Pablo Zavala · AI Safety Evaluation · Research Engineering
Temporal Admissibility: Auditable Decisions by Construction
A formal finance manuscript makes time a contract, so every decision reads only data published before it, look-ahead bias vanishes by construction, and each policy becomes a deterministic, auditable artifact, with a conceptual bridge to verifiable AI decisions.
A backtest is a promise about the past. The promise holds only when every historical decision used solely the information available at that historical moment. Once a single component peeks at a price, a filing, or a headline published after the decision it informs, look-ahead bias contaminates the record, and any measured performance turns suspect. My manuscript *Temporally Admissible Belief-to-Policy Compilation* (February 2026) attacks that failure at its root by making time a formal contract rather than a coding convention.
A caveat belongs at the front. The manuscript is pure theory. Across twenty-nine pages it derives every mathematical step in full, yet it reports zero experiments, zero datasets, and zero simulations. Read what follows as an architecture with its proofs, held separate from any empirical result.
Temporal Admissibility Turns Time Into A Contract
Temporal admissibility, the manuscript's central invariant, holds that every component of the decision pipeline reads only data whose publication timestamp precedes or equals the decision time. The construction starts from a bitemporal data model, where each record carries two timestamps: a *knowledge time*, marking when the underlying event occurred, and a *publication time*, marking when the record reached the system. Decisions key off the publication time, because a fact that has already occurred yet remains unpublished stays outside legitimate reach.
An operator the paper writes AS_OF(t) enforces the rule by restricting any data query to records published at or before time *t*. Those admissible records generate an increasing family of information sets, a *filtration* in the measure-theoretic sense, meaning a nested sequence of σ-algebras that grows as time advances. From that construction the paper proves its anchor result: whenever every data-access function respects the AS_OF guard and downstream modules consume only guarded outputs, the emitted policy becomes measurable with respect to the decision-time information set. The guarantee holds deterministically, for every outcome, rather than merely with probability one (almost surely).
The payoff is auditability by construction. Each decision becomes a deterministic artifact of the information available when the system made it, so a reviewer can replay the archived data and reconstruct the identical decision. Replay verification gains logical meaning, and the backtest contamination that White (2000) and López de Prado (2018) warn about loses its foothold.
Option Prices Encode A Market Prior
The pipeline builds two beliefs about the future and studies their disagreement. The first belief, the *market-implied prior*, comes straight from traded option prices through the Breeden-Litzenberger identity (Breeden and Litzenberger, 1978).
Consider a European call option, a contract paying the amount by which an asset price exceeds a fixed strike at expiry. The identity states that the second derivative of the call price with respect to strike, scaled by a compounding factor (the reciprocal of the discount factor), equals the risk-neutral probability density over future asset prices, meaning the distribution the market implicitly prices for where the asset will land. Curvature in the price-versus-strike curve, in plain terms, encodes what the market believes.
Real markets quote prices at finitely many strikes, so the paper approximates that second derivative with a finite difference on an unevenly spaced grid, and it confronts an honest tension. A coarse grid tames sampling noise while blurring detail, whereas a fine grid sharpens detail while amplifying microstructure noise, so the variance of the estimate grows like the fourth power of the inverse grid spacing. A convex shape-projection resolves the conflict, forcing the recovered prices to obey arbitrage-free curvature while damping high-frequency noise, so the extracted prior stays a valid probability distribution.
A Thesis Posterior Lives On A Simplex
The second belief, the *thesis posterior*, encodes the agent's own view, assembled from macroeconomic indicators, textual evidence, and knowledge-graph signals. Every such view has to remain a valid probability distribution, so the paper places it on the probability *simplex*, the set of weights across outcome bins that stay at or above zero and sum to one, using a concrete three-bin version for the outcomes down, flat, and up.
Belief updates arrive as *multiplicative tilting operators*, which reweight each bin by a strictly positive factor and renormalize. The paper proves that such operators keep any distribution on the simplex and stay locally Lipschitz, a smoothness property meaning that a bounded input change produces a bounded output change, which caps how hard gradients push back during training.
Calibration earns a rigorous anchor through the *logarithmic scoring rule*, which rewards a forecast by the log-probability it assigned to the realized outcome. The paper shows the rule is strictly proper, since truthful reporting uniquely maximizes the expected score, and that the gap between a truthful report and any other equals the Kullback-Leibler divergence, the information-theoretic distance from one distribution to another. Honest probability reporting and divergence minimization become the same objective.
Divergence Geometry Measures Disagreement
Disagreement between the market prior and the thesis posterior drives every downstream decision, so the paper measures it with a composite divergence built from three complementary parts.
A Kullback-Leibler term captures interior miscalibration, meaning mismatched likelihood ratios across bins. A tail-disagreement term compares the probability mass each distribution assigns to its extreme outcomes, surfacing divergence at the tails that interior bins would hide. A dependence-mismatch term, built from the Frobenius distance between correlation matrices, catches divergent co-movement across assets that any single-asset comparison would overlook. Combining all three prevents one failure mode from dominating the signal, and each term stays differentiable enough to feed the training machinery downstream. Separately, the paper develops a Wasserstein-1 distance over ordered outcome bins, drawn from optimal transport (Villani, 2009), which measures the cheapest plan to move probability mass from one distribution to another and reduces to a closed form summing gaps between cumulative distributions.
