# Overview and publication identity

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Learning Effective Interfaces from Opaque Stochastic Systems:  
Capacity, Selection, and Validation Limits

 Jeremy Rodgers  
 Independent Researcher  
 Website: [everythingequation.com](https://www.everythingequation.com)  
 DOI: [10.5281/zenodo.23075824](https://doi.org/10.5281/zenodo.23075824)

 29 September 2026  
 Revised preprint v2: post-hoc optimization sensitivity included

  

**Abstract.**

An effective stochastic interface can be precisely specified without being reliably recovered from restricted observations. We study this gap in finite software investigations, culminating in a same-evidence comparison on 48 opaque systems. A portfolio of probabilistic automata and controlled hidden-state models passes 1,063 of 1,152 registered complete-law tests at total-variation allowance 0.15, compared with 970 for a passive tree control and 869 for a minimax tree bank. A prespecified secondary portfolio without the bespoke group-aware candidates reproduces the broad gain. An elementary post-reveal capacity check rules out insufficient architectural expressiveness: all targets fit the general 16-state instrument family. Under the original fitting budget, however, only 39 fixtures receive an individually passing produced candidate and 37 receive one from calibration selection. A separate post-hoc sensitivity analysis targets the 11 failures, using six starts per latent size and at most 600 rather than 60 updates on unchanged public data. The expanded portfolio selects a passing model on five failures and contains one on seven. Four passing controls retain their original selections. Thus the original candidate-production gap is materially budget-sensitive, while selection and residual fitting failures persist. Exact conditional diagnostics show that the challenge regressions involve mixing preparation-dependent responses rather than simple loss of the observed challenge. Paired fixture summaries, full-law re-evaluation, and retrospective policy-equivalence audits support transparent reporting without altering primary scores. The study separates capacity, finite-budget production, selection and validation coverage; its same-author, outcome-selected sensitivity is not an independently authored benchmark or a new primary result. 

 **Keywords:** stochastic system identification; probabilistic automata; hidden-state models; model selection; optimization sensitivity; interface abstraction.