I ∝ (1 − S) / S

Completeness, not specificity.

Status: a mental model, not tested. Direction only. No experiment tests this relation (logbook: no tier, nothing to grade). No constant, no proof, and no prediction about magnitude.

Reads as

I is the expected number of correction cycles. S is completeness: how much of what must be true the specification states. The more the specification leaves open (the larger 1 − S), the more correction cycles you should expect before the output is right. The count grows faster as S approaches zero. The formula gives the direction, not a count per freedom.

S is not the specificity dial. Completeness is how much of what must be true the spec states; specificity is how much of the how it pins, and the two are independent (Compendium section 4.5.1). The course also uses the word “dial”, for how much of the disciplines you apply, which is a third, separate thing. The per-project proxy S_realized is a different quantity again and does not validate the formula.

What it is for

It is a way to see why writing the spec first pays off: every ambiguity you close before generation is one fewer thing the assistant decides on its own, and one fewer thing you correct afterwards.

What it is not

It is not a result and it is not a claim under test. It does not tell you how many cycles a given spec will cost. In its stricter form it is I = k · (1 − S) / S with k unknown, in cycles, and S has no operational definition beyond the proxy S_realized. It has not been tested across practitioners.

Evidence

No experiment tests this relation. The AX conditions were improved by the author as they went, and AX scored structure on the retired 14-point rubric (logbook tier D, a demonstration, for the later conditions); it did not record correction cycles, so it is not offered as support. A cross-practitioner study that records correction cycles against specification completeness is future work.

Where to read more

• Spec completeness: what a complete spec carries.
• The evidence: what AX showed, with its bounds.
• Compendium section 9.4 (the convergence spiral): the statement and caveats, in the Compendium. Its wording of the evidence is looser than this page; this page follows the experiment logbook and the White Paper.