Your terse and borderline patronizing answers aren’t helping to advance the conversation, though you do link to an important book.

Capers Jones’ work does not “disprove” the triangle, and doesn’t even mention it. If anything, he implies that quality is a more complicated subject than the simple triangle implies, in that lower quality will have non-linear negative impacts on the project cost, time, and scope.

This is the triangle: https://en.m.wikipedia.org/wiki/Project_management_triangle

The original triangle assumes that as a PM, if you don’t recognize the trade off among scope, time, and cost, quality will suffer. This is true even with Jones’ data, but it is trite. The practices that help to ensure quality that are outside the triangle’s intent as a guideline: it is necessary to recognize these trade offs, but not sufficient, to ensure on-time, on-budget, sufficient quality and scoped delivery. One could manage tradeoffs among the time/cost/scope variables and still screw up their product’s quality due to poor methods and practices. Which is obvious, when you think about it.

Jones’ book also has a number of flaws - it’s hard to put his recommendations in practice (its more a survey than a “how to”), and he lacks data on a number of effective , newer practices that involve both quality, improved velocity, and requirements gathering or product/market fit. The result is that he tends towards promoting older practices that help quality but don’t have much impact on whether you’re building the right thing in the first place. To be fair, he admits this throughout the book, but being a data guy, shrugs and moves on to discuss what works with the data he has. A classic case of “looking for your car keys under the street lamp”. Nevertheless, it illustrates why quality pays for itself, which makes it important.