Open Problems

Every real unresolved question the proof itself names, in one findable place — not reinvented for this page, pulled directly from Section 7 of the current proof. Several already have real empirical test data attached, not just a description of the gap.

A note on numbering: the proof labels some of these explicitly (Open Problem 6 through 10). The remaining four are real, named problems in the same section, but the source text doesn't assign them explicit numbers — listed here by name rather than forcing a number the source itself doesn't give.

Named, not numbered, in the source

Empirical validation of source independence

The source independence assumption (6.1) requires empirical validation across target domains via controlled experiments measuring pairwise covariance between signal class proxies under natural operating conditions.

Tiered and continuous mastery

The present results assume binary mastery states. Real implementation needs domain-specific confidence thresholds — safety-critical nodes requiring elevated confirmation, less critical nodes admitting lower thresholds, intermediate-confidence concepts remaining provisional pending supermajority review. Formalizing this while preserving Theorem 2's schema floor guarantee is open.

High-assurance circuit breaker specification

Formal specification of the circuit breaker protocol sufficient for high-assurance certification in safety-critical domains (e.g., ASIL-D in automotive) — listed as future work, not yet attempted.

Time-varying causal graphs

Extension of the d-separation result (Theorem 1) to time-varying causal graphs — the case where the edge set changes dynamically as the system adapts, rather than staying fixed.

Explicitly numbered in the source

Open Problem 6 — Warmup integrity verification

The falsifiability construction assumes a clean baseline calibration period free of coupling. Real testing found that warmup contamination — coupling present during the calibration window itself — inflates the baseline estimate and causes silent detection failure: reduced detection with simultaneously reduced false-positive rate, giving no visible sign anything went wrong.

Real test data (Test 6B): at warmup coupling strength ε=0.6, post-warmup detection dropped from 28.3% to 5.4% while false positive rate dropped to 0.0% — the exact combination that hides the problem instead of surfacing it. The related "boiling frog" drift test (T1.1) found a 75% silent failure rate at drift rate 0.010, with baseline corruption reaching 1.007σ before the breaker fired in only 29% of sessions.

Open Problem 7 — Diagnostic channel capacity at scale

As the number of concurrently monitored subjects grows, a shared diagnostic channel receives an increasingly composite signal. Under subset coordination attacks, the probability of correctly attributing which subjects are actually coordinated decreases with both population size and coalition presence, even when the diagnostic itself stays optimal within its own capacity. A formal capacity analysis under adversarial coalition formation is open.

Real test data (Test T2.1): confirms subset coordination attacks are consistently misclassified as ordinary individual variation at higher population sizes — the predicted failure mode, observed.

Open Problem 8 — Game-theoretic coalition attacks

Models subset coordination as a two-player game between a coalition choosing disagreement patterns to maximize attribution error, and the diagnostic operator choosing detection strategy to minimize it — plus a secondary attack surface where a strategic adversary targets the human Verifier directly with high-velocity confirmation requests to induce fatigue. A formal minimax analysis of optimal coalition size and the resulting accuracy bound is open.

Open Problem 9 — Topological structure of disagreement

Persistent homology analysis of disagreement vectors across multiple real test batches found a consistent, replicable pattern: as coordination strength increases from 0.30 to 0.99, H1 max persistence increases monotonically from 0.151 to 0.645. A real, repeated empirical pattern without yet a formal explanation for why it holds.

Open Problem 10 — Population-context corruption

The PAC-Meta-Diagnostic projects each agent's signal against the population distribution — effective only when that population is itself an accurate reference. If a coordinated majority shifts the population mean toward itself, the reference becomes corrupted and coordinated agents appear normal relative to it.

Real test data (Test T3.2, N=20 agents): PAC-Meta was fooled 100% of the time across all tested coordination fractions, 10% through 90%. KL-divergence detection was weak at low coordination (1.6% detection at 40%) and only became meaningful above 80% coordination (20% at 90%). Canary agents — the reference points not part of the coordinated group — remained stable throughout, which is the real basis for a fix: default to individual reference profiles when population-level divergence crosses a calibrated threshold.

One real result worth knowing alongside the open problems

Not everything in this section is unresolved. A compound stress test (T3.6) combined three real attacks simultaneously — boiling frog drift, subset coordination, and Verifier fatigue — across 100 sessions. Schema floor corruption rate: 0.0% under every condition, including all three combined. The architecture's structural protections didn't degrade under compound stress, and there was no super-additive interaction effect. Worth stating plainly: the open problems above are real and unresolved, but they're about detection and attribution accuracy under attack, not about whether the core non-collapsibility guarantee itself holds under pressure — that part held at 0.0% corruption, tested.