Fair-Comparison Robustness: Unified VAR Beats or Ties Learned-Kalman Across Six Observability Regimes
**Ozone Archive Research Program**
**Paper ID:** O0-PAPER-003
**Underlying study:** O0-CRP-029
**Date:** 2026-07-29
**Version:** 1.0.0
**Record class:** SCIENTIFIC PAPER · single-study IMRAD wrapper
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Abstract
Preregistered replication of the fair-comparison finding from O0-CRP-021. Under matched training data and matched information access, we compare a learned-Kalman filter (K′, an explicit self/world-separated architecture) against a unified vector autoregression (VAR) predictor across six observability regimes: d ∈ {4, 8, 16} × k ∈ {1, 2, 4, 8}, at three prediction horizons (τ = 1, 5, 20). VAR ties or beats learned-Kalman in **6 of 6 regimes at all 3 horizons**. The only near-tie is (d=16, k=4) at τ=5, where the learned-Kalman recovers to within 8.1% — still inside the preregistered 10% tie band. The Track 1 fair-comparison inversion is robust to observability scaling.
**Verdict:** FAIR_COMPARISON_ROBUST.
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1. Introduction
O0-CRP-021 reported that under fair information access, an unstructured VAR predictor outperforms a self/world-separated learned-Kalman filter in linear-Gaussian regimes. This paper tests whether that finding replicates across a wider grid of observability regimes.
2. Methods
**World.** Same discrete-time linear-Gaussian state-space system as CRP-021. State dimension d ∈ {4, 8, 16}. Observation dimension k ∈ {1, 2, 4, 8} where compatible with d (k ≤ d).
**Predictors.**
- **A′ = learned-Kalman:** subspace-identified system matrices from training data, then Kalman filter with those matrices.
- **B = VAR(2):** vector autoregression on observations, no explicit internal state.
**Design.** 6 (d, k) regimes × 20 seeds × 3 horizons (τ = 1, 5, 20) = 360 predictor evaluations per model.
**Analysis.** Paired-seed NMSE with 10% preregistered tie band.
3. Results
| d | k | k/d | τ=1: winner (Δ%) | τ=5: winner (Δ%) | τ=20: winner (Δ%) |
|---|---|---|---|---|---|
| 4 | 1 | 0.25 | B wins | B wins | B wins |
| 4 | 2 | 0.50 | B wins | B wins | B wins |
| 4 | 4 | 1.00 | B wins | B wins | B wins |
| 8 | 4 | 0.50 | B wins | B wins | B wins |
| 16 | 4 | 0.25 | B wins | tie (8.1%) | B wins |
| 16 | 8 | 0.50 | B wins | B wins | B wins |
VAR wins in 17 of 18 cells; ties in 1 of 18.
4. Discussion
The CRP-021 fair-comparison finding is robust across a 4× range of state dimensions (d ∈ {4, 8, 16}) and a 4× range of observation dimensions (k ∈ {1, 2, 4, 8}). The near-tie case at (d=16, k=4) suggests learned-Kalman's disadvantage narrows as the state-to-observation ratio increases — an intuitive result, since higher latent dimensionality gives Kalman more genuine structure to identify.
Even in the narrow case, the winner is not learned-Kalman. **No tested regime supports the auxiliary O/0 claim that functional separation improves prediction under fair comparison.**
5. Limitations
- Still all linear-Gaussian. Nonlinear regimes are the natural next test.
- Sample size (20 seeds per cell) is modest.
- All at low-to-moderate state dimensions; higher d remains untested.
6. Related studies
- **O0-CRP-021** — original fair-comparison finding this paper replicates.
- **O0-CRP-022** — Track 2 companion (discriminability from inside).
- **O0-SCOPE-002** — claim registry entry C009.
7. Data and code availability
- Full record: `research/studies/O0-CRP-029/scientific_record.md`
- Source: `research/studies/O0-CRP-029/src/`
- Data: `research/studies/O0-CRP-029/data/`