Math RefereeAn explicit power saving for the exact discrete Fourier transform
A logarithmic power saving in exact complex arithmetic
The proposed argument
The manuscript proposes a uniform exact DFT speedup by amplifying a finite saving for one two-coordinate kernel. Exact-width Fourier compilation and synchronized tensor sectors transfer that saving to small prime factors; a charged Bluestein reduction covers every length. Appendix A separately develops effective symbolic uniformization.
This reading guide covers the 31-page September 25 main manuscript. The finite-tensor and integer-multiplication companions are separate. Appendix A supplies a complementary qualitative route; the quantitative main argument uses the explicit network. Human assessment remains pending.
Reading order
- 01
1. Freeze the computational question
Read the root and operation contract before comparing bounds.
- 02
2. Obtain and amplify a finite saving
Track arbitrary auxiliary contents, residual dimensions and exact recursive batches.
- 03
3. Compile at the original width
Follow Newton/Toeplitz factorization and dirty-coordinate replay.
- 04
4. Synchronize the axes
Pack sectors and charge all prefix traversal and scalar products.
- 05
5. Cover every transform length
Check prime widths, CRT, chirp padding, the fixed-kernel transform and root extraction.
- 06
Appendix A: a separate qualitative route
Finite algebra extraction and a bounded printer complement the explicit main construction.
Follow the dependencies
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Your independent assessment
Check the computational model, arbitrary-content network identity and residual saving. Follow exact-width compilation, sector packing and all-length root/preparation costs. Assess Appendix A separately and compare prior lower bounds under their precise hypotheses.