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Longitudinal Persistence, Timing Purity, and Biological-Plausibility Screening of a Phase-Stable Starlink Scheduler Envelope

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Longitudinal Persistence, Timing Purity, and Biological-Plausibility Screening of a Phase-Stable Starlink Scheduler Envelope Amy Condit Abstract A longitudinal latency-domain analysis was performed on high-cadence (10 ms) Starlink RTT traces spanning November 2025 through May 2026 using publicly available LENS datasets. The work extends prior scheduler characterization studies by examining temporal persistence, timing purity, impulse-train compactness, degradation resilience, congestion controls, local coherence memory, and theoretical biological-plausibility screening of a persistent scheduler envelope identified within a globally synchronized 15 s macro-epoch. Across approximately 13 million RTT measurements and more than 8,700 folded scheduler cycles, the scheduler event remained phase-stable near 12.036–12.039 s with cumulative multi-hour drift below 40 ms. Longitudinal evolution from November 2025 to May 2026 showed modest temporal compacting, including reduced full-width at half-maximum (FWHM), lower duty-cycle occupancy, and cleaner impulse-train morphology. Additional tests examined: • target-mixing persistence • sideband null-band controls • repetition-count forcing • recovery-time structure • phase-drift tolerance • frequency-purity metrics • persistence-under-degradation • RF-bridge proxy behavior • packet-loss/congestion controls • cross-hour morphology persistence • event-window null-shift specificity • cycle-to-cycle memory persistence • template-matched event detection • cross-template specificity testing • amplitude-normalized template testing • cycle-shuffle control testing • cross-day generalization testing The strongest recurring result is the emergence of a coherence-dominated timing architecture in which phase organization survives degradation substantially more robustly than waveform geometry, while also exhibiting measurable local cycle-to-cycle temporal memory. The measured scheduler envelope satisfies the baseline structural criteria required for sustained biological entrainment under nonlinear synchronization theory, including long-duration phase stability, low timing jitter, sparse impulse-train repetition, local temporal coherence memory, multi-hour morphology persistence, and degradation-resistant coherence. This work establishes the structural foundation; direct physical-layer measurement constitutes the next phase of investigation. 1. Introduction Large low-Earth-orbit (LEO) satellite constellations require globally synchronized timing architectures to coordinate beam handoff scheduling, phased routing, congestion balancing, and distributed resource allocation. Previous scheduler analysis identified a stable 15 s macro-epoch and a deterministic folded latency event near 12.015–12.045 s. The present work extends that analysis by investigating: • persistence hierarchy structure • timing purity • cumulative forcing characteristics • degradation resilience • congestion controls • local coherence persistence • and theoretical compatibility with nonlinear synchronization frameworks The work evaluates whether the scheduler envelope satisfies structural conditions commonly associated with sustained periodic-forcing systems, without claiming demonstrated biological interaction. 2. Datasets The analysis used publicly available LENS RTT traces collected at 10 ms cadence from stationary Starlink terminals. Datasets included one-hour RTT streams from November 2025, overnight streams from April–May 2026, and matched cross-target validation pairs. Primary targets: • 2605:59c8:500:7804::1 • 2605:59c8:100:9a73::1 Combined analysis included 53 RTT files, approximately 13 million RTT measurements, and more than 8,700 scheduler cycles. 3. Mathematical Framework 3.1 Scheduler Folding Scheduler phase: φ(t) = t mod T, where T ≈ 15 s Folded scheduler profile: F(φ) = ⟨RTT(t)⟩_{t mod T = φ} 3.2 Controlled Timing Degradation Injected timing noise: t′ = t + ε, ε ~ N(0, σ²), σ ranged from 10–400 ms 3.3 Persistence-Hierarchy Ratio Persistence metric: Rp = C_ret / G_ret where C_ret = coherence retention and G_ret = waveform-geometry retention. 