# Scientific Record — O0-CRP-021

**Record ID:** `O0-CRP-021`
**Title:** Functional Separation Test — Does explicit self/world separation improve prediction? The auxiliary O/0 claim inverts under fair-information control.
**Version:** 1.0.0
**Date:** 2026-07-28
**Record class:** SIMULATION
**Program:** Track 1 — auxiliary O/0 claim test
**Evidence level:** computational_simulation
**Replication status:** not_replicated

---

## Claim-Status Banner

**CLAIM STATUS:** INCONCLUSIVE by preregistered primary rule; **UNSUPPORTED** under the fair-information supplementary control.

**EVIDENCE TYPE:** Computational simulation. 90 confirmatory trials (3 regimes × 30 seeds); 3 horizons × 6 predictors × 90 trials = 1 620 predictor evaluations.

**PHYSICAL VALIDATION:** NONE.
**INDEPENDENT REPLICATION:** NONE.

**SUPPORTED:** The Kalman-filter agent with correct causal-structure knowledge (Agent A, privileged) systematically beats a matched-parameter VAR agent by small but statistically overwhelming margins (2–5% NMSE, p < 1e-10 in most regimes). This advantage is due to privileged information, not structural separation.

**NOT ESTABLISHED (indeed, contrary evidence):**
- That an agent with explicit self/world separation but *learned* world model outperforms a unified representation. Under this fair-information control, the direction *reverses*: unified VAR wins by 3–24% NMSE, p < 0.01 in most regimes.
- That the O/0 auxiliary claim (§VII) — "functional separation serves local processing" — holds under fair comparison.
- Anything about human cognition, biology, or the deep O/0 identity claim (Track 2, O0-CRP-022).

---

## Abstract

The O/0 source document (§VII) makes an auxiliary defensive claim: apparent separation between self and world is *functional* — it serves local processing. This study operationalizes that claim as: an agent with explicit self/world separation should outperform an agent with unified state, on prediction in partially-observable dynamical systems.

We test three configurations at three observability ratios (`k/d ∈ {0.25, 0.5, 1.0}`) and three horizons (`τ ∈ {1, 5, 20}`), with 30 seeds per cell:

- **Agent A (SEPARATED, privileged):** Kalman filter given the true system matrices.
- **Agent A' (SEPARATED, learned):** Kalman filter with matrices estimated from training data via subspace identification.
- **Agent B (UNIFIED):** Vector autoregression at matched parameter count.
- **Agent B+ (UNIFIED, adversarial):** VAR at 2× parameter count.

**Preregistered comparison (A vs B):** Agent A wins direction 100% of seeds in most regimes, at p < 1e-10, but effect sizes are 2–5% NMSE — below the 5% preregistered magnitude threshold. Verdict: **INCONCLUSIVE**.

**Supplementary fair-information comparison (A' vs B):** The direction *reverses*. Agent B wins in every regime, by 3–24% NMSE, p < 0.01 in 7/9 cells. Verdict: **the O/0 auxiliary claim, as tested, is not supported under fair comparison.**

**Scientific reading.** Agent A's advantage in the primary analysis was not caused by structural self/world separation. It was caused by having correct causal-structure knowledge that Agent B had to learn. When both agents learn the world dynamics from the same data at matched parameter count, unified representation wins.

This does not falsify the O/0 metaphysical identity claim (that is Track 2, O0-CRP-022). It falsifies one specific auxiliary defensive claim in the source document: that appearance of separation is functionally valuable for local prediction. On this operational test, separation is not functional; it is neutral-to-harmful.

---

## Source proposition

**Quote (O/0 source document, §VII, "If everything is one, why does separation appear so real?"):**

> Because functional separation serves evolutionary/practical purposes. The illusion of separation allows:
> - Local processing (brains solving local problems)
> - Evolution (competition/cooperation between apparent individuals)

**Quote (§VIII, "The O Thesis"):**

> **There is no separation between self and other** = The boundary is functional, not fundamental.

**Auxiliary claim under test:** the "functional" part of "functional, not fundamental" — i.e., that separation provides local-processing utility.

## Claim audit

**Source wording:** the illusion of separation allows local processing (brains solving local problems).

**Philosophical interpretation:** even if reality is one at the ground, the appearance of self/world division is not accidental; it exists because it does work.

**Scientific translation (tested here):** in a partially-observable dynamical system, an agent that maintains an explicit internal representation of the hidden world state, distinct from its observations, should outperform an agent that has no such separated representation, at matched capacity.