A Convex Compiler Turns Belief Into Policy
A compiler converts that disagreement signal into a portfolio through a convex projection. The compiler seeks weights close to a raw target while paying a transaction-cost penalty for turnover, subject to linear constraints: a capital budget, position bounds, turnover and leverage caps, sector limits, and governance rules.
Because the objective stays strictly convex and the feasible region forms a polyhedron, the paper proves a unique global solution exists whenever the constraints admit any feasible point. The Karush-Kuhn-Tucker conditions, the standard optimality certificate for a constrained convex problem, then supply more than a solution. Each constraint earns a dual variable, a *shadow price* reading as the marginal cost of tightening that limit. A large shadow price flags a constraint that materially shapes the allocation, so an analyst can interrogate which limits, whether capital, turnover, a sector cap, or a governance rule, bind the decision. The compiler thereby produces a policy alongside a legible account of why the policy took the shape it did.
Robustness Enters Through Wasserstein Ambiguity
Point estimates of expected return stay uncertain, so the paper hardens the compiler against distributional error. Rather than trusting a single estimate, it optimizes against the worst distribution inside a *Wasserstein ambiguity set*, a ball of distributions within a chosen transport radius of the empirical data.
Kantorovich duality makes the worst case tractable, converting an optimization over infinitely many distributions into a one-dimensional problem plus one term per data point. Applied to mean-variance objectives, the robust version reduces to familiar quantities plus explicit penalties that grow with the ambiguity radius, so distributional caution surfaces as interpretable variance inflation and return shrinkage rather than a hidden parameter tweak. Conditional Value-at-Risk (Rockafellar and Uryasev, 2000), the expected loss in the worst tail fraction of outcomes, is a well-known convex risk measure that fits the same mold, and the manuscript names it as a compatible risk measure rather than working the extension out.
Two further extensions round out the architecture while preserving its guarantees. A bilevel *decision-focused learning* layer trains the belief model by the quality of the decisions it produces, differentiating through the optimizer itself via the implicit function theorem. A reinforcement-learning adaptation head, analyzed as a two-timescale stochastic approximation with Robbins-Monro convergence conditions, adjusts online. Regardless of what either layer proposes, the convex projection runs last, so every emitted portfolio lands inside the feasible set by construction.
Auditability By Construction Transfers Beyond Finance
Strip away the finance, and a transferable idea remains: a decision pipeline can carry its own audit guarantee in its structure rather than bolting one on afterward. Temporal admissibility makes provenance a precondition, since each artifact depends only on inputs a reviewer can enumerate and re-access, and convex compilation makes the final step inspectable, since every binding constraint announces itself through a shadow price.
Such a posture rhymes with a theme across my other work: high-stakes automated decisions deserve inspectable records rather than fluent assertions. My Tribunal prototype pursues the same discipline for AI decisions, recording proposals, objections, vetoes, and dissent in a hash-chained ledger so a reviewer can replay how an answer survived challenge. One system constrains which information a decision may touch; the other constrains how a decision gets recorded. Both trade a confident black box for an artifact a skeptic can reconstruct.
The connection stays conceptual. My manuscript proves properties about a financial architecture, and the safety relevance travels as an analogy, auditability designed into the pipeline, rather than as a demonstrated result about AI oversight. Even as an analogy, the design lesson lands cleanly: build the audit into the mechanism, and every output arrives already reviewable.
Boundaries
- **Formal manuscript.** The document is a twenty-nine-page theory paper of definitions, propositions, theorems, and full derivations, requiring outside references only for foundational existence theorems.
- **Full derivations, zero empirics.** Every mathematical step appears in the text, yet zero experiments, datasets, simulations, or reported results accompany them; each performance-related property remains a theorem about the architecture, held separate from any measured outcome.
- **Finance domain.** The results concern financial decision systems specifically, covering option-implied densities, portfolio constraints, and market ambiguity sets, so transfer to other domains stays untested.
- **Implementation mentions describe design, held apart from experiments.** Passing references to an "implemented system" (for instance the three-bin down/flat/up posterior) record design choices; the manuscript reports zero runs, metrics, or evaluations of any such system.
- **AI-oversight relevance is a conceptual transfer.** The bridge to auditable AI decisions rests on shared design posture, auditability by construction, rather than on a safety result, a benchmark, or a claim about deployed oversight.
Sources
- My manuscript (PDF): Temporally Admissible Belief-to-Policy Compilation, a filtration-constrained, divergence-driven, convex-projected architecture for auditable financial decision systems, research manuscript, February 2026.
- Breeden and Litzenberger, "Prices of State-Contingent Claims Implicit in Option Prices," *Journal of Business*, 51(4):621-651, 1978.
- Villani, *Optimal Transport: Old and New*, Springer, 2009.
- Rockafellar and Uryasev, "Optimization of Conditional Value-at-Risk," *Journal of Risk*, 2(3):21-41, 2000.
- Mohajerin Esfahani and Kuhn, "Data-driven distributionally robust optimization using the Wasserstein metric," *Mathematical Programming*, 2018; Blanchet, Chen, and Zhou, "Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances," *Management Science*, 2022.
- White, "A Reality Check for Data Snooping," *Econometrica*, 2000; López de Prado, *Advances in Financial Machine Learning*, Wiley, 2018 (on backtest contamination).
- My essay Tribunal: When AI Decisions Need a Ledger.