The substrate catalog is the instrument. βrel(h) regresses 226 cross-object pairs across 5 altitude shells; the strongest pair correlates at r = +0.949 across 159 days, in 300–350 km shared shells, between two unrelated active payloads. Independent objects measure the same atmospheric forcing — the residuals are common-mode signal, not per-object noise.
Definitions: ρobs,i is the King-Hele residual atmospheric density inferred from object i's dh/dt; ρbase,i is the Vallado-climatology baseline at the same altitude. wi weights low-|σmag| dead-mass objects (clean atmospheric line-integrators) over high-coupling cascade participants (whose orbits cross too many wakes to be clean). βrel(h) is the linear sensitivity of normalized drag enhancement to apdaily, fit per-shell from differenced residuals over a 159-day window. Both observables refresh daily against the F2-validated GFZ-Potsdam 95-year archive.
| Shell (km) | n_obj | βrel p25 | βrel median | βrel p75 | positive sign |
|---|---|---|---|---|---|
| 200–250 | 10 | 0.0106 | 0.0640 | 0.0681 | 8/10 |
| 250–300 | 31 | -0.0020 | 0.0128 | 0.0142 | 19/31 |
| 300–350 | 32 | 0.0010 | 0.0066 | 0.0066 | 25/32 |
| 350–400 | 28 | -0.0038 | 0.0092 | 0.0102 | 18/28 |
| 400–450 | 23 | -0.0024 | 0.0122 | 0.0140 | 16/23 |
A15 (per-object correlation): 16 of 42 objects pass at r ≥ 0.3, 81% positive correlation. A16 (cross-object differenced-residual correlation): 163 of 226 pairs positive (72%); strongest pair r = +0.949. A17 PASS: βrel monotonic with altitude across the populated cohort.
| Shell (km) | n_obj | F factor | departure from Vallado |
|---|---|---|---|
| 450–500 | 12 | 0.88 | -12% below baseline |
| 550–600 | 11 | 2.01 | +101% above baseline |
| 600–650 | 24 | 1.34 | +34% above baseline |
| 650–700 | 6 | 1.13 | +13% above baseline |
| 700–800 | 34 | 1.38 | +38% above baseline |
| 800–900 | 8 | 3.61 | +261% above baseline |
| 900–1000 | 25 | 1.82 | +82% above baseline |
| 1000–1200 | 21 | 1.21 | +21% above baseline |
| 1200–1500 | 5 | 1.46 | +46% above baseline |
F = 1.0 means observed atmospheric density matches the Vallado climatological baseline at that altitude. The 850 km shell sits at F = 3.61 (3.6× nominal) — the catalog detected a real local thermospheric anomaly the climatology cannot. Coverage gaps where n_obj < 5 are surfaced explicitly per audit claim A9, not extrapolated.
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