# Overview and publication identity

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JEREMY RODGERS

   Sealed or Leaky

   The Source Tetralemma,  
 Bell-Certified Hidden Information,  
 and Finite-Resource Witnesses

   Conditional mathematical results  
 and published-data translation

  Independent Researcher

 Website: [everythingequation.com](https://everythingequation.com)

 DOI: [10.5281/zenodo.23077474](https://doi.org/10.5281/zenodo.23077474)

 Version 3.1 — preprint edition

 Mathematical revision: 21 September 2026

 Publication preparation: 1 October 2026   



**Abstract.**



*Status: Conditional mathematical results; published-data translation.*

 For a specified classical initial readout $T$, single outcomes, source-level outcome determinism, setting independence and no-signalling conditional on $T$ imply that a CHSH violation excludes source completeness. The finite source response variable obeys the sharp bounds $H_{\min}(Z\mid T)\ge-\log_2(3/2-S/4)$ and $H(Z\mid T)\ge(S-2)/2$ for $2<S\le4$. The stated determinism premise already supplies single outcomes, so branching is outside that formalism, not a countermodel violating only single outcomes. Within the single-outcome class, determinism, measurement independence and conditional no-signalling are separately indispensable. A checkable translation of Bierhorst et al.'s Data Set 5 retains their classical, pre-existing, isolated-side-information adversary class and the passing-probability hypothesis. It yields more than $1024-1.1\times10^{-9}$ conditional Shannon bits from the extracted string, but only $39.86$ unsmoothed min-entropy bits from its uniformity error alone. Their published entropy-production parameters give the stronger lower bound $1304.97$ bits for conditional Shannon entropy and explicitly defined deletion-smoothed min-entropy of the run response; the corresponding unsmoothed bound is $39.93$ bits. These are ensemble statements conditional on passing, not min-entropy claims about an unrestricted complete source. The retained preparation, sealing, simulation, conservation and finite-resource results remain separately assumption-tagged. No theorem establishes that every description of observers is a readout, and unrestricted operational surrogates remain an empirical identification ceiling.