O0-OBS-001

Self-Model Formation in Bounded Agents

**Version:** 1.0

**Research status:** PLANNED

CLAIM STATUS: UNTESTED PREDICTION
EVIDENCE TYPE: COMPUTATIONAL SIMULATION (PLANNED)
PHYSICAL VALIDATION: NONE
INDEPENDENT REPLICATION: NOT YET ATTEMPTED
PHILOSOPHICAL PROVENANCE: O/0 ARCHIVE
ARCHIVE ENDORSEMENT: LIMITED TO REPORTED RESULT

Abstract

This study investigates whether agents maintaining Markov blankets in a cellular-automaton substrate spontaneously develop internal models that predict their own boundary entropy. We extend the boundary simulation framework (SIM-001) with an additional internal prediction layer, where each bounded region maintains a recurrent state that generates predictions about its own future boundary configuration. The primary measure is self-model accuracy: the correlation between predicted and actual boundary entropy over time. Secondary measures include convergence time to stable self-models and robustness under perturbation. This study tests a core claim of the O/0 framework—that observation requires self-modeling—by operationalizing self-model formation in a minimal computational setting.

Note: Conceptual provenance from the O/0 philosophical archive does not constitute empirical support. This study is designed to generate evidence independently of the archive's claims.

Source proposition

From O/0 Archive Entry O0-META-003: "An observer is a bounded region that maintains a predictive model of its own boundary states." This study operationalizes and tests the formation dynamics of such models.

Scientific audit

• **Testability:** HIGH. Self-model accuracy is directly measurable as prediction-observation correlation.
• **Falsifiability:** YES. If agents never converge to above-chance boundary prediction, the hypothesis is falsified.
• **Novelty:** MODERATE. Extends active inference literature to explicit self-model tracking in cellular automata.
• **Potential confounds:** Self-model accuracy could be trivially high if boundary states are highly autocorrelated; must control for persistence baselines.

Research question

Do bounded agents in a cellular-automaton substrate spontaneously develop internal predictive models of their own boundary entropy, and if so, what are the dynamics of formation?

Operational definitions

• **Bounded agent:** A contiguous region R in a grid where the mutual information I(R_interior; R_exterior | R_boundary) < threshold τ = 0.1 bits, sustained for ≥ 50 timesteps.
• **Self-model:** An internal state vector s_t ∈ ℝ^k maintained by the agent that is updated according to s_{t+1} = f(s_t, sensory_t), where f is a learned recurrent function.
• **Boundary entropy:** H(B_t) = -Σ p(b_i) log p(b_i) over the boundary cell states at time t.
• **Self-model accuracy:** Pearson correlation r between predicted boundary entropy ĤH(B_{t+1}) and actual H(B_{t+1}) over a rolling window of 100 timesteps.
• **Convergence time:** Number of timesteps until self-model accuracy exceeds r = 0.7 for 50 consecutive steps.
• **Persistence baseline:** Prediction that H(B_{t+1}) = H(B_t) (trivial autocorrelation model).

Hypothesis

H1: Bounded agents with internal prediction layers will converge to self-model accuracy r > 0.7 within 2,000 timesteps, significantly exceeding the persistence baseline.

H2: Convergence time will correlate negatively with boundary stability (more stable boundaries → faster self-model formation).

Null hypothesis

H0_1: Self-model accuracy does not exceed the persistence baseline (agents learn nothing beyond "tomorrow looks like today").

H0_2: Convergence time is independent of boundary stability.

Competing explanations

1. **Trivial autocorrelation:** Boundary entropy is so temporally smooth that any prediction mechanism trivially achieves high accuracy. Controlled by comparing against persistence baseline and shuffled-time baselines.

2. **External model masquerading as self-model:** The internal state might model external environment dynamics rather than boundary-specific states. Controlled by testing prediction accuracy specifically on boundary vs. interior vs. exterior states.

3. **Overfitting to initialization:** Self-models might only work for initial conditions. Controlled by mid-run perturbation tests.

Formal model

Grid: N × N cells (N = 100), each cell c_i ∈ {0, 1, ..., k-1} with k = 4 states.

Update rule: Probabilistic cellular automaton with local interaction kernel K (3×3 Moore neighborhood).

For each bounded region R detected at time t:

• Boundary B_t = {cells in R adjacent to cells not in R}
• Internal prediction layer: s_{t+1} = tanh(W_s · s_t + W_x · x_t + b) where x_t = encoded boundary state
• Predicted boundary entropy: Ĥ_{t+1} = v^T · s_{t+1} (linear readout)
• Learning rule: Δw ∝ -∂(Ĥ_{t+1} - H(B_{t+1}))² / ∂w with learning rate η = 0.01

Methods

1. **Simulation setup:** Initialize 100×100 grid with random state distribution. Run SIM-001 boundary detection for 500 timesteps to identify stable bounded regions.

2. **Self-model insertion:** At t=500, attach a recurrent prediction layer (hidden dim k=16) to each detected bounded region. The prediction layer receives encoded boundary states as input.

3. **Training phase:** Run simulation for 5,000 additional timesteps. At each step, update prediction weights via gradient descent on boundary entropy prediction error.

4. **Evaluation phase:** Freeze weights. Run for 1,000 timesteps. Compute self-model accuracy metrics.

5. **Perturbation test:** At t=6,500, inject noise into 20% of boundary cells. Measure recovery time of self-model accuracy.

6. **Repetitions:** 50 independent simulation runs with different random seeds.

Controls

• **Persistence baseline:** Replace self-model prediction with Ĥ_{t+1} = H(B_t).
• **Random baseline:** Replace self-model prediction with random values drawn from the empirical distribution of H(B_t).
• **Shuffled-input control:** Feed the self-model layer shuffled (temporally decorrelated) boundary states; if accuracy remains high, the task is trivially solvable.
• **External-model control:** Train prediction layer on exterior