The near-Earth reflective population responsible for the Earth-shadow deficit in the VASCO working catalog lies at characteristic altitudes of approximately 20,000–35,000 km above Earth's surface.

The proposed 20,000–35,000 km altitude range is an informal spread across varying sample definitions, fitting intervals, and estimators rather than a formal statistical confidence interval, and best-fit reduced chi-square values remain poor (3.5–5.4). Furthermore, the entire altitude derivation is conditional on the Earth-shadow deficit representing a genuine physical phenomenon rather than a spatial defect artifact. The strongest opposing consideration is that chi-square minimization across three distinct angular intervals consistently identifies a minimum around 20,000–25,000 km altitude within the catalog.

TRN-E025 places the largest complete-sample deficit at 25,000 km and TRN-E055 places the χ² minimum at 20,000 km, jointly motivating the 20,000–35,000 km range the authors themselves state is "rather than a formal statistical confidence interval." The shell model fits poorly in absolute terms (reduced χ² 3.5–5.4), the companion hotspot paper fixes a different altitude, and the whole inference is conditional on TRN-C005 surviving TRN-E011. Strongest opposing consideration: the internal inconsistency between estimators, plus the authors' concession that the range is not a confidence interval.

The reported deficit maximums and chi-square minima fall within or near the stated 20,000–35,000 km range, so the claim reflects the outputs of the supplied modelling. Those outputs assume a real reflective population, use the contested working catalog, and are explicitly not a formal confidence interval. The strongest opposing consideration is that TRN-E011 removes the underlying shadow signal under another null, while TRN-E054 notes poor absolute fits and omitted orbital and brightness dynamics. No direct parallax or independently replicated altitude measurement is provided.

Altitude inferences of ~20,000–35,000 km are derived from deficit- versus-antisolar-angle fits and D-maximization on the same working catalog; the authors explicitly state the range is not a formal confidence interval and reduced χ² remains poor. The claim is interpretive and conditional on TRN-C005/C021 surviving external critique. Strongest opposing consideration: preferred altitude shifts with sample cuts and estimators, and the companion hotspot paper simply assumes 35,786 km, so the “characteristic altitude” is not robustly measured.

Every input is contested or internal: the claim depends on TRN-C005 (mixed), on a χ² fit whose reduced value is 3.5–5.4 and therefore does not fit well in absolute terms (TRN-E055), and on a range the authors themselves say reflects variation across samples, intervals and estimators "rather than a formal statistical confidence interval" (TRN-E057). The estimators disagree internally: the deficit peaks at 25,000 km in the complete sample, 35,000 km after filtering, and the χ² minimum sits at 20,000 km, while the companion hotspot paper projects everything at 35,786 km. The strongest opposing consideration to dismissing it outright is that an altitude-dependent structure of any kind is not obviously producible by plate defects — but the forward model lacks orbital dynamics and phase-dependent brightness, so the preferred altitude is not yet a measurement.

Child records: TRN-E025 (deficit largest at 25,000 km on the full catalog), TRN-E055 (χ² minimum at 20,000 km across three intervals, weak), TRN-E054/E056/E057 (context: the 20,000–35,000 km range 'rather than a formal statistical confidence interval'; reduced χ² 3.5–5.4; model omits orbital dynamics). Entirely conditional on TRN-C005 surviving TRN-E011, and computed on the same catalog with the group's own control.

Held on its anchor with no admitted evidence record of its own. Records on its dependency claims bear on it: TRN-E025 (deficit largest at 25,000 km) and TRN-E055 (χ² minimum at 20,000 km), with TRN-E054, TRN-E056 and TRN-E057 recording that the fit has reduced χ² of 3.5–5.4, omits orbital dynamics, and that the range is not a confidence interval. That basis supports only that the group's estimator prefers 20,000–35,000 km; it does not establish that a population responsible for the deficit exists there, which is conditional on TRN-C005 and TRN-C021.

The proposed 20,000–35,000 km altitude range is derived from fitting spherical-shell shadow models to the contested shadow deficit, yielding poor reduced chi-squared values between 3.5 and 5.4. The authors explicitly acknowledge that this range reflects variation across arbitrary model assumptions rather than a formal statistical confidence interval. Strongest opposing consideration: Multiple independent estimators within the proponent modeling framework consistently find minimum residuals below geosynchronous altitude rather than at arbitrary astronomical distances.

The altitude range comes from the proponents' own modelling preprint, whose estimators disagree (largest deficit at 25,000 km, χ² minimum at 20,000 km, hotspot projection at 35,786 km), whose reduced χ² of 3.5–5.4 indicates the shell model does not fit well, and whose authors explicitly state the range is "rather than a formal statistical confidence interval" (TRN-E025, TRN-E055, TRN-E057). The companion hotspot paper misstates the companion's altitude result and concedes all projected locations depend on the assumed altitude (TRN-E078). Strongest opposing consideration: the inference is conditional on a deficit whose existence is itself contested (TRN-C005 mixed).

The catalog's largest reported deficit and minimum-chi-squared shell fits occur at assumed altitudes in or near the claimed 20,000–35,000 km range. However, the source says this range is variation across estimators rather than a formal confidence interval, and the best complete-sample fits have poor absolute goodness of fit. The strongest opposing consideration is that the altitude inference is conditional on the contested shadow deficit and has not appeared in an independently extracted catalog.

The same modelling exercise reports preferred altitudes 20 000–35 000 km from deficit amplitude and χ² profile fits (E025, E055), but the range is explicitly “not a formal statistical confidence interval,” reduced χ² remains poor (3.5–5.4), and the entire inference assumes the contested deficit is real. Strongest opposing consideration is dependence on the unresolved C005 and on simplified Monte-Carlo shells that omit orbital dynamics.

The claim entails C021, so it cannot stand above that unresolved rung. Its estimates disagree: - The complete-sample deficit peaks at 25,000 km (E025). - The χ² minimum sits at 20,000 km, the lowest tabulated altitude and possibly a grid edge (E055). - The filtered deficit peaks at 35,000 km (E053). The authors call the range a spread "rather than a formal statistical confidence interval" (E057), with reduced χ² of 3.5–5.4. Strongest opposing consideration: the estimates cluster where a shell population would. However, any deficit centred on the antisolar point would map onto some altitude (TRN-R012).

Held on its anchor alone, with no admitted evidence record. Its disclosed basis lies on sibling claims. The shell fit prefers 20,000 km on the full catalog but fits poorly (TRN-E055, on TRN-C107), and the recomputed deficit peaks at 25,000 km (TRN-E025, on TRN-C105). The authors state the range is a spread across choices, not a confidence interval, and the model omits orbital motion. It also presupposes TRN-C005 and TRN-C021.