# Travel times, columns and rare interactions

Run `python reproduce.py` with numpy and matplotlib. Standalone hypothetical models; runtime versions and generator SHA256 are recorded. CSVrows:603radar,101particle columns,2424count budgets and21concentration profiles, total3149.

Radar: depth=velocity*two-way-time/2. Time0..200ns at assigned uniform velocities.05/.10/.15m/ns. At100ns and.10m/ns the inferred vertical depth is5m. This is a straight vertical ray in a uniform medium; layering, dispersion, attenuation, reflections, lateral paths and unknown velocity can invalidate a simple depth interpretation. It does not identify composition or establish a utility map.

Profiles: two vertically stacked1000m slabs. Lower concentration0..2mg/m³ by.1, upper=2-lower. Every case has geometric column2000mg/m²=2g/m². A shared integral does not identify the vertical profile. No spectral weighting, cloud response or atmospheric retrieval is modeled.

Particle columns: density2.7g/cm³, length.1..100m on101logarithmic points. Nucleon column approximately density*length*100*6.02214076e23 percm². Optical depth tau=column*sigma with nominal sigma1.10e-38cm² per nucleon. Probability=-expm1(-tau), avoiding cancellation in1-exp(-tau). Nominal iron charged-current data near1.1GeV are transferred approximately to generic rock; target composition, neutrino energy and interaction channel matter. The cited cross-section uncertainty0.15e-38cm² is recorded but NOT propagated into these curves or the UI. No source, detector or spatial-resolution design follows.

Counts: each column is combined with incident counts10^9..10^16 at eight integer powers and efficiencies.1/.5/1. Expected mean lambda=N*P*eta. An explicitly independent ideal Poisson model has relative standard deviation1/sqrt(lambda), NOT a measured error bar or complete uncertainty budget. Zero expected counts return undefined relative standard deviation (blank/null), not zero or a finite precision. The model omits background, correlations, detector dead time, efficiency drift and cross-section uncertainty. At small lambda the relative standard deviation can exceed1; this is not a Gaussian confidence interval.

Checks compare tiny probabilities against tau-tau²/2+tau³/6 (maxrelative difference2.23e-16), independently convert the column through SI units, check radar default, constant geometric profile column, zero expected count, inverse-square-root count scaling and8invalid guards. Figures in SVG/PDF/PNG show velocity ambiguity and conditional probability/count limits. No heating, excavation, hazard prediction or operational experiment is proposed.

Sources: [USGS ground-penetrating radar field-method context](https://pubs.usgs.gov/of/2001/0425/intro.html); [PDG neutrino cross-section review](https://pdg.lbl.gov/2024/reviews/rpp2024-rev-nu-cross-sections.pdf). Numerical parameters are assigned examples; no measured study is reproduced as new data.