost bounds - #7345
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…regation and explicit binary and tape cost bounds
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Result
Construct evaluated replication a_n, width B_n, leaf P_n and expanded unit O_n at all ranks through N for fixed separated default-height rules, without enumerating paid paths. Product aggregation preserves each chronological exit denominator.
Novelty and predecessors
#4507/#5071 give gcd/LCM batching and #4638/#5962 give width bounds; this adds exact all-rank generation with indexed Npolylog(N) bit work and a separately charged N^2polylog(N) fixed-tape simulation.
Verification
Author/independent arithmetic replay; 336 complete ranks and exit-pooling counterexamples at n=12 and 135. Run python3 -I -W error -B research/quantitative-rank-library/verify.py.
Limits and kappa
Metadata only: no emitted native word; selected ambient A=153^1920 is outside the default m=A specialization. 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/022461f115369efd988ef8c459907f5544bb8bb3/research/quantitative-rank-library