# E02-F — frequency, dose and recovery pilot

Status: unregistered pilot protocol. No specimens have been made, trained or tested.
This material-specific softening study is separate from the normalized M03-D stiffening
oscillator. A scalar fading state is not return-point memory or a learning algorithm.

## Primary observation and sign

Use force–displacement tangent stiffness K over a frozen low-amplitude strain interval,
at a fixed probe rate, temperature and preload. Define positive softening D=1-K/K0.
Calibrate fixture compliance and slip. A resonance readout is secondary unless its
observation model is calibrated: for unchanged effective mass, D=1-(fn/fn0)^2, while
relative stiffness change is +(fn/fn0)^2-1. The approximation for softening is
-2*(fn-fn0)/fn0. The original plan confused stiffness change and positive softening.
For a single underdamped ringdown, fn=fd/sqrt(1-zeta^2). A driven peak frequency is not
automatically fn. Damping, preload and fixture changes can mimic a stiffness change.

## Material and loading

Choose and record one material grade, batch, cure schedule, age and specimen geometry
after screening. Ecoflex 00-30 is a candidate for a literature-aligned pilot; evidence
for Ecoflex does not establish Dragon Skin 10 behavior. Follow the selected manufacturer's
current cure instructions; no invented post-cure schedule. Existing Ecoflex work already
reports cyclic softening, recovery and temperature/rate effects (Liao et al., 2020).
Absence from a short literature search is not proof of novelty.

Specify engineering strain epsilon(t)=0.25-0.25*cos(2*pi*f*t): 0–50% strain. Its maximum
strain rate is 0.5*pi*f, or 0.785/s at 0.5 Hz and 7.854/s at 5 Hz. Measure specimen strain
directly; a crank setting does not account for compliance, backlash or grip slip.

| Arm | Frequency | Cycles | Duration |
|---|---:|---:|---:|
| T1 | 0.5 Hz | 1500 | 50 min |
| T2 | 5 Hz | 1500 | 5 min |
| T3 | 5 Hz | 15000 | 50 min |
| T4 | 0.5 Hz | 150 | 5 min |

T1/T2 matches cycle count; T1/T3 and T4/T2 match duration. T1/T4 and T3/T2 compare dose
within frequency. No single pair isolates every effect. Strain, drive and dissipative
writing laws can be confounded by saturation, recovery, heating and cumulative cycles.
Include conventional viscoelastic and Mullins-effect rivals and specify their equations
and fitted parameters before a confirmatory model comparison. Loop work per cycle is
not automatically the instantaneous cp² writing rate or entirely dissipated heat.

## Acquisition, controls and readout disturbance

Acquire synchronized force and displacement with a proposed >=1 ksample/s/channel target,
anti-alias filtering and a validated phase delay; determine actual bandwidth from pilot
waveforms and loop-area convergence. An HX711 provides 10 or 80 samples/s; at 5 Hz that
is only 2 or 16 samples per cycle, insufficient to assume accurate loop area without
validation. An accelerometer is not a substitute for calibrated strain and force.

Measure calibrated mid-gauge temperature and relevant gradients. Display resolution is
not differential uncertainty. Match the entire thermal history in heat-only controls,
not just peak temperature. Include duration-matched 5-minute and 50-minute sham controls;
pilot thermal profiles determine additional heat-only arms before confirmation. A fixed
20-minute cooldown and a hypothetical two-minute time constant do not prove equilibrium.
Freeze an observed stability rule and internal/surface gradient allowance after the pilot.

Probe-only controls must quantify how much the low-amplitude readout itself writes or
erases memory. Randomize specimens within batches and blind analysis labels where possible.
Keep calibration/pilot specimens separate from confirmatory ones. Exclusions for tearing,
slip, acquisition loss and thermal excursions need objective thresholds fixed beforehand.
Use guards against motor pinch points, a temperature shutdown and containment for tearing.

Follow recovery at frozen times, e.g. immediately after the qualified cooldown, 24 hours
and seven days. Do not perform a destructive amplitude sweep at 24 hours on specimens
whose seven-day memory will be interpreted; use a separate cohort or defer it until last.
A single fixture holding 36 strips for seven days each implies about 252 fixture-days.
Validate removable clamp cartridges or parallel fixtures, or allow a longer schedule.

## Inference and power

Primary contrast: mean D(T2)-D(T1) at one prespecified post-cooldown time. A proposed
practical margin is 0.02 (two percentage points), requiring pilot justification.
Use specimen-level uncertainty with batch effects; repeated readings are not new specimens.
Ratios are secondary and require an identified nonzero denominator. Six specimens per arm
is a pilot, not a demonstrated powered confirmatory design. The supplied normal-approximation
planner targets a two-sided 95% interval above the positive practical margin with 90% power,
assuming independent equal-sized groups. For SD 0.02 and true effect 0.05 it suggests 10 per
group; effect 0.03 suggests 85. These are sensitivity examples, not a final sample size:
use a small-sample, batch-aware calculation, multiplicity plan and attrition allowance.

Freeze the primary time, margin, variance estimate, sample count, exclusions, stopping rule,
thermal matching and rival predictions before registering a confirmatory experiment.
A robust effect would discriminate only the tested material models under these controls;
it would not uniquely establish a memory-writing mechanism or validate M03-D.

Primary sources: https://doi.org/10.1016/j.polymertesting.2020.106478 ;
https://cronfa.swan.ac.uk/Record/cronfa53806 ; https://doi.org/10.1098/rspa.1999.0431 ;
https://cdn.sparkfun.com/datasheets/Sensors/ForceFlex/hx711_english.pdf .