## A Falsifiable Modeling and Measurement Program {#sec-impact-research-program}

The [AffineDrift epic](https://github.com/D-sorganization/AffineDrift/issues/4253)
owns theory and evidence. The
[Tools epic](https://github.com/D-sorganization/Tools/issues/5068) owns reusable
kernels, contracts and analysis. The
[UpstreamDrift epic](https://github.com/D-sorganization/UpstreamDrift/issues/9700)
owns engine integration and reproducible studies. Detailed source ownership and
existing test coverage are recorded in the linked inventory; a new solver must
integrate with these capabilities rather than duplicate them.

### Model Ladder

| Tier | Retained Physics | What It Can Establish |
|---|---|---|
| R0 | Detached rigid bodies, full inertia, instantaneous normal impulse | Analytic limits, frame conventions and impulse accounting |
| R1 | Existing lumped ball–head–hands chain | Sensitivity within its one-dimensional, initially relaxed assumptions |
| R2 | Distributed loaded shaft, head inertia, grip impedance | Local shaft response, preload, modal phase and torque transmission |
| R3 | Finite-duration frictional contact and flexible head/face | Launch, contact history and structural ringdown with spatial dependence |
| R4 | Qualified radiation and measurement transfer | Pressure spectra, directivity and decay at declared observers |
| R5 | Controlled physical and perceptual experiments | Equipment-specific effect sizes and population-specific sweetness ratings |

Moving from one tier to the next requires evidence, not simply more degrees of
freedom. Retain the simpler tiers as falsification references. A scalar
restitution coefficient cannot also supply a unique contact-force waveform for
R3 or sound prediction for R4. Several time histories can have the same impulse.

### Candidate Hypotheses and Falsifiers {#registered-hypotheses}

These are candidates for preregistered studies, not records of completed trials
or public preregistrations. Fix the intervention, operating range, primary
outcome, uncertainty treatment and equivalence margin before collecting the
confirmatory data.

| Hypothesis | Intervention and Control | Observable That Could Falsify It |
|---|---|---|
| Local shaft coupling alters eccentric impact | Same head/ball rigid state and contact law; attach/detach the shaft with declared initial conditions | Launch/spin and head rotation difference smaller than the registered equivalence margin |
| Tensile preload changes relevant modes | Hold material properties and measurement boundary fixed; sweep measured tension | Frequency/FRF changes inconsistent with loaded-beam prediction within uncertainty |
| Grip primarily alters later vibration in a tested regime | Match delivery; vary grip impedance; retain early and late windows | A repeatable early contact/launch change, or no predicted late modal change |
| Elastic phase matters beyond rigid delivery | Match rigid twist/pose and contact location; vary feasible modal phase | No reproducible change over the registered phase/energy range |
| Sound differences contain timbre information | Blind original-level and level-matched trials | Discrimination disappears after matching levels and controlling equipment/strike |
| Proposed acoustics model predicts a mechanism | Calibrate on separate fixtures; predict withheld clubs/strikes/microphone positions | Spectral/decay errors exceed limits despite matching ball launch |

Do not assume every effect is monotone. A phase-dependent or resonant response
may change sign. Construct physically compatible prestressed initial states;
removing the shaft without accounting for its energy is an intervention, not a
conservation-preserving state mapping. Report both the changed energy and the
meaning of the counterfactual.

### Verification Before Fitting

1. Establish analytic impulse and beam limits, dimensional consistency, common
   frames and units, and exact source provenance. Require symmetry/positive
   definiteness where applicable and refuse singular unsupported inputs.
2. Demonstrate momentum and energy/work accounting; conservative gyroscopic
   terms must do no spurious work, passive damping must not generate energy,
   and contact must not become adhesive without a declared law.
3. Refine time step, mesh, modal bandwidth and separation-event location
   independently. A converged ball speed does not prove a converged high-frequency
   pressure spectrum. Compare full and reduced frequency responses over the
   intended band, including antiresonances and phase.
4. Verify moving/inertial frame agreement and the mapping between engine
   generalized velocities and exported point wrenches. Engine agreement is
   numerical verification, not validation of tissue or shaft parameters.
5. Use independently measured mass/inertia, stiffness, damping and radiation
   data for calibration. Reserve configurations, trials or clubs for prediction;
   do not fit restitution separately in every comparison and then attribute the
   residual to shaft coupling.

Every implementation follows tests first (RED → GREEN → refactor), Design by
Contract, Law of Demeter and DRY. Shared physical laws live in Tools; UpstreamDrift
uses thin adapters; AffineDrift presents versioned evidence without silently
importing mutable neighboring repositories. Existing protected monograph
artifacts and synthetic study qualification retain their present boundaries.

### Measurements and Identifiability

Start with static mass/CG/inertia and shaft EI/GJ profiles. Use impact-hammer or
shaker tests for unloaded, tensioned and gripped configurations, recording
complex force-to-velocity responses and sensor mass loading. A held-club modal
test alone cannot identify all rotational grip impedances; excite and measure
the necessary ports or document the unobservable parameters.

Progress from a controlled plate/ball fixture to free-head and assembled-club
impacts, then robot or repeatable launch rigs, and finally players. For each
shot retain ball/head motion, actual contact position, force or validated
force reconstruction, strain/acceleration and calibrated microphone recordings.
State sampling rates and anti-alias filters relative to the retained bandwidth;
sub-millisecond contact demands more temporal resolution than ordinary swing
motion capture. Audio sampling does not substitute for force measurement.

Synchronize clocks and estimate channel delays. Preserve raw recordings and
calibration versions, reject clipping/double hammer hits, distinguish direct
sound from room reflections, and record ball temperature, wear, surface
moisture, tee/turf contact and the test environment. Wind noise and automatic
gain control can make otherwise convincing recordings unusable for amplitude
comparisons.

Fit a sensitivity/identifiability model before asking for player effects.
Separate equipment parameters, trial noise, sensor uncertainty and participant
variation. Use within-player and within-club repeated trials, randomized order,
registered primary outcomes, confidence/credible intervals, and an explicit
multiple-comparison policy for spatial/spectral maps. Determine sample size
from a pilot variance and a prespecified smallest meaningful effect; an
unsupported fixed sample count is not a power calculation.

### Completion Criteria and Present Status

The current deliverable is a corrected theoretical treatment, a source-grounded
inventory, linked implementation work, and the first rigid contact verification
foundation. Distributed coupled contact, calibrated radiated sound and the
player comparison remain research milestones. A reported small effect must come
with a tested configuration, uncertainty and a declared equivalence margin; a
reported large effect needs the same controls.

The scientific question is therefore open in a precise way: which differences
survive matched delivery, which originate in local elastic dynamics or the grip
boundary, which change launch, and which remain audible only in ringdown?