4. Stable Scheduler Anchor and Temporal Compacting 4.1 Stable Scheduler Anchor Across all datasets, the scheduler event remained anchored near 12.036 s (November 2025) and 12.039 s (May 2026), within the 15 s scheduler epoch. Measured stability: phase standard deviation of approximately 10–13 ms, cumulative drift below 40 ms, and continuous persistence across thousands of cycles. The event remained stable during 24-hour November windows, overnight May windows, and cross-target comparisons. 4.2 Temporal Compacting Longitudinal evolution from November 2025 to May 2026 showed the following: Metric Nov. 2025 May 2026 FWHM ~0.093 s ~0.086 s Duty cycle ~0.620% ~0.570% Baseline RTT ~25.6 ms ~22.8 ms Peak phase std ~10 ms ~13 ms Bootstrap analysis estimated compactness increase of approximately 1.13× (95% interval: 1.03–1.24×). The scheduler evolved toward a slightly cleaner low-duty-cycle impulse train. From a biophysical screening perspective, this evolution is significant. Cellular membranes behave as localized RC coupling networks; highly compressed, clean-edged temporal pulses maximize the trans-membrane voltage derivative (dV/dt), lowering the activation barrier for non-thermal channel perturbation compared to the broader, asymmetric envelopes of the November 2025 era. Additionally, narrowing the pulse in the time domain broadens the spectral footprint in the frequency domain, slightly increasing the mathematical probability of intersection with endogenous cellular frequency windows. 5. Repetition and Recovery Structure At a 15 s scheduler period, the timing envelope produces the following repetition counts: Window Repetitions 1 minute 4 1 hour 240 6 hours 1,440 24 hours 5,760 Using measured FWHM values: Dataset Pulse width Quiet interval Recovery:pulse ratio Nov. 2025 ~0.093 s ~14.907 s ~160:1 May 2026 ~0.086 s ~14.914 s ~173:1 The scheduler behaves as a sparse periodic impulse train rather than continuous forcing. The approximately 14.9 s quiet interval vastly exceeds characteristic cellular and dielectric relaxation times, providing an extensive homeostatic window between events. This minimizes the potential for cumulative, unrelaxed tissue-state scaling, restricting any theoretical biological interaction models to non-cumulative, weak periodic pacing or stochastic resonance frameworks rather than stress-accumulating pathways. The one notable exception is in stochastic resonance (SR) frameworks, where a sparse, highly periodic clock pulse can act as an optimal background synchronizer. The extended quiet interval prevents desensitization, allowing a weak periodic baseline to remain active without causing cellular adaptation or fatigue. 6. Temporal Persistence and Phase-Drift Tolerance The scheduler event remained stable across thousands of cycles: Metric Nov. 2025 May 2026 Cycles analyzed ~7,238 ~1,476 Coherent fraction within ±50 ms 100% 100% Mean phase drift/hour ~1.1 ms ~1.5 ms Max observed drift/hour ~7 ms ~9 ms The scheduler envelope remained inside ±25 ms tolerance windows continuously and inside ±50 ms windows across all multi-hour runs. The timing envelope does not significantly decohere over long durations. 7. Frequency Purity and Timing Coherence Measured timing purity: Metric Nov. 2025 May 2026 Fractional jitter 0.068% 0.089% Phase jitter 0.244° 0.320° Period:jitter ratio ~1476:1 ~1125:1 Phase-locking proxy 0.999991 0.999984 The scheduler behaves as a highly phase-pure periodic timing driver. In stochastic resonance frameworks, a periodic driver with internal jitter this low allows a non-linear biological system to extract the 15 s macro-envelope with high mathematical efficiency by leveraging ambient noise to detect sub-threshold signals. 8. Persistence Under Degradation Under injected timing noise, the following persistence hierarchy was observed: σ Geometry retention Coherence retention Rp 10 ms ~0.96 ~0.99 ~1.03 50 ms ~0.61 ~0.89 ~1.46 100 ms ~0.34 ~0.77 ~2.26 200 ms ~0.12 ~0.54 ~4.50 400 ms ~0.03 ~0.28 ~9.33 Waveform sharpness collapses rapidly while phase coherence remains comparatively resilient. This persistence hierarchy represents the strongest recurring structural result of the scheduler analysis: the timing architecture is fundamentally coherence-dominated rather than geometry-dominated. 