Every verification standard is a claim about whose mathematics you are standing on. Ours should be checkable like everything else we publish. Below is the full lineage of the MIZAN engine — two statistical literatures and one cryptographic one — with exact citations and, for each, the specific thing the machine enforces. Where enforcement is partial or verifier-side rather than in-circuit, that is stated, because the boundary is the product.
The rule this page runs on
Attribution, not endorsement. None of the authors named here has reviewed, approved, or endorsed MIZAN, and nothing on this page should be read as implying otherwise. The citations run in one direction: we implement their published work, and we take responsibility for the implementation.
01The measure itself
In the machine — the base statistic every credential commits, computed net of the committed, disclosed costs, at a calendar-honest periods-per-year (the annualization itself is checked; inflating it was the first bug our own verifier caught in production).
The first school asks: given how the result was found, how much of it is luck?
Probabilistic Sharpe Ratio (PSR)
In the machine — recomputed inside the proof since era v11; the flagship credential reads PSR 0.7226 against the 0.95 bar and is published as NOT significant.
Deflated Sharpe Ratio (DSR)
In the machine — recomputed in-circuit since era v10, with the correction's key input — the number of trials — bound as the leaf count of a committed Merkle tree rather than self-reported. That binding is MIZAN's contribution; the correction is theirs. Our own flagship reads DSR 0.6779: not significant, published as-is.
Probability of Backtest Overfitting (PBO / CSCV)
In the machine — combinatorially symmetric cross-validation enforced in-circuit: S=16 blocks, all C(16,8)=12,870 splits enumerated, no sampling. Flagship reads PBO 0.0759.
Combinatorial Purged Cross-Validation (CPCV)
In the machine — purged, embargoed combinatorial paths proven in-circuit; the flagship's 5th-percentile path Sharpe is +0.003, and the credential says so.
03The multiple-testing program — White, Hansen, Harvey & Liu
The second school asks: out of everything that was tried, does the best survivor mean anything at all?
The Reality Check
In the machine — the intellectual foundation of the v11 multiple-testing suite: the null that the best model has no predictive superiority over the benchmark, tested across the full committed set, not the published survivor.
Superior Predictive Ability (SPA)
In the machine — Hansen's studentized, less-conservative refinement of the Reality Check, enforced in-circuit since era v11 over the committed trial set.
The haircut, and the minimum backtest length
Harvey, C.R. & Liu, Y.,
"Backtesting," Journal of Portfolio Management 42:1 (2015); Harvey, C.R., Liu, Y. & Zhu, H.,
"…and the Cross-Section of Expected Returns," Review of Financial Studies 29:1 (2016).
In the machine — the multiple-testing haircut logic informs the v11 gate family; MinBTL (minimum backtest length for the number of trials) is consistency-checked verifier-side, not yet fully in-circuit — an honest boundary we state everywhere the claim appears.
The garden of forking paths
In the machine — the diagnosis the committed trial ledger answers: even an honest researcher cannot count their own forks after the fact, so the ledger forces the count to exist before evaluation. The trial you didn't commit is a trial the credential doesn't cover — stated as a boundary, not hidden.
04The cryptography — proof instead of trust
The third literature had the enforcement mechanism the first two lacked.
Zero-knowledge proofs
In the machine — the founding idea: prove a statement true while revealing nothing else. Here: the statistics are real; the strategy stays sealed.
Merkle commitments
In the machine — twice, load-bearing both times: the price data is pinned to a Merkle root the proof must match, and the trial set is a Merkle tree whose leaf count IS the trial count. The tree is why N cannot be understated.
STARKs — scalable, transparent proofs
Ben-Sasson, E., Bentov, I., Horesh, Y. & Riabzev, M.,
"Scalable, transparent, and post-quantum secure computational integrity," IACR ePrint 2018/046.
In the machine — the proof system class every credential is minted in: no trusted setup, transparent, post-quantum-resistant. A 220 KB credential verifying in ~81 ms exists because of this line of work.
Count them: Sharpe; Bailey, Borwein, López de Prado, and Q.J. Zhu; White, Hansen, Harvey, Liu, and H. Zhu — two different Zhus, four years apart, both load-bearing; Gelman and Loken; Goldwasser, Micali, and Rackoff; Merkle; Ben-Sasson, Bentov, Horesh, and Riabzev. Twenty authors. The engine also runs on the RISC Zero zkVM — an engineering debt we acknowledge to its builders, distinct from the scholarly lineage above.
Two literatures, on the same campuses, across the same decades, that never met in a single system. MIZAN is the bolt between them.
What is ours, stated once and hedged: the committed trial ledger that turns N from a self-reported input into a structural property of the proof; era law, so a credential names its judge forever; and the practice of publishing our own refusals — including the flagship failure above — on the same wall as the passes. To our knowledge, no other production system enforces both statistical schools inside a zero-knowledge proof. That claim is falsifiable, and this page is part of how you'd falsify it.
Correction policy: if any citation above is imprecise, tell us and we will fix it publicly — the same rule we apply to our own numbers. [email protected]