ALRP: The Floor That Does Not Rise - A Formal Analysis of the ARSI–Longevity Resonance Paradox: Reset Events, Queueing Instability, and the Hard/Soft Floor Distinction

ALRP — the ARSI–Longevity Resonance Paradox, named in the companion paper (Huynh, 2026a) — is formalized in this paper and argued to describe a structural dynamic without precedent in the history of technology diffusion. ALRP's defining feature is not that a technology fails to diffuse equitably — a well-documented phenomenon in existing diffusion-of-innovations theory (Rogers, 1962). ALRP's defining feature is that the same engine generating biological asymmetry — ARSI is simultaneously the only plausible engine capable of resolving that asymmetry through diffusion, and that this dual function does not converge toward symmetry, because each new discovery event resets the race before the previous leg completes. The paper formalizes ALRP's asymmetry gap, Δ(t), as the workload process (equivalently, virtual waiting time) of a queue with Poisson arrivals and a general, time-varying arrival rate — a well-established object in applied probability (Kleinrock, 1975); the time-varying generalization used here follows standard results for queues with non-stationary arrivals (Massey, 1985). Δ(t) jumps upward at each Biological Zero-Day Mechanism (BZM) reset event and is drawn down continuously by ongoing diffusion between events, floored at zero. The reset events' arrival rate is supplied directly by BZM's own Compound Poisson Jump Process, established in the companion formalization (Huynh, 2026d) at λ_bz ≈ 0.5 year⁻¹; treating the resulting gap as a full workload process additionally requires reset-event sizes to admit a well-defined expected value, an assumption this paper states explicitly rather than treats as already established. Under this formalization, the system exhibits queueing-type instability — permanent rather than transient backlog — once the compounding arrival rate of discovery events exceeds the bounded rate at which diffusion can process them. The paper disaggregates that diffusion rate into the four sequential stages a discovery must actually pass through — clinical validation, manufacturing scale-up, regulatory review, distribution and pricing — and argues, using ordinary bottleneck logic for stages arranged in series, that clinical validation for longevity-specific endpoints is a hard floor no plausible capital investment shortens, since biomarker proxies such as DunedinPACE (Belsky et al., 2022) mitigate but do not eliminate the need for long-horizon outcome validation, while the remaining three stages are soft or semi-soft floors that investment can move. The paper connects this instability condition to the corpus's Sandbox Geometry (Huynh, 2026, SBEA5), in which entropy accumulation turns permanently positive under structurally the same condition — a production term permanently exceeding a dampening term — offered as a structural correspondence between two formal traditions describing the same underlying phenomenon, not as a claim of mathematical identity between the two models. An illustrative, explicitly sensitivity-bounded numerical estimate places ALRP's instability threshold t* within roughly nineteen months to four years of the 2026 baseline across a wide range of assumed diffusion-capacity values, a range whose narrowness is shown to be a property of exponential threshold-crossing under logarithmic parameter uncertainty rather than an independent empirical validation in its own right. The paper grounds ALRP in five literatures that anticipate structural fragments of the paradox without combining them into its compound claim. Van Valen's (1973) Red Queen hypothesis supplies the logic of continuous adaptation required merely to hold relative rather than absolute position, though ALRP departs from it by locating the race within one generative process rather than between two competing populations. Hirsch's (1977) theory of positional goods explains why the asymmetry gap remains politically salient even as absolute outcomes improve for everyone. Aghion and Howitt's (1992) quality-ladder growth model supplies microfoundations for why innovation-driven systems do not structurally converge to distributional equilibrium, with ALRP adding that the rate of new rungs appearing is itself accelerating. Ablon and Bogart's (2017) RAND study of the zero-day vulnerability lifecycle supplies empirical diffusion-lag data from the security domain BZM's own name is drawn from — evidence of the same discovery-outpaces-remediation pattern in an adjacent field. Bostrom's (2002) analysis of differential technological development explains why no individual actor can unilaterally decelerate a compounding discovery frontier without ceding competitive disadvantage to actors who do not. None of the five, individually or in combination, anticipates ALRP's specific mechanism: a single engine, rather than two competing ones, generating both the asymmetry and its only plausible remedy, at rates that structurally cannot converge. The paper closes by arguing that F2 is more demanding than existing coordination-focused proposals assume: F2 investment directed at ALRP's hard floor specifically, rather than at governance capacity in general, is the only category of investment this formalization identifies as capable of moving the paradox's trajectory.