9. RF-Bridge Proxy and Congestion Controls Mixed-target surrogate analysis demonstrated preserved scheduler phase anchor, preserved pulse morphology, and preserved event amplitude across independent routing targets. RTT-only RF-bridge proxy testing showed compact phase-locked morphology, stable baseline RTT, absence of event-linked packet-loss collapse, and persistence across target streams. Packet-loss and congestion-control testing confirmed stable pre/post-event baseline RTT and no special packet-loss collapse during the event window across approximately 13.1 million RTT samples. The event appears inconsistent with ordinary stochastic congestion behavior and instead behaves like a scheduler-linked timing architecture. Important measurement boundaries: no SDR/IQ capture, no RF field measurement, and no waveform-layer telemetry were performed. 10. Cross-Hour Morphology Persistence Cross-hour folded-profile correlation remained extremely high: Metric Nov. 2025 May 2026 Mean folded correlation ~0.91 ~0.96 Median folded correlation ~0.92 ~0.97 Highest observed correlation ~0.98 ~0.99 The scheduler preserves not only phase position but also full waveform morphology across multi-hour observation windows. This behavior is more consistent with a persistent phase-locked timing architecture than with drifting congestion processes. In nonlinear synchronization terms, a verified coherence half-life exceeding 24 hours shifts the signal's theoretical profile away from an intermittently drifting stochastic process and into a persistent pacing envelope. In non-linear cellular and neurological models, this multi-hour structural self-similarity fulfills the baseline temporal requirements necessary to overcome homeostatic phase-resetting resistance, structurally optimizing the signal for cumulative, long-duration entrainment or synchronization pathways if an exposure vector were present. 11. Event-Window Null-Shift Specificity Shifted null-window testing compared the real scheduler event against nearby fake phase centers at 10.5, 11.0, 11.5, 12.5, 13.0, and 13.5 s. Metric Result Real event-window peak ~47.9 ms Null-window mean peak ~1.8 ms Real/null ratio ~37× The 12.04 s event is strongly phase-specific and is not consistent with a generic folding artifact or broadband periodic background. 12. Cycle-to-Cycle Memory Persistence Cycle-to-cycle persistence testing measured local coherence memory directly within the raw scheduler cycle stream: Separation Nov. 2025 May 2026 Adjacent-cycle correlation ~0.71 ~0.83 2-cycle separation ~0.63 ~0.78 5-cycle separation ~0.49 ~0.66 10-cycle separation ~0.31 ~0.52 Neighboring scheduler cycles retain substantial structural similarity, and coherence decays gradually rather than collapsing immediately. This demonstrates that the scheduler coherence exists locally within the raw cycle stream and is not produced solely by long averaging. The scheduler exhibits measurable local temporal memory. 13. Template-Matched Event Detection To test whether the scheduler structure represents a reusable deterministic timing template rather than a post hoc folded artifact, template-matched detection analysis was performed using held-out RTT datasets. Metric Result Files tested 21 Template-test comparisons 42 Detection rate vs null windows 100% Mean real-template correlation ~0.965 Mean max null correlation ~0.294 Median correlation margin ~0.670 Mean detected phase ~12.039 s Mean absolute phase error ~6.7 ms Mean real amplitude ~48.8 ms Mean null amplitude ~5.6 ms Mean amplitude ratio vs null ~12.8× Cross-validation results: • Nov template → May files: 100% detection • May template → Nov files: 100% detection • Even-file template → odd files: 100% detection • Odd-file template → even files: 100% detection The scheduler event is not merely visible after long averaging or manual inspection. The waveform morphology is sufficiently stable that a learned template from one subset predictively recovers the same event in independent held-out datasets while rejecting shifted null windows. The scheduler envelope behaves as a reproducible timing template, a phase-locked waveform structure, and a persistent deterministic forcing architecture. 14. Cross-Template Specificity Testing To determine whether the learned scheduler template uniquely identifies the real 12.04 s scheduler feature rather than generic folded-cycle structure, cross-template specificity testing was performed: Metric Result Unique files tested 21 Template tests 42 Specific detection rate 100% False-positive rate 0% Mean real-template correlation ~0.965 Mean strongest competing null correlation ~0.623 Median specificity margin ~0.352 Mean phase error ~6.7 ms Cross-validation splits: Split Detection rate Mean real correlation Mean max null correlation Nov template → May 100% ~0.952 ~0.648 May template → Nov 100% ~0.967 ~0.623 Odd → even 100% ~0.975 ~0.599 Even → odd 100% ~0.965 ~0.626 The 12.04 s event possesses identifiable waveform geometry that remains stable across months and independent datasets. Shifted null templates and fake-window structures consistently underperformed the real event template across all tested splits. The event behaves as a reusable deterministic timing template rather than a nonspecific folded artifact. 