QUESTIONS.md

Open questions

The live research backlog. Each entry graduates into the paper's arguments or into its own investigation; nothing is deleted, only marked resolved with a pointer to where the answer lives.

1. Formalizing the advantage condition under heavy tails

The condition — specialization gain per period > fatal-event frequency × price of compensation — needs a distribution over "fatal events" to be well-posed, and tail events are precisely what history underestimates. Is there a robust (minimax / heavy-tail-safe) version? What does the condition look like when the frequency estimate itself carries fat uncertainty?

Status (2026-07-13): minimax form now in hand — Theorem A (PROOFS.md §11) proves the worst-case version $\underline c(1-\alpha_0)(g+p) > \bar\varepsilon \delta(L-p) + c_d$, which uses only an upper bound $\bar\varepsilon$ on fatal mass and an upper bound $\delta$ on miss rate — never a point estimate of the frequency. Open remainder: making $\bar\varepsilon$ itself adversarial/unknown (vs. a declared budget), and the clustered-events non-i.i.d. regime flagged in FORMALIZATION.md §5.

2. Detector economics

When is detection provably cheaper than competence? The intuition is NP-flavored — verifying is easier than solving — but intuition is not a bound. Make it precise or drop it. A useful target: conditions under which a detector with cost o(competence cost) achieves a given miss rate.

Status (2026-07-13): now load-bearing, not just a curiosity — Theorem A (PROOFS.md §11, Remark 3) shows the architecture survives arbitrary loss severity $L$ only if miss rate shrinks as $\delta = O(1/L)$, which by the hypothesis-testing bound costs rent $c_d \sim \log L$. Cheap detection is exactly what keeps leakage bounded at logarithmic price — so this question's answer sets the sustainable ceiling on $L$ (exponential in the premium margin). Resolving the verification-vs-generation unit model (FORMALIZATION.md §8, via doubly-efficient proofs) would upgrade this from asymptotic to exact.

Lifecycle addendum (PROOFS.md §12): once the detector must be learned, detection economics gains a second bill — a one-time training cost linear in $L$ (rare-event certification of a near-zero miss rate), on top of the per-period $O(\log L)$ rent. Amortized, the advantage condition survives learning; the scarce input is labeled fatal examples, which a well-run system stops producing — a market for labeled catastrophes, demand priced at $O(L)$ per fatal category.

3. Adversarial removal

An opponent who crafts situations the detector misses defeats the whole architecture at its single point of failure. What does the detector constraint demand under adversarial distribution shift? Does the detector need diversity (multiple cheap detectors) the way the value theory says portfolios do?

Status (2026-07-13): one-shot case resolved — the adversary choosing the distribution once is exactly PROOFS.md Theorems 1–2 (value collapse inside a confounded defect). Open remainder: the iterated game with a learning detector, and detector diversity as a defense.

4. The human case

The founding statement is about individuals realizing potential. Treat with care: the ethics of calling a person's deficiency an advantage, and who owns the compensation channel — autonomy vs. dependency on the compensator. The economic framing that is clean for artifacts is loaded for people.

5. Composition

A fleet of removable-defect specialists vs. one generalist. The value theory's diversity results suggest the fleet wins, but every specialist carries its own detector — where does the summed cost of N detectors flip the answer? Related: can detectors be shared (one router, many experts), and what does sharing do to the single-point-of-failure problem in #3?

Status (2026-07-13): the router half is now priced — Theorem R (PROOFS.md §8) shows menu-of-specialists + direction router = one generalist detector, with the gap to ideal bounded by router confusion × (A+B); the router is itself a detector and obeys detector economics (O(1/L) fatal-side confusion at O(log L) rent). Open remainder: aggregating N detector rents vs one generalist's carrying cost, and whether iterated routing telescopes (PROOFS.md §14, item 4).

6. Is "removable" one concept or three?

Permanent removal (buy the capability — the defect becomes a capability), momentary removal (escalate this once), interpretive removal (the sealed-frame case, where the seal is never lifted and removal means compensating its fatal case). One spectrum, or three mechanisms that deserve separate treatment?

Status (2026-07-13): first hard evidence the split is real, on a different axis than expected — observation defects and capacity defects provably differ (PROOFS.md): transductive access rescues capacity defects and never observation defects, so a unified removability theorem was the wrong target. Also: removability is a coefficient ($\sigma_0$, residual separability), not a yes/no.

Refined (later same day) by Theorem 2′ (PROOFS.md §7): the value formula does unify — for any detector class, premium = support function of the class's ROC set at the economic price vector, coefficient = zero-leak capture capacity $\bar\sigma_0$; Theorem 1′ is the σ-algebra special case. So removability is priced identically for both defect types; the genuine split is joint realizability — whether one member of the class serves all confusable directions at once. One concept for the price, (at least) two for the escape routes.