The Service-Life Trajectory: A Label-Free Degradation Gauge, Its Competence Boundary, and the Drift a Frozen One-Byte Monitor Must Survive

The Service-Life Trajectory: A Label-Free Degradation Gauge, Its Competence Boundary, and the Drift a Frozen One-Byte Monitor Must Survive Randolph James Ferlic, M.D. and Kimberly Kate Ferlic — Fieldstone Analytics, LLC, Austin, TX, USA Preprint · Zenodo DOI: 10.5281/zenodo.23321165 · CC-BY 4.0 · Community: spiral-domain-encoder-campaign · a characterization of previously filed and published methods; no new algorithmic subject matter is disclosed. Abstract A frozen, deterministic, class-discriminant single-token encoder reduces a window of sensor features, through a fixed supervised projection and a small quantized codebook, to one 8-bit symbol and a bounded lookup-table decision; a label-free companion monitor — a self-twin — reads the nearest-centroid distance of each window to a codebook fit on healthy, in-distribution data. Every prior characterization of this device tested it on a time snapshot: train once, evaluate once, on data drawn from one window of calendar time. Deployment is not a snapshot. A fielded sensor runs for months to years while the monitored entity wears, operating conditions cycle, and the sensors themselves age. This paper tests the one deployment regime the program had not exercised head-on — the service-life trajectory — with two pre-registered questions. First: does the label-free self-twin track degradation as it accumulates over an entity's life? Second: does the frozen token survive the slow drift of months-to-years, and if not, is the drift a defect of the token or of the data? The degradation gauge. On a run-to-failure turbofan benchmark, the self-twin novelty is a near-perfect monotone wear gauge — median per-engine Spearman(remaining-useful-life, novelty) = −0.936 across one hundred engines, with a fixed-horizon detection area under the receiver-operating curve of 0.960 — and it replicates across all four subsets of the benchmark (including the hardest, six operating conditions and two fault modes) and across a second physical modality (a hydraulic test rig, cooler-degradation Spearman +0.921, area 1.000). The gauge is not trivial: it is at parity (within 0.005 area) with the standard unsupervised monitors it would otherwise require a separate subsystem to compute — Mahalanobis distance, the principal-component reconstruction (Q) statistic, Hotelling's T² — yet it is the same one-byte artifact that already performs the classification; a naive single-sensor monitor fails outright (area 0.590), and the only thing that clearly beats the free monitor is a label-trained random-forest regressor (area 0.984). The honest positioning is therefore a free, unsupervised health index at parity with classical monitors, not a supervised remaining-useful-life competitor — the free first tier of a prognostic stack rather than a replacement for a label-trained RUL model. A single fleet-level alarm threshold transfers across held-out units without per-unit tuning, at a controlled false-alarm rate it delivers a median detection lead of 62 % of life, and the verdict is stable across seeds. The competence boundary. The gauge is a graded clock only when degradation is a monotone departure from one coherent healthy manifold (mechanical wear, hydraulic cooling); for a multi-class chemical sensor array drifting over thirty-six months it is a loud detector but not a monotone clock (per-batch novelty 27–111× baseline, yet rank correlation with calendar time only 0.15), and it is blind to degradation modes that leave no signature in the cheap features (a hydraulic valve, Spearman 0.13). This is the program's competence-zone law restated on the service-life axis. Drift, and whether it is the token's fault. On the chemical corpus the frozen token falls from 0.980 at commissioning to 0.365 three years later — but a strong model is no refuge: a 300-tree random forest drifts worse (gap 0.369 vs the token's 0.170), so the loss is physical sensor aging in the data, not a token defect. The drift is mitigable, and the mitigation is a commissioning protocol composed with a filed label-free adaptation: labeling a budget of windows across time rather than in a single snapshot recovers more than the same budget spent at once (+0.16 at matched cost, control-confirmed), and stacked with filed label-free recentering it restores late-life accuracy to 0.586; the recentering lever beats an unsupervised domain-adaptation baseline (correlation alignment gives essentially no help here). Triggering recommission on the self-twin's level is a negative result — its non-monotone magnitude makes it a poor scheduler — so the monitor should raise the alarm and a calendar should set the cadence. Deployment requirements, surfaced honestly. Four deployment requirements fall out of the hardening: the gauge needs a sensor-validity gate (a dropped sensor zeroes a channel and silently halves the gauge, ρ −0.94→−0.62; a standard