Fourier duality and spectral gap — both load-bearing, both unexamined

Instrument audit — Fourier duality and spectral gap

Audited together, by usage count rather than by suspicion.

Fourier duality. grep -ic "fourier" on the dictionary returned three. Two of the three are the same phrase, "Legendre as tropical Fourier". Fourier duality is placed on the index zero times — for a concept the dictionary leans on constantly, it has no entry of its own.

Spectral gap. Ten mentions. Every one is a table row reading "mass gap = spectral gap". Cheeger appears zero times. Spectral-gap arguments were supplied in three sections by Markov chains without anyone checking that those arguments require reversibility — which is where CASE-13 (is reversibility load-bearing, or incidental?) starts.

Verdict. Both load-bearing, both unexamined. The audit's finding is the absence of an examination, established by counting; it does not supply one. The spectral-gap half went on to CASE-13, settled by run 024. The Fourier half has no follow-up filed here.

Where the reasoning is. Run in the genesis chat (72cc6f92-e583-4b1c-82a5-591c1be06e23); the counts are quoted from the transcript. Filed retroactively 2026-09-13 from notes/DIGEST-genesis-chat.md.