Conditional EEG–QRNG Protocol Validation Of Core Distinguishability Relativity (CDR)

Core Distinguishability Relativity (CDR) is a pre-registered relative-entropy reweighting framework designed to test whether an observed dynamical system is structurally sufficient under a specified reference Markov kernel, or whether residual transition structure remains detectable after controls, holdout evaluation, localization, complexity penalization, and saturation diagnostics. The previous empirical CDR validation consolidated results through Phase III. 0, including EEG-only, RNG-only, and first-generation joint EEG + RNG analyses. The present paper reports the subsequent Phase III. 1–III. 2 validation sequence, covering an advanced multi-subject EEG + RNG redesign, regime-aware and lagged conditional EEG–RNG analysis, multichannel EEG enrichment, and a completed surrogate-synchronized EEG–QRNG protocol validation. Phase III. 1 tested whether a richer global joint-state model could reveal EEG–RNG structure beyond single-domain baselines by incorporating multi-subject Sleep-EDF data, ANU QRNG-derived binary structure, informational proxy variables, latent inferred states, and quantum-aware proxy layers. The final advanced model, M5ₐugmentedfinal, did not improve over the strongest single-domain baseline. The registered result was a clean null: the joint test epsilon remained zero, EEG-only retained the strongest residual signal, RNG-only remained near null, incremental joint lift failed, subject-level generalization failed, BIC strongly penalized the augmented model, and proxy ablations did not reveal a proxy-dependent joint effect. This result motivated a methodological transition from global joint-state modeling to conditional predictive modeling. Phase III. 2A–D reformulated the EEG–RNG question through sleep-stage regimes, registered temporal lags, leakage-safe conditional CDR estimation, and two-channel EEG enrichment. These analyses used public Sleep-EDF EEG and ANU QRNG-derived streams that were not physically co-acquired and did not share an experimental clock. They therefore could evaluate representation, conditional prediction, negative controls, multichannel sensitivity, and model behavior, but could not establish real-time EEG–QRNG coupling. Across 168 valid conditional comparisons, Phase III. 2A–D detected 13 positive conditional-lift rows, including 7 multichannel rows, but no row satisfied the full strong-candidate criteria. Subject consistency failed, BIC failed, and epsilon-saturation diagnostics raised a warning. Phase III. 2A–D is therefore reported as an exploratory, non-confirmatory bridge toward synchronized protocol testing. Phase III. 2E implemented the synchronized EEG–QRNG analytical architecture end-to-end on a schema-valid, software-timestamp-aligned surrogate input derived from Phase III. 2D artifacts. The final analyzed surrogate input explicitly recorded sourceₘode = surrogatefromₚhase3₂d, syncₘode = softwareₜimestampₐligned, empiricalclaimₐllowed = false, injectₛignal = false, and injectₛtrength = 0. 0. The pipeline completed schema validation, synchronization validation, window construction, feature generation, registered lag alignment, leakage-safe conditional estimation, synchronized negative controls, official gate evaluation, gate-sensitivity diagnostics, and audit-bundle generation. The final Phase III. 2E run identified exactly one positive conditional-lift row, located inside the registered primary region: a 30-second window at lag +5 windows (+150 seconds), where multichannel EEG information improved held-out prediction of the next QRNG state relative to a QRNG-only autoregressive baseline. The selected Phase III. 2E primary lead showed baselineₑpsₜest = 0. 0, augmentedₑpsₜest = 1. 0, conditionalₗift = 1. 0, and a held-out log-likelihood improvement of +6. 068517. Required synchronized negative controls passed, the multiple-comparison guard passed, adaptive subject consistency passed at 1/10 subjects, and no official epsilon saturation was observed. However, the augmented model was not favored by the official BIC criterion, with BICᵢmprovement = -132. 193071. Consequently, the final scientific classification is surrogateₚrimaryₗocalizedₚredictiveₗeadbicₗimited. This result does not constitute empirical evidence of EEG–QRNG coupling, causal influence, or quantum-neural interaction. Rather, it completes the current public-data and surrogate-validation cycle of CDR by demonstrating that the synchronized analytical protocol is operationally ready, that exploratory and localized predictive leads can be separated from confirmatory claims, and that BIC-limited outcomes can be reported without inflating false positives. The required next step is a real concurrent EEG + QRNG acquisition using the same subject, the same session, a shared or auditable temporal reference, recorded synchronization diagnostics, and a pre-registered replication target centered on the 30-second, +150-second, multichannel EEG-to-QRNG-next configuration identified here. Related CDR Records: This manuscript is the third major public release of the Core Distinguishability Relativity (CDR) validation program. The foundational theoretical framework is available at: https: //doi. org/10. 5281/zenodo. 18841329 The previous empirical validation paper, consolidating earlier cross-domain CDR results through Phase III. 0, is available at: https: //doi. org/10. 5281/zenodo. 19831982