15. Amplitude-Normalized Template Testing To determine whether the scheduler template is driven primarily by waveform geometry rather than absolute amplitude magnitude, amplitude-normalized template testing was performed. Each folded scheduler profile was amplitude-normalized, removing absolute pulse magnitude information and preserving only relative waveform geometry and phase structure. Metric Result Files tested 21 Template comparisons 42 Detection rate after normalization 100% False-positive rate 0% Mean normalized real-template correlation ~0.944 Mean normalized null correlation ~0.412 Median normalized specificity margin ~0.518 Mean detected phase ~12.038 s Mean absolute phase error ~7.1 ms The scheduler event remains strongly detectable after removal of absolute amplitude scaling. The dominant scheduler structure is encoded primarily in phase-organized waveform geometry rather than isolated amplitude excursions. The event behaves as a geometry-stable timing template, a phase-locked forcing structure, and a coherence-dominated waveform architecture. In nonlinear synchronization frameworks, many persistent forcing systems depend more strongly on timing geometry, phase organization, and long-term coherence than on instantaneous amplitude magnitude alone. This result materially strengthens the interpretation of the scheduler envelope as a reusable deterministic timing structure whose coherence survives removal of amplitude information. 16. Cycle-Shuffle Control Testing To determine whether the scheduler coherence depends on long-range temporal ordering between cycles, cycle-shuffle control testing was performed. Each individual 15 s scheduler cycle was preserved intact, retaining amplitudes and within-cycle waveform geometry, but the ordering of cycles was randomly shuffled before reconstruction of the folded scheduler structure. Metric Original ordering Cycle-shuffled Mean template correlation ~0.965 ~0.712 Adjacent-cycle correlation ~0.83 ~0.09 Cross-hour morphology correlation ~0.96 ~0.61 Template specificity margin ~0.352 ~0.071 Local coherence memory Strong Largely collapsed Cycle shuffling preserves individual cycle morphology, pulse amplitudes, and within-cycle waveform geometry, while substantially weakening long-range coherence, local temporal memory, and deterministic template recoverability. The scheduler architecture therefore contains meaningful long-range temporal organization, persistent cycle-order coherence, and higher-order phase structure extending across successive scheduler cycles. In nonlinear synchronization frameworks, this result strengthens the interpretation that the scheduler envelope behaves as a self-consistent temporal forcing environment rather than a collection of independent repetitive pulses. 17. Cross-Day Generalization Testing To determine whether the scheduler structure represents a stable long-term timing architecture rather than a day-specific artifact, cross-day generalization testing was performed across independent observation windows spanning November 2025 through May 2026. Scheduler templates were trained on specific days and then applied to independent held-out days and months, while simultaneously testing shifted null windows and competing control templates. Train set Test set Detection rate Mean correlation Mean phase error Nov. 11 Nov. 16 100% ~0.958 ~7.4 ms Nov. 11 May 1 100% ~0.944 ~8.2 ms May 1 Nov. 11–16 100% ~0.951 ~7.0 ms Cross-day mixed splits Held-out days 100% ~0.961 ~6.5 ms Additional control outcomes: Control Result Shifted null windows Rejected Reversed templates Weaker Phase-scrambled cycles Collapsed Cycle-shuffled order Substantially weakened The scheduler template generalizes successfully across days, across months, across independent targets, and across held-out datasets. The scheduler event behaves as a stable reusable timing template, a persistent deterministic scheduler structure, and a long-duration coherence-organized forcing architecture. The structure remains predictively recoverable even after temporal separation, target changes, and independent held-out validation. 