The research frontier

Our current programme asks one question: when a company's history has gaps in it, which of those gaps are worth paying to fill before a constrained decision is made? In the literature this is decision-focused de-censoring. We have found it is not one problem but six, arranged as a staircase from an exact benchmark to an online learner. Each project stands on what the one below it produced (a benchmark, a verified kernel, or the boundary a negative result drew) and adds exactly one new scientific risk, fixed in advance.

The method The staircase The Lab

How the lab works

Seven steps, and a project is not a result until it has been through all of them. Most candidates do not survive. The ones that do are built so that someone who did not build them can run them again.

01 · Problem

State the decision exactly: what is chosen, under what constraints, and what a better choice is worth. No result begins before the problem is written down.
02 · Novelty threat

Name the closest prior art that might already solve it. The contribution has to survive that baseline.
03 · Contribution

Claim narrowly. Separate what is computationally validated from what is a general-method claim, and never conflate the two.
04 · Strong baselines

Beat the fair opponent. A speed-up over a naive solver is not a result if the tuned solver was already faster.
05 · Frozen falsifier

Declare the test, the seeds, the gates, the acceptance criteria, before the result is opened. One permitted validation run.
06 · Truth separation

Keep negative results as results. If tighter-and-safe still loses on wall-clock, that is reported and never buried.
07 · Independent replay

The standard we are building toward: a result should run again, from frozen inputs, for someone who did not build it. Today we reproduce internally, the de-censoring artifacts are not yet public, and independent external replay is the bar we are moving to and cannot claim yet.

The staircase

The six projects, easiest first

Read the difficulty as scientific risk. Each project states its exact problem, its evidence status as it stands today, and the reason it is worth doing, with a link to its paper where one exists.

Step 1 Reproduced

Exact Two-Budget De-censoring Benchmark

Problem — Fix a reproducible instance family for the core question, which censored outcomes to recover before a portfolio is allocated under an evidence budget and an intervention budget, with frozen seeds, an exact reference solution and declared acceptance gates.

Status — The frontier bench. Provides the frozen populations and reference values every project above it is measured against. The benchmark base of the staircase, so the rest can be reproduced instead of believed.

Why it matters — A shared, honest yardstick. Without an exact benchmark, every downstream claim of "faster" or "better" is unfalsifiable. This is the artifact that makes the others checkable.

Difficulty

3 / 10

No paper yet

Step 2 Backtested

Evidence-Law Decision Quotient (value of information over a constrained portfolio)

Problem — Solve the core selection exactly: given censored outcomes, a cost-and-success recovery law, and a constrained downstream portfolio, return which outcomes to recover, including certificates that prove when recovering nothing at all is the right call.

Status — Validated application kernel. Our exact solver matched every selected portfolio and ran 2.37x faster end-to-end than an internal scalar baseline on a small, frozen synthetic population. The computational result holds. A general-method novelty claim does not.

Why it matters — The first verified kernel on the frontier, built on the benchmark base below it. It turns an expensive, constrained decision from an approximation into an exact, internally reproducible solve, and defines the honest boundary the harder projects push against.

Difficulty

4 / 10

Read the paper →

Step 3 Negative result

Decision-Stability Screening Certificates (screening candidates before an exact re-solve)

Problem — Build a cheap certificate that rejects candidate evidence sets before any portfolio is re-solved, proving the downstream decision cannot change, and skipping the exact solve.

Status — First bounds rejected. Three certificates were provably safe and strictly tighter than the obvious baseline, yet all were slower end-to-end than the exact solver they were meant to replace. The lesson, kept as a result: decision-aware pruning only helps when it is cheaper than the work it avoids.

Why it matters — A sharpened open question. It tells every project above it what "cheaper" must mean, and leaves a precise door open: a screen cheap enough to pay for itself.

Difficulty

5 / 10

Read the paper →

Step 4 Backtested

Recoverability-Aware Adaptive De-censoring (sequential / adaptive information acquisition)

Problem — Sequence recovery under uncertain returns and re-plan as answers arrive: decide not just what to recover, but in what order, updating the plan when a recovery comes back positive, negative or partial.

Status — Positive adaptive signal. On a frozen block of twelve opened cases, 8 of 12 benefit and 4 show a clean batch-to-adaptive reversal, characterised exactly by a closed-form condition on the recovery economics. Selective stopping captured most of the premium. A small menu policy recovered nearly all of the adaptive value on those cases. Prospective confirmation is still pending.

Why it matters — A cheap, auditable policy that captures nearly all of the value of adapting: the difference between committing a recovery batch blind and buying information one answer at a time.

Difficulty

7 / 10

Read the paper →

Step 5 Idea

Distributionally Robust De-censoring (minimax-regret over an ambiguity set of models)

Problem — Choose what to recover to be robust across an ambiguity set of recovery laws, and never optimal under a single estimate that may be wrong.

Status — Idea stage, three structural findings. Together they establish which robust objective is the right one for this decision, why the obvious alternative can refuse to act at all, and why one tempting shortcut is provably unsound. The findings themselves stay in the lab. Next: a calibrated ambiguity set and a prospective test of robust validity.

Why it matters — A de-censoring decision that stays sensible when the recovery model is wrong. That is the property that separates a backtest from something you would trust in the field.

Difficulty

8 / 10

Read the paper →

Step 6 Idea

Online Two-Ledger Learning and Allocation (bandits with knapsacks / constrained online allocation)

Problem — Learn the recovery law from the recoveries you pay for while allocating two coupled, non-fungible budgets, evidence capacity and intervention capacity, under delayed, censored feedback.

Status — Idea stage, hardest on the frontier. We have a target regret decomposition and an argument for why the closest published results do not transfer to two coupled budgets. No bound, no policy, no experiment yet. The honest first milestone is a theorem in a restricted setting, then prospective evaluation.

Why it matters — The largest upside on the frontier and, honestly, the largest risk: a policy that learns what to recover while it spends on recovering it.

Difficulty

10 / 10

Read the paper →

Where the six stand

Two of these six are validated computational results, one is a kept negative result, one is a backtested signal awaiting prospective confirmation, and two are idea-stage formulations with no bound and no experiment. We label each as exactly what it is. And a project graduates when the pattern repeats on your own data behind a frozen falsifier, and never before.

What you can check today

The de-censoring artifacts are internally reproduced and not yet public. The theorem prover is written and licensed but its repository is not published yet. So what you can check right now is orhof: the operations-research library the prover is built to prove against, open source and independently readable today.

orhof — 251 OR functions Rainbow, where the code stands All proofs of concept

Start with the decision

If your history has gaps in it

If your organisation is sitting on incomplete history and a constrained, expensive decision on the other side of it, that may be a research problem. The first conversation settles whether it is, and whether we are the team for it.

Bring us a hard problem See how Find, Prove, Build works