# Section 14: What the results establish about source reality

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<a id="section-14"></a>

## 14 What the results establish about source reality

 

*Status: Proved conditional conclusions.*

 A specified classical initial readout is incomplete if the unchanged Bell premises hold and $S>2$. The finite response entropy bounds distinguish Shannon entropy from guessing entropy and are sharp in the no-signalling class. This is not a proof that every description of observers is incomplete: (NS) must apply to the particular information being considered, and (D) is a physical premise rather than an experimental consequence of Bell violation.

The corrected tetralemma retains four explicit models without changing the premises to protect a false independence claim. Within the single-outcome class, (D), (MI) and (NS) each admit a separate countermodel when omitted. Branching abandons that scalar-outcome class; deterministic evolution of a complete vector does not satisfy (D) as written. The three-way alternative criticized in Proposition [2.8](/sealed-or-leaky/the-source-tetralemma#tet:trilemmafails) remains false.

The Bierhorst translation is genuinely finite-sample but is not unconditional. It uses the published entropy-production and soundness theorems for the original classical pre-existing adversary class, the actual causal-padding convention, a conservative correction for the printed Bell coefficients, and explicit postselection normalization. Under $\pi\ge\kappa$, nearly $1024$ Shannon bits follow from the extracted output; the aggregate entropy-production certificate gives the stronger $1304.97$-bit Shannon and deletion-smoothed response bounds. Neither gives $1024$ unsmoothed min-entropy bits of a complete source. Without a pass-probability lower bound, the threshold test of Lemma [3.12](/sealed-or-leaky/experimental-anchoring#exp:thresholdtest) still gives a conditional frequentist rejection bound for complete deterministic B-admissible models, not a posterior probability of an ontology.



*Status: Retained model-relative implications.*

 The trine results concern distinctions between ontic preparation distributions with equal density matrices. They do not establish incompleteness of every pure ray, universal wavefunction or individual state. The POVM and simulation results concern one declared preparation domain and apparatus class. The conservation result tracks exactly which tests remain accessible, rather than confusing fine-grained reversibility with observable recoverability.

Within the declared finite pilot constitution, the retained-record calculations include preparation, export, drainage, memory and gas-comparison errors. They are conditional predictions, not observed departures from quantum theory. The undrained endpoint asymptotic does not supply a retained reader at its larger scale. The massive writer construction uses its own constitutive laws. Mathematical nonequilibrium reweightings and hypothetical wires do not become physically available because a sensitivity calculation exists.



<a id="paragraph-18"></a>

#### Remaining gaps, not strengthened claims.

 

*Status: Not established.*

 The materials do not independently establish universality of deterministic source dynamics, completeness of any physical access catalogue, exact sequential setting independence for the pseudorandom implementation, an actual adversarial pass-probability lower bound, quantum-side-information security for the Bierhorst translation, or the microscopic implementation of the retained model-relative witnesses. The central-value Hensen, Rosenfeld and Storz numbers remain illustrations rather than finite-sample entropy certifications. The unavailable trial statistics are identified in Section [3](/sealed-or-leaky/experimental-anchoring#exp:section); no trial-level data have been invented.



<a id="paragraph-19"></a>

#### Other no-go results and the operational ceiling.

 

*Status: Literature scope and proved identification boundary.*

 Bell and CHSH constrain local response models with their setting-law premises <a id="citation-43"></a>[[3](/sealed-or-leaky/references#bib-Bell64), [4](/sealed-or-leaky/references#bib-CHSH69)]; they do not exclude every deterministic completion. Colbeck–Renner uses its own free-choice and extension-access conditions <a id="citation-44"></a>[[5](/sealed-or-leaky/references#bib-CR11)], not merely the existence of an unread source variable. PBR uses preparation independence to constrain overlaps of ontic laws <a id="citation-45"></a>[[9](/sealed-or-leaky/references#bib-PBR12)]; $\psi$-onticity is not $\psi$-incompleteness. Theorem [5.1](/sealed-or-leaky/operational-equivalence-and-its-restricted-alternatives#op:surrogate) remains decisive for unrestricted alternatives: reproducing every admitted complete record law supplies an operationally indistinguishable surrogate. None of the present conditional results identifies a unique underlying source or proves an unconditional ontology of observers.