Matroid online allocation research simulator

Edition: 8 October 2026. Initial decision: Defer direct product. The product interpretation and pricing are hypotheses; independent proof and buyer validation remain open.

Research finding

The one-sample matroid prophet result guarantees only an absolute reward fraction 2^-310 and does not assert a polynomial-time implementation. Independence and matched sample/value distributions are part of the statement.

Problem and buyer

A marketplace or resource-allocation researcher may want irrevocable choices under quotas with sparse historical information. Real demand can be correlated and can drift away from the independent-sample model.

What the finding could enable

A research simulator could isolate structural insights and test better behavior in a restricted matroid family. The theorem currently supports a theoretical feasibility result, not a commercially meaningful minimum revenue fraction.

Technical and commercial limits

The extremely small guaranteed fraction is around 4.8 times 10^-94. It does not imply useful empirical reward, learning under distribution shift or arbitrary quota systems. A feasible set family must actually satisfy matroid axioms.

Minimal architecture

Matroid model validator -> independent distribution fixtures -> online-policy simulator -> offline optimum reference -> expected reward report. Keep correlations and adversarial arrival policies as separate tests.

Existing alternatives and differentiation

Existing allocation policies and optimization modeling are substitutes. A restriction with a much stronger effective ratio is necessary to justify a business application.

Monetization hypothesis

Hypothesis: a research partnership rather than a revenue-optimization SaaS. Commercial development is deferred until a practical rule and meaningful empirical improvement are established.

Validation experiment

Compare partition-matroid cases with simple thresholds and greedy policies under independent and correlated values. Measure runtime and reward over many independent trials, not a single favorable run.

Conditions to reject or defer

Reject the direct product if the ratio remains the only performance evidence or if the independence assumptions fail for all reachable buyers.

Next concrete action

Inspect the hidden-vector selection construction for a implementable restricted case and record where the constant losses occur.

Source evidence

Repository sources are pinned to revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Selected scope notes and manuscript statements have been reviewed to the extent described above; these links do not represent successful kernel checks.

Family 111

Subject: One-sample matroid prophet inequalities against an almighty adversary.