validity-check-and-impute step restores roughly half and, crucially, flags it — detection recall 0.94 at a 0.01 % false-flag rate with no harm to the clean gauge); commissioning needs cleaner labels than a tree model (the supervised projection is modestly more label-noise-sensitive, +0.034 vs a random forest at 20 % label noise); an int8 edge deployment preserves the decision in the competence zone (≥99 % agreement on separable data, less outside it); and confidence must be recalibrated per epoch under drift (a commissioning temperature does not transfer, but per-epoch recalibration cuts the calibration error 59 %). The monitor you get for free also detects novel classes (open-set area 0.96–1.00), and the token is bit-exact deterministic throughout. A single theme runs through the drift and the requirements: the binding constraint on a frozen-token deployment is labeled commissioning data, not compute or model capacity — the drift is mitigated most by when you label, the chief requirement is label cleanliness, and the companion sizing study shows the token is label-hungry — so the deployment economics turn on a one-time labeling budget a buyer can plan rather than on continual retraining. The synthesis is that a frozen one-byte monitor does hold up over a service life — as a graded gauge where degradation is monotone and single-manifold, as a loud detector everywhere it is a per-entity construct, and against drift that is physical and model-agnostic — provided four standard deployment requirements are met, each of which is characterized here. No new algorithmic subject matter is disclosed; every result is a property of a previously filed and published method, or a comparison against standard tools, measured on public data. Highlights · A label-free degradation gauge, for free — on run-to-failure turbofan data the self-twin novelty is a near-perfect monotone wear gauge (median per-engine Spearman(remaining-useful-life, novelty) = −0.936 across 100 engines; fixed-horizon detection area 0.960), replicating across all four benchmark subsets (including six operating conditions and two fault modes) and a second physical modality (hydraulic cooling, Spearman +0.921, area 1.000). It is the same one-byte artifact that already classifies — no second model, no labels, no added footprint. · Not trivial, and operationally usable — the gauge is at parity (within 0.005 area) with the standard monitors it replaces (Mahalanobis, principal-component Q-statistic, Hotelling T²) while a naive single-sensor monitor fails (area 0.590); a single fleet threshold transfers across held-out units without per-unit tuning; at a controlled false-alarm rate the median detection lead is 62 % of life; and the verdicts are stable across seeds. · A sharp competence boundary — the self-twin is a graded clock only under monotone departure from one coherent healthy manifold; it is a loud detector but not a clock for in-span multi-class sensor drift (novelty 27–111× baseline over 36 months, yet rank-with-time ρ = 0.15), and blind to degradation with no feature signature (a hydraulic valve, ρ = 0.13). The competence-zone law, restated on the service-life axis. · Drift is real but model-agnostic — over a thirty-six-month chemical sensor array the token drifts from 0.980 at commissioning to 0.365, but a 300-tree random forest drifts worse (gap 0.369 vs 0.170), so the loss is physical sensor aging, not a one-byte-bottleneck defect. · Drift is mitigable by a protocol, not a bigger model — labeling across time beats spending the same labeling budget at commissioning (+0.16 at matched 445-window budget, control-confirmed); stacked with filed label-free recentering it restores late-life accuracy to 0.586; the recentering lever beats unsupervised domain adaptation (correlation alignment gives ~no help). Self-twin-triggered recommission is a negative result — use the monitor to alarm, a calendar to schedule. · Four deployment requirements, surfaced with mitigations — a sensor-validity gate (a dropped sensor silently halves the gauge; a validity-check-and-impute gate detects at 0.94 recall, 0.01 % false-flag, no clean-gauge harm, and recovers ~half, flagging the rest); cleaner commissioning labels than a tree (+0.034 vs a random forest at 20 % label noise); int8 edge deployment safe in the competence zone (≥99 % decision agreement on separable data); and per-epoch recalibration under drift (a commissioning temperature fails; per-epoch cuts calibration error 59 %). Free: open-set/novel-class detection (area 0.96–1.00) and bit-exact determinism. · Honest integrity checks — two pre-registered expectations the data did not meet are reported as misses, not re-framed as successes: an operating-condition competence wall that did not appear (the per-entity gauge is condition-robust), and the self-twin's expected role as a monotone age-clock that was refuted (it is a detector, not an odometer). What this record contains · Manuscript_Paper58.pdf — the service-life-trajectory characterization (6 figures, 42 referenc