research
- 2026 Allocating Cents Without Losing the Total Splitting an integer-cent amount in proportion to weights creates fractional claims on indivisible units. This note derives largest-remainder allocation using only integer division. It prove… technical note pdf · txt
- 2026 Equal Totals Do Not Identify Equal Records A reconciliation can reproduce both the number of records and their total amount while containing the wrong records. This note gives an explicit counterexample, proves the additional inclusi… technical note pdf · txt
- 2026 Idempotency Is an Invariant An idempotency key is useful only when the stored key and the protected effect evolve together. This note defines a small ledger state machine and proves, by induction, that one committed ef… technical note pdf · txt
- 2026 Matching Marginals Is Not Matching Data A synthetic dataset can match every one-variable frequency in a reference dataset while reversing its relationships completely. This note constructs such a pair, derives the complete feasibl… technical note pdf · txt
- 2026 Retry Budgets and Collision Bounds A retry policy should state which resource it bounds. This note separates a deterministic bound on attempts and elapsed time from a probabilistic model of success. It derives finite geometri… technical note pdf · txt
- 2026 Absence of Errors Is Not Evidence of Completeness A fiscal product that books webshop revenue without a human watching the feed has to answer a question that looks too simple to write down: how do we know that what arrived is everything tha… working paper pdf · txt
- 2025 When Summation and Rounding Fail to Commute The questions in this paper are elementary. They can be stated in one line each, and a reader who has divided integers will already suspect the answers. That is not a reason to leave them un… working paper pdf · txt