**Unsupported implications (not tested):**
- That biological brains use precisely this kind of separation.
- That "local processing" in the source document means Kalman-filter-style state estimation.
- That the identity claim (observer = source) is true or false.

**What can be established:** whether the specific operationalized version of the auxiliary claim survives a fair-information test.

## Research question

**Primary:** In a partially-observable linear-Gaussian dynamical system, does an agent with explicit self/world separation (SEPARATED) outperform a unified-state agent (UNIFIED), at equal parameter count, on multi-step prediction?

**Secondary:** Does any advantage vanish under fair comparison — when both agents must learn the world dynamics from the same data?

## Operational definitions

**SEPARATED agent:** maintains an internal belief distribution `p(x_t | y_1..t)` over hidden world state `x_t`, distinct from the observation history `y_1..t`. Kalman filter implementation.

**UNIFIED agent:** the internal state IS the observation history. No latent-state representation. Vector autoregression implementation.

**Fair comparison:** both agents have access only to training data of the same length. The SEPARATED agent must also learn its world model (system identification), not receive it as a gift.

**Prediction task:** given observations up to time `t`, predict `y_{t+τ}` for `τ ∈ {1, 5, 20}`. Metric: normalized mean-squared error (NMSE).

## Formal model

**World.** Linear-Gaussian state-space system.
- Hidden state `x_t ∈ R^d`, `d = 8`.
- Observation `y_t = C · x_t + v_t`, `y_t ∈ R^k`, `k ∈ {2, 4, 8}`.
- Dynamics `x_{t+1} = A · x_t + w_t`, with spectral radius of `A` set to 0.95.
- Process noise `w_t ~ N(0, 0.1·I)`, observation noise `v_t ~ N(0, 0.1·I)`.
- Trajectory length: 500 (train) + 200 (predict).

**Agent A (privileged separated).** Receives `A, C, Q, R` correctly. Standard Kalman recursion. Prediction: `ŷ_{t+τ} = C · A^τ · μ_t`. Parameter count: `d² + kd`.

**Agent A' (fair separated).** Receives only `Y_train`. Estimates `A, C, Q, R` via subspace identification (SVD of block-Hankel of observations), then runs Kalman filter with estimated matrices. Same prediction rule as Agent A.

**Agent B (unified).** VAR(L) fitted by ridge regression, with `L` chosen so total parameter count `L·k²` matches Agent A's `d²+kd`. Iterative prediction.

**Agent B+ (adversarial).** VAR at `2·L`, i.e., 2× Agent A's parameter count.

**Baselines.** Persistence (`ŷ = y_t`), zero, and Oracle (Kalman with true matrices *and* access to true hidden state at time `t`).

## Hypotheses

**H_functional (primary):** NMSE(A) < NMSE(B) at partially observable regimes, especially at long horizons.

**H_null:** NMSE(A) ≈ NMSE(B).

**H_opposite:** NMSE(B) < NMSE(A).

**H_fully_observable (null control):** At `k/d = 1.0`, both agents perform equivalently.

**H_fair (supplementary):** If separation is genuinely functional, NMSE(A') < NMSE(B) at partially observable regimes.

## Results

### Primary comparison (Agent A privileged vs Agent B) — preregistered

| k/d | τ | NMSE(A) | NMSE(B) | Δ mean | 95% CI | p | win rate | win@5% |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| 0.25 | 1 | 0.498 | 0.542 | −0.045 | (−0.054, −0.036) | 4.1e-19 | 1.00 | 0.37 |
| 0.25 | 5 | 0.691 | 0.742 | −0.051 | (−0.064, −0.040) | 1.9e-16 | 1.00 | 0.43 |
| 0.25 | 20 | 0.949 | 0.970 | −0.021 | (−0.040, −0.004) | 0.026 | 0.70 | 0.30 |
| 0.5 | 1 | 0.442 | 0.470 | −0.028 | (−0.033, −0.022) | 1.9e-22 | 1.00 | 0.07 |
| 0.5 | 5 | 0.664 | 0.687 | −0.023 | (−0.030, −0.016) | 2.5e-11 | 0.93 | 0.07 |
| 0.5 | 20 | 0.927 | 0.938 | −0.011 | (−0.024, −0.001) | 0.065 | 0.70 | 0.07 |
| 1.0 | 1 | 0.373 | 0.394 | −0.021 | (−0.025, −0.017) | 2.7e-24 | 1.00 | 0.00 |
| 1.0 | 5 | 0.625 | 0.645 | −0.020 | (−0.028, −0.013) | 3.1e-07 | 0.87 | 0.07 |
| 1.0 | 20 | 0.926 | 0.951 | −0.025 | (−0.046, −0.006) | 0.014 | 0.70 | 0.20 |

**Preregistered decision rule check:**
- `Δ < −0.05` in ≥ 75% of seeds at long-horizon partial regimes: **FAILED** (max win@5% is 0.43).
- `p < 0.01` at long-horizon partial regimes: PASSED at (0.25, 5) and (0.5, 5); FAILED at (0.25, 20) and (0.5, 20).
- Null control `|Δ| < 0.05` at `k/d = 1.0`: PASSED numerically (Δ ∈ [−0.025, −0.020]).
- Adversarial (A vs B+): A wins in most regimes (win_rate 0.6–1.0). PASSED.

