# Resource tradeoffs under declared assumptions

Run `python reproduce.py` with numpy and matplotlib. Four CSVs contain1,943rows:1,010 energy combinations,905 thermal samples,19 orbital candidates and9 optical sensitivities. These are hypothetical calculations, not measured savings, service latency or mission performance. Runtime versions and reference hashes are recorded.

## Same assigned CPU load, different power assumptions

Five identical hosts each have100 CPU-unit capacity. Total assigned CPU load W from0 to500 by5 is evenly divided over n=1..5 active hosts; utilization u=W/(100n). A case is feasible only when W<=100n. Infeasible rows retain inputs but have blank output fields. Assigned CPU load is maintained over 60 s; no executed work, completion or latency model. The same W is compared across choices of n. CPU units here are synthetic capacity-load units, not calibrated performance counters.

Active host power is70+180u² watts. Unused hosts either draw zero (off) or70W each (powered idle). Facility energy is total host power times60s times fixed PUE1.3. PUE is an assigned multiplier, not a cooling simulation. Energy per assigned CPU-load unit is undefined at W=0, represented by an empty CSV field. At zero work the selected n hosts still remain powered, so off-mode energy is not zero; the separate all-hosts-off option n=0 is outside this grid. At W=100, off-mode powers for n1..5 are250,230,270,325,386W; idle-mode powers are530,440,410,395,386W. This ranking comes from the chosen quadratic power law.

## Exact bounded thermal response

Thermal comparison uses constant W=100 distributed over n active hosts. Each active host has P=70+180/n²W, ambient and initial temperature25°C, thermal resistance0.1K/W and time constant300s. T(t)=25+0.1P[1-exp(-t/300)], sampled0..1800s by10. This is the exact first-order constant-power RC solution. The recurrence includes the required input factor(1-exp(-dt/tau)); it is independently checked against the closed form. It replaces an earlier arbitrary update and does not inherit any old thermal-policy claims. Heat coupling, fan control, temperature-dependent losses and throttling are absent. The longer thermal run is separate from the60-second energy interval and assumes assigned load continues unchanged.

## Orbital geometry and optical scale

Circular two-body orbits use mu398600.435507km³/s², spherical radius6378.137km, altitude200..2000km by100, minimum elevation30°. Angular rate n=sqrt(mu/r³), period2pi/n, speed sqrt(mu/r). Central half-angle psi=acos((R/r)cos(e))-e, and ideal visibility interval2psi/n. This assumes a central overpass of a stationary target with no Earth rotation; it is not a site/date pass predictor.

Near-nadir Rayleigh separation scale is1.22*lambda*h/D, all lengths in metres. Baseline wavelength550nm and aperture0.10m. This is not pixel ground sample distance and is not constant across the visibility interval. Atmosphere, pointing, pixels, noise, drag and lifetime are excluded. Chosen requirements scale<=5m and visibility>=120s select300–700km inclusive. Nine sensitivities use wavelengths450/550/650nm and apertures.05/.10/.20m. All19 baseline points are non-dominated for minimizing scale and maximizing visibility; strict improvement is required for domination, so equal points do not dominate each other. Pareto status does not select priorities or imply mission permission.

## Checks and evidence

All energy identities, zero-work undefined denominator, idle power boundaries and exact RC step/closed-form agreement pass. Independent ray/sphere triangle intersection agrees with visibility within5.12e-13s. Existing orbital results agree within1.78e-15 numerically after renaming the optical field; all nine sensitivity selections agree. Original prototypes/results are unchanged. The server model is newly specified, not an exact replay of the older scheduler. No measured hardware or physical validation follows.

Sources: [Google Borg research](https://research.google/pubs/large-scale-cluster-management-at-google-with-borg/) for allocation context; [JPL astrodynamic parameters](https://ssd.jpl.nasa.gov/astro_par.html); [NASA orbital mechanics](https://science.nasa.gov/learn/basics-of-space-flight/chapter3-1/). Model parameters and requirements are assigned teaching choices.


The portable numeric-baseline.json contains neutral reference numbers for standalone reproduction; no project prototype directory is required. energy_per_cpu_unit is energy per assigned CPU-load unit, not per job. Generator and reference hashes are recorded.