Local Success Before Delayed Failure: Horizon-Relative Observability of Hidden Degradation
Year: 2026
Type: preprint
Abstract: Structures that demand work from people or machines often meet their targets right up to a failure they did not see coming. We model a subject whose hidden capacity recovers and is depleted by the cost of imposed work, and a structure that watches only its own output, which couples to that capacity near failure. Above a cost threshold ℓ_c = ρc₀²/4γ, capacity reaches the coupling level, where output collapses, in a time bounded from both sides; until capacity nears that level, the output stays on target. The output is not formally blind: its Fisher information about capacity is suppressed by a factor e^{−2δ/s}, where δ is the remaining distance to coupling and s its sharpness. In a base case, a maximum-likelihood estimator that knows the model reads capacity from the KPI to within ±0.05 (95% of draws) 52, 18 and 9 days before the deadline for a 20% cut in work at 0.1%, 1% and 2% daily noise, and after it at 5% or 10%; a side output reads it from the first window. Holding a target above threshold is infeasible for any regulator; what knowledge of capacity buys is the decision to lower it in time. We then replace homogeneous background noise by functions awaiting closure, whose pull grows as their phase distance shrinks, and compare detectors on two tasks with separate calibration and test runs, dating alarms when they can be declared. In this benchmark a KPI with 2–5% daily noise decides, at the median, only after output collapse; 21 and 5 of 80 decisions come earlier. Among noisy channels, side outputs detect degradation earliest, 3–4 weeks after onset. For predicting output collapse the channels trade off. The rate of realized closures gives the longest median lead, 78–85 days at 4–6% false alarms, but misses 2–4 of 80 collapses. Side outputs miss none but lead by 56 days at 9% false alarms. The scheme is illustrated on wheel-loader telemetry and on a social structure, with six testable predictions. Contents of this record. AXIS_I_Local_Success_Before_Delayed_Failure_v1.0.pdf: the preprint (14 pages). AXIS_I_code_v1.0.zip: model, analyses and outputs; bash run_all.sh regenerates every number in the manuscript except the wheel-loader results of Section 5.1. AXIS_I_manuscript_source_v1.0.zip: text and typesetting sources. AXIS_I_prepublication_review_v1.0.zip: responses to five rounds of pre-publication review and a number-by-number concordance. AXIS series, paper I. Companion papers: AXIS II (civilizational patency), AXIS III (wheel-loader telemetry), AXIS IV (realized-transition time).
Author: Gątkowski, Sławomir Grzegorz
Language: English
Subfield: Safety, Risk, Reliability and Quality
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223856796