REPLICATION · O0-CRP-029

Track 1 R1 · Fair-Comparison Robustness — VAR beats or ties learned-Kalman across 6 (d, k) observability regimes at 3 horizons

STATUSVerdict: FAIR_COMPARISON_ROBUST. Substantive reading: in all 6 regimes at all 3 horizons (18 cells), VAR (unified representation) ties or beats learned-Kalman (explicit self/world separation). 0 of 18 cells show significant advantage for the explicit-separation architecture. Combined with CRP-021, coverage is now 9 regimes × 3 horizons = 27 cells with 0 cells against.
EVIDENCE TYPECOMPUTATIONAL · 6 regimes (d ∈ {4,8,16}, k ∈ {1,2,4,8}) × 20 seeds × 3 horizons.
REPLICATIONREGISTERED · nonlinear world (tanh dynamics), sparse observation matrix, non-stationary dynamics.
PHYSICAL VALIDATIONNONE
VERSION1.0.0
DATE

O0-CRP-029 — Scientific Record

**Title:** Fair-Comparison Robustness Across Extended Observability Regimes

**Program:** Track 1 followup R1

**Version:** 1.0.0

**Status:** COMPLETED · Executed 2026-07-28

**Preregistration:** v1.0.0 frozen before execution

Claim status

CLAIM STATUS: **FAIR_COMPARISON_ROBUST · CRP-021 finding replicates across 6 regimes and 3 horizons**

EVIDENCE TYPE: COMPUTATIONAL SIMULATION

PHYSICAL VALIDATION: NONE

Key finding

**Across all six (d, k) regimes at all three prediction horizons (τ = 1, 5, 20), Agent B (VAR — unified representation) ties or beats Agent A' (learned Kalman filter — explicit self/world separation).** In 0 of 18 (regime × horizon) cells does A' significantly beat B by > 20%. The CRP-021 "functional separation not supported at fair comparison" finding replicates across a much larger observability landscape.

Results by regime

| (d, k) | τ=5 A' NMSE | τ=5 B NMSE | B advantage % | B wins? |

|---|---|---|---|---|

| (4, 1) — small d, heavy partial | 0.752 | 0.718 | +4.5% | yes |

| (4, 2) — small d, moderate | 0.730 | 0.672 | +7.9% | yes |

| (4, 4) — small d, full obs | 0.769 | 0.694 | +9.8% | yes |

| (8, 4) — medium d (anchor) | 0.754 | 0.701 | +7.0% | yes |

| (16, 4) — large d, heavy partial | 0.862 | 0.931 | −8.1% | tie (within 10%) |

| (16, 8) — large d, moderate | 0.839 | 0.786 | +6.2% | yes |

At all three horizons, B ties or beats A' in **6 of 6 regimes**.

Positive control: oracle beats A' in all six regimes.

Preregistered verdict: **FAIR_COMPARISON_ROBUST**.

Substantive reading

1. **The CRP-021 fair-comparison result is robust to state-space dimension.** Testing from d=4 through d=16, across k/d ratios from 0.25 to 1.0, the unified VAR representation continues to match or beat the explicit self/world separation representation.

2. **The (16, 4) regime is the only near-tie case.** At d=16 with k=4, the learning problem is hardest (heavily partial observation at high dimension), and A' has a slight edge (8.1% at τ=5). This is *within* the preregistered 10% tie band, so it doesn't count as regime-dependence.

3. **The auxiliary functional-separation claim remains UNSUPPORTED at fair comparison.** Combined with CRP-021, this now covers 9 regimes × 3 horizons = 27 cells, with 0 cells showing significant advantage for the explicit-separation architecture.

Figures

![AL_vs_B_tau5](figures/01_AL_vs_B_tau5.png)

![relative_advantage](figures/02_relative_advantage.png)

Adversarial interpretation

  • **Could unified VAR win because of higher effective parameter count?** No — matched-param version is used (Agent B). Adversarial +2× (Agent Bp) exists but is not counted for the primary verdict.
  • **Could VAR win because system-ID fails in Kalman A'?** The `identify_system` succeeds for all regimes reported. When system-ID fails, the study drops the trial.
  • **Could higher d degrade both agents equally?** No — the oracle (which has access to true state x) continues to significantly outperform both, so a discriminating signal is present.

Not established

  • Anything about nonlinear systems.
  • Anything at d > 16.
  • Anything about biological brains — this is a purely linear-Gaussian toy.
  • That explicit self/world separation is *never* useful. There may be regimes we haven't tested (very sparse observations, structured noise, non-stationary dynamics) where it helps.

Cross-study implications

Combined with CRP-021, the auxiliary O/0 claim "functional separation serves local processing" is now UNSUPPORTED across 9 regimes and 3 horizons in linear-Gaussian systems. The next discriminating followup should be *nonlinear* dynamics, where explicit self/world separation could be more informative (registered).

Replication procedure


cd research/studies/O0-CRP-029/src
python run_study.py    # ~30s
python analyze.py

Reuses O0-CRP-021 `run_trial`, `KalmanAgent`, `VARAgent`, `identify_system`.

Registered followups

  • R1: Nonlinear world (add tanh nonlinearity to state dynamics), same architectures.
  • R2: Sparse observation matrix C (block structure).
  • R3: Non-stationary dynamics.

Revision history

  • v1.0.0 (2026-07-28): initial record.

Figures

Figure from O0-CRP-029: 01 AL vs B tau1
Figure from O0-CRP-029: 01 AL vs B tau1
Figure from O0-CRP-029: 01 AL vs B tau5
Figure from O0-CRP-029: 01 AL vs B tau5
Figure from O0-CRP-029: 01 AL vs B tau20
Figure from O0-CRP-029: 01 AL vs B tau20
Figure from O0-CRP-029: 02 relative advantage
Figure from O0-CRP-029: 02 relative advantage

Source proposition

“Followup R1 registered in O0-CRP-021 manifest. Tests whether the fair-comparison finding depends on state-space dimension d or generalizes.”

Conceptual provenance is not empirical support.

Related records

O0-CRP-021