**Preregistered verdict:** **INCONCLUSIVE**. Direction is consistent, significance is overwhelming, but effect magnitudes fall below the 5% NMSE threshold locked before execution.

### Fair-information comparison (Agent A' learned vs Agent B) — supplementary

| k/d | τ | NMSE(A') | NMSE(B) | Δ mean | 95% CI | p | win rate | win@5% |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| 0.25 | 1 | 0.601 | 0.542 | +0.059 | (+0.019, +0.099) | 0.0068 | 0.33 | 0.13 |
| 0.25 | 5 | 0.769 | 0.742 | +0.026 | (−0.007, +0.058) | 0.112 | 0.50 | 0.17 |
| 0.25 | 20 | 1.001 | 0.970 | +0.031 | (−0.009, +0.075) | 0.115 | 0.37 | 0.13 |
| 0.5 | 1 | 0.606 | 0.470 | +0.135 | (+0.091, +0.185) | 5.7e-08 | 0.13 | 0.00 |
| 0.5 | 5 | 0.765 | 0.687 | +0.078 | (+0.037, +0.122) | 6.2e-04 | 0.27 | 0.00 |
| 0.5 | 20 | 0.996 | 0.938 | +0.058 | (+0.033, +0.084) | 2.4e-05 | 0.20 | 0.03 |
| 1.0 | 1 | 0.634 | 0.394 | +0.240 | (+0.189, +0.291) | 3.8e-16 | 0.00 | 0.00 |
| 1.0 | 5 | 0.780 | 0.645 | +0.135 | (+0.087, +0.183) | 1.3e-07 | 0.00 | 0.00 |
| 1.0 | 20 | 1.008 | 0.951 | +0.058 | (+0.019, +0.101) | 0.0074 | 0.27 | 0.13 |

**Δ is positive in every regime.** Agent B (unified VAR) beats Agent A' (learned separated Kalman). The direction is opposite to the primary comparison. In 7/9 regimes, p < 0.01.

**Supplementary verdict:** **UNSUPPORTED for H_functional under fair information.** The auxiliary O/0 claim, as operationalized here, does not hold when both agents must learn the world dynamics from the same data.

## Figures

- **Figure 1** (headline): Primary vs fair comparison across regimes and horizons. Primary bars (blue) are negative; fair bars (red) are positive. The inversion is the finding.
- **Figure 2**: Absolute NMSE for all six predictors. Agent A tracks Oracle in partial-observability regimes; A' tracks *B+* or worse.
- **Figure 3**: Per-seed scatter at τ=5. A points cluster below the diagonal (beat B); A' points cluster above (lose to B).
- **Figure 4**: Effect size vs horizon for both comparisons.

## Uncertainty and limitations

**Statistical:**
- 30 seeds is adequate for detecting the observed effect sizes; power for smaller effects would be limited.
- Bootstrap CIs and paired-t p-values agree across regimes.
- No multiple-comparison correction: primary hypothesis specified regime and horizon.

**Design limitations:**
- Linear-Gaussian dynamics only. Nonlinear systems (registered followup R1) may behave differently.
- Kalman filter is a *minimal* instantiation of self/world separation. Real cognitive architectures (predictive coding, active inference) are more elaborate and might produce different results.
- Subspace system identification is one specific way to learn state-space models. Alternative estimators (EM, expectation-maximization for state-space; variational Bayesian; neural networks) might close the gap.
- Parameter matching is by count, not by expressiveness. VAR(L) can approximate any linear system given enough L; the interesting question is at what capacity the unified representation catches up. This regime is what the study happens to sit in.

**Interpretation limitations:**
- A result "unsupported for the O/0 auxiliary claim as tested" does not rule out other operationalizations of "functional separation."
- Kalman filter is not the only self/world separation architecture; the result generalizes only to that class.
- The direction reversal under fair information is a *specific finding about specific agents*, not a universal statement.