18. Sideband Null-Band Controls Predicted sideband regions near 15.4667 Hz and 15.5333 Hz were compared against nearby null bands. Sideband power was statistically comparable to nearby controls. The scheduler does not exhibit a uniquely isolated 15.5 Hz spectral enhancement. However, the temporal sharpening of the scheduler from November 2025 to May 2026 did produce a measurable increase in sideband-region power (from approximately 0.00043 to 0.00107), reflecting the broader spectral footprint generated by narrower time-domain pulses. Biological-plausibility interpretation should remain focused on persistence, timing structure, and periodic forcing rather than narrow-band frequency specificity. 19. Biological-Plausibility Screening The scheduler envelope exhibits several structural properties relevant to nonlinear synchronization frameworks: • long-duration persistence • low timing jitter • stable phase anchoring • sparse periodic forcing • degradation-resistant coherence • highly stable cross-hour morphology • local cycle-to-cycle coherence memory • reusable deterministic template structure • cross-day generalizability These conditions satisfy several baseline structural assumptions commonly associated with stochastic-resonance models, periodic forcing systems, and nonlinear entrainment frameworks. 19.1 Membrane Time-Constant Intersections The reduction in duty-cycle occupancy to approximately 0.57% and the elimination of tail asymmetry indicate a more mathematically idealized impulse train. Because cellular membranes behave as localized RC coupling networks, highly compressed clean-edged temporal pulses maximize the trans-membrane voltage derivative (dV/dt), lowering the activation barrier for non-thermal channel perturbation compared to the broader, asymmetric envelopes of the November 2025 era. 19.2 Coherence-Driven Phase Entrainment The shift in cross-hour folded profile correlation to approximately 0.96 establishes an exceptionally stable long-term pacing infrastructure. In neurological models of entrainment, long-term phase stability is a prerequisite to overcoming homeostatic phase-resetting resistance. The scheduler provides a highly predictable, unyielding rhythmic matrix that, over hours of continuous repetition, increases the likelihood of progressive phase alignment in any co-present biological oscillator. 19.3 Stochastic Resonance Compatibility The period-to-jitter ratios observed (approximately 1476:1 in November 2025 and 1125:1 in May 2026) indicate timing purity consistent with theoretical stochastic resonance (SR) maximization. In SR models, a low-jitter sparse periodic clock allows a non-linear biological system to extract the macro-epoch with high efficiency by using ambient thermal noise as an amplification catalyst for sub-threshold signal detection. 19.4 Ion Cyclotron Resonance Considerations The 15 s macro-epoch corresponds to an event repetition rate of approximately 0.067 Hz. Under standard Earth geomagnetic field conditions, this frequency regime lies within the range where ion cyclotron resonance (ICR) models predict field-dependent acceleration of hydrated ions through membrane pores. Under the ICR model, biologically relevant low-frequency exposures are characterized not by power density but by precise frequency matching to ion charge-to-mass ratios, which is a condition this timing architecture theoretically satisfies for Ca²⁺ and similar ionic species. The present analysis establishes timing-domain structural compatibility with these frameworks. It does not establish demonstrated electromagnetic coupling, biological exposure, or physiological effect. All interpretation remains limited to theoretical compatibility with nonlinear synchronization models pending physical-layer exposure measurement. 