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Standard FFT pulsar searches sum harmonic powers and discard Fourier phases. For narrow pulses (1–2% duty cycle), losing phase buries the signal near the spectral noise floor: in archival Parkes LMC data, PSR J0443−68 sat at spectral S/N 5.8 at 32 harmonics, folded to 10.7, and confirmed at S/N 70.

Sifting near that noise floor by period and harmonic fold recovered 5 LMC pulsars (including 3.85 s J0520−67) and the SMC’s slowest radio pulsar (1.33 s J0103−72). Scott Ransom’s CoherentSearch.jl fixes the root loss: sinc-interpolating 60 complex harmonics into folded profiles with analytic σ.

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