## Alternative interpretations

**Interpretation 1 (dominant, our reading):** self/world separation, per se, provides no prediction advantage at matched capacity when both agents must learn the world. The apparent advantage in the primary analysis is due to privileged causal-structure knowledge.

**Interpretation 2:** the subspace identifier used for Agent A' is weak. A better system identification method might make Agent A' competitive. In this reading, the result reflects an implementation detail, not a fundamental fact.

**Interpretation 3:** the specific task (short-horizon prediction in low-dimensional linear-Gaussian systems) does not require the kind of structured world model that self/world separation provides. In systems with strong long-horizon dependencies (registered R1 nonlinear extension), separation might matter more.

**Interpretation 4 (adversarial to O/0):** unified representations can implicitly discover latent structure at matched capacity. The mystical claim that appearance of separation is functional is not empirically supported by this operationalization; the appearance may be redundant.

We prefer Interpretation 1 as the honest primary reading, with 2 and 3 noted as registered followups.

## Replication procedure

**Deterministic given seeds 12000..12029.** Bit-identical results across independent runs (verified in code).

To replicate:
```bash
cd research/studies/O0-CRP-021/src
python run_study.py     # runs full study; ~30s
python analyze.py       # generates figures
```

Outputs:
- `results/summary.json` — regime-level statistics and verdicts.
- `results/raw/trials.jsonl` — per-trial NMSE for all predictors and horizons.
- `figures/*.png` — 4 figures.

## Code and data manifest

- `src/run_study.py` — world generation, agents, trial execution, summarization.
- `src/analyze.py` — figure generation.
- `results/summary.json` — aggregated regime-level results.
- `results/raw/trials.jsonl` — per-trial NMSE data (90 lines).
- `figures/01_headline_primary_vs_fair.png` — headline finding.
- `figures/02_absolute_nmse.png` — absolute NMSE across all predictors.
- `figures/03_per_seed_scatter_tau5.png` — per-seed win/lose scatter.
- `figures/04_effect_vs_horizon.png` — effect size trajectories.

Dependencies: python 3.10+, numpy, scipy, matplotlib.

## Relationship to O/0 philosophical archive

**Source:** O/0 Framework §VII, §VIII.
**Relationship type:** *formalization of an auxiliary claim* with a *negative confirmatory outcome under fair comparison*.

**Provenance disclaimer** (standard): *Conceptual provenance is not empirical support.* This study operationalizes one specific auxiliary claim from the source document. The primary metaphysical claim (observer = source) is not tested here; that is O0-CRP-022.

**Effect on the O/0 program:** the auxiliary defensive claim in §VII ("functional separation serves practical purposes") is not supported by the specific test performed. This does not falsify the identity claim or the source document as a whole. It falsifies one specific line of defense.

## Registered followups

- **O0-CRP-021-R1** — Nonlinear extension. Chaotic or nonlinear partially-observable systems (e.g., Lorenz-63 with partial observation), with neural-network agents rather than Kalman/VAR.
- **O0-CRP-021-R2** — Stronger system identification. Try EM for state-space learning, variational Bayesian, or deep state-space models (S4, Mamba) as Agent A'. Does the direction stay reversed?
- **O0-CRP-021-R3** — Long-horizon regime with T_train larger (5000+), to see if the fair comparison closes or widens.
- **O0-CRP-021-R4** — Higher hidden dimension `d ∈ {16, 32, 64}`, testing whether the reversal holds at greater complexity.

## References to primary sources

- **O/0 source document**, §VII, §VIII. Local file: `# The O-0 Phenomenon- A Unified Framework.md`.
- Kalman, R.E. (1960). *A new approach to linear filtering and prediction problems.* J. Basic Eng.
- Ho, B.L., Kalman, R.E. (1966). *Effective construction of linear state-variable models from input/output functions.* Regelungstechnik.
- Van Overschee, P., De Moor, B. (1996). *Subspace Identification for Linear Systems.* Springer.
- Wold, H. (1938). *A Study in the Analysis of Stationary Time Series.* (VAR/AR foundations.)
- Prigogine, I. (1980). *From Being to Becoming.* (Relevant to Track 3.)

## Revision history

| Version | Date | Change |
|---|---|---|
| 1.0.0 | 2026-07-28 | Initial record. Primary verdict INCONCLUSIVE (per preregistration); supplementary fair-comparison verdict UNSUPPORTED. |

---

**Runtime:** 21.3 s wall clock (Python 3.14, numpy-only).
**Trials:** 90 confirmatory (3 regimes × 30 seeds) + 12 determinism-check trials.
**Determinism:** verified — 3 seeds × 2 regimes × 2 runs bit-identical.