# AC12: conditional tidal-response inference

This is a standalone scientific teaching experiment. It contains original **synthetic** complex Love responses of a uniform-density incompressible Maxwell world. It contains no Cassini radio data, no measured Titan response, and no Lab Engine code.

Requires Python 3.11 or later, standard library only.

```sh
python3 analyze-response.py --input data --output rerun-output
```

The script reads the frozen CSV inputs; it does not regenerate random data. `data/provenance.json` specifies the synthetic generator, units, errors and scope. The expected output is in `expected-output/`. Independent detached runs were checked with CPython 3.13.11 and 3.9.6. The conditional one-parameter profile uses analytic response derivatives with bracketed roots, and writes chi-squared and viscosity to ten significant digits; this removes irrelevant minimizer-roundoff differences far below the assumed data errors.

Expected central results:

- Effective stiffness `z_h * mu_E`: about 825,175,861 Pa.
- Maxwell time: about 88,602.5 s.
- Six standardized residuals, two effective parameters, chi-squared about 4.00403.
- Every shell/solid row has exactly the same external response at every frequency under the stated rescaling.
- When elastic modulus is fixed exactly at 3.5 GPa, quarter-kilometre grid best thickness is 50.5 km; the local profile-increase-of-one grid interval is 49.5–51.75 km.
- The deliberately nonpassive positive-imaginary record is rejected under the positive-time-exponential convention.

`fitted_response.csv` contains observed/predicted components and every standardized residual. `shell_solid_family.csv` includes a fully solid alternative. Some thin alternatives exceed the interactive modulus range; their material plausibility is not asserted. `conditional_thickness_profile.csv` conditions on an exactly known modulus. `summary.json` records units, input hashes and limitations. Values close to the noisy best fit need not equal the noiseless Lab default.

The radial and gravity Love responses obey a fixed ratio only because **both layers have the same density**. This exact degeneracy is not a general theorem about stratified moons. The world radius is 500 km, density 1000 kg/m³, parent mass 5e26 kg, orbital semimajor axis 3e8 m and physical eccentricity 0.005. The three probe frequencies are teaching harmonic probes, not three observed constituents of a real moon.

The response uses `Re(amplitude * exp(+i omega t))`. A passive Love response has negative imaginary part. A paper's positive reported loss coefficient may use another convention and must be translated before comparison.

Physical reference: Beuthe, arXiv:1410.4735v1, 17 October 2014, Appendix A equations 105–116; Appendix C Maxwell correspondence; Appendices E/G work and eccentricity tide. Published DOI: https://doi.org/10.1016/j.icarus.2014.10.027. The public script evaluates the published shell geometric factor; the Lab independently solves the traction system. No publisher code or paper PDF is redistributed.

Actual-planet context and future-observation context are separate: Petricca et al. (2025), DOI https://doi.org/10.1038/s41586-025-09818-x; Petricca & Buccino (2026), DOI https://doi.org/10.1029/2026GL125753. This package does not reproduce their mission analysis, interior posteriors or forecast.

Original analysis script and original synthetic scientific materials: MIT license, included as LICENSE. Cited scientific papers retain their own licenses.