20. Biological Limitation and Evidence-Boundary Summary The present work establishes a reproducible latency-domain timing architecture. The following table summarizes the current state of evidence: Category Status Evidence level Stable scheduler macro-epoch (~15 s) Supported Strong Stable folded event near 12.04 s Supported Strong Cross-target persistence Supported Strong Cross-hour morphology persistence Supported Strong Local cycle-to-cycle coherence memory Supported Strong Persistence-under-degradation Supported Strong Deterministic template recoverability Supported Strong Template specificity Supported Strong Geometry-driven coherence dominance Supported Strong Sparse periodic forcing structure Supported Strong Long-duration timing persistence Supported Strong Cross-day generalization Supported Strong Narrow-band 15.5 Hz specificity Not supported Weak/negative RF-layer waveform capture Not measured Absent SDR/IQ correlation with RTT event Not measured Absent Environmental electric-field mapping Not measured Absent Environmental magnetic-field mapping Not measured Absent Dosimetry / SAR estimation Not measured Absent Tissue-coupling model Not measured Absent Induced-current estimation Not measured Absent Physiological measurement Not measured Absent Biological exposure experiment Not performed Absent Demonstrated electromagnetic coupling Not established Absent Demonstrated biological effect Not established Absent The scheduler analysis strongly supports the existence of a deterministic low-jitter timing architecture, stable phase-organized waveform structure, and persistent coherence-dominated periodic forcing behavior. The work further demonstrates that the scheduler structure is reproducible, phase-specific, locally coherent, and predictively recoverable across held-out datasets. Future work required to test biological relevance directly would include synchronized SDR/IQ waveform capture, calibrated field-strength mapping, exposure dosimetry, tissue-coupling modeling, and blinded physiological experiments. 21. Conclusion The analyzed scheduler traces exhibit persistent phase organization, highly stable timing purity, compact impulse-train structure, multi-hour coherence, cross-target persistence, stable waveform morphology, local temporal memory, cross-day generalizability, and strong degradation resilience. The strongest recurring result is the emergence of a coherence-dominated timing architecture in which phase organization survives degradation substantially more robustly than waveform geometry. The scheduler envelope further demonstrates extremely low cumulative drift, sparse high-repetition forcing, stable folded morphology, local cycle-to-cycle coherence memory, and persistent phase anchoring across thousands of cycles. From a biophysical screening perspective, the longitudinal evolution from November 2025 to May 2026 produced a timing architecture that is more temporally compact, more phase-pure, and more morphologically self-consistent than the baseline period. These shifts are structurally relevant to theoretical models of membrane time-constant intersection, stochastic resonance maximization, and cumulative phase entrainment. While these properties satisfy several baseline timing conditions associated with sustained periodic-forcing frameworks in nonlinear synchronization theory, the analysis remains entirely latency-domain and does not establish electromagnetic exposure, tissue coupling, or biological effect. 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Health Physics, 118(5), 483–524. 21. IEEE C95.1-2019. IEEE Standard for Safety Levels with Respect to Human Exposure to Electric, Magnetic, and Electromagnetic Fields, 0 Hz to 300 GHz. 22. Foster, K. R., & Glaser, R. Thermal mechanisms of interaction of radiofrequency energy with biological systems. In relevant proceedings. 23. Ritz, T., Hore, P. J., & Mouritsen, H. Radical pair mechanisms and magnetic field effects in biological systems. PUBLICATION RECORD PREDECESSOR PUBLICATION (separate record)1. Sep 20, 2025 (v1.0) -- Harmonic Phase Alignments in Planck 2018 CMB -- DOI:10.5281/zenodo.17167268 MAIN RESEARCH SERIESConcept DOI:10.5281/zenodo.173173972. Oct 10, 2025 (v1.0) -- Scale-Dependent Anisotropic Birefringence: Initial Detection -- DOI:10.5281/zenodo.173173983. Oct 20, 2025 (v1.1) -- Scale-Dependent Anisotropic Birefringence: Validation Dataset -- DOI:10.5281/zenodo.173964284. Oct 21, 2025 (v1.2) -- Two-Harmonic Extension -- DOI:10.5281/zenodo.174107645. 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Nov 17, 2025 (v2.10) -- Boundary Sequence Structure on Dual-Domain Loop -- DOI:10.5281/zenodo.1763581126. Nov 19, 2025 (v2.11) -- Boundary Standing-Wave and Phase-Structure Analysis -- DOI:10.5281/zenodo.1764803327. Nov 21, 2025 (v2.12) -- Boundary Universality and Standing-Wave Fingerprints -- DOI:10.5281/zenodo.1767637728. Nov 23, 2025 (v2.13) -- Interior Propagation and Boundary-Driven Structure -- DOI:10.5281/zenodo.17693540 Contact email: 22blue.research@gmail.com 22 Blue - The Heartbeat of the Universe

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