The Resonant Squeak Cascade: Named Ignorance, Verified Insufficiency, and the Ledger That Wouldn't Close

A research team can name an unknown, and the name can become the problem. This paper examines a single engineering investigation: a production-scale sequence model trains cleanly at one sequence length and exhausts memory at another, on the same hardware, after three separate real and verified fixes. The investigation's earlier sessions had assigned the unexplained residual a name — the resonant squeak cascade — and the name was the problem. Not because it was wrong, but because it was finished. It looked like an explanation, sounded like a mechanism, and satisfied the social and documentary demand for an answer, while the underlying accounting remained open by roughly a factor of two. Six concepts organize the case, and none of them is about memory. Named ignorance is a placeholder that terminates inquiry by appearing to complete it. The legibility tax is why good names for unknowns survive regardless of their truth. Verified insufficiency is the state of a fix that is real, necessary, and demonstrably not the cause. Closure arithmetic is the refusal to accept any account in which the books do not balance. The fourth-instance rule obliges a team to promote a recurring bug shape from incident to invariant. Attribution inversion names the tendency to blame the most legible recent event rather than the oldest surviving evidence. The case closed. The placeholder was retired into an enumerated, measured accounting, and the original question was answered end to end on real hardware. The methodological residue is the point: Sections 1-9 demonstrate the disciplines on one concrete, receipt-carrying case; Section 10 shows that each discipline transfers, unmodified, to incident response, process improvement, budget reconciliation, operations safety, and vendor attribution — any setting with a measurable budget, a record, and handoffs. The rules that forced closure were cheap and mechanical. What they require is not domain expertise, but a refusal to let a good name stand in for a closed ledger. The framework is derived from research practice, not presented as an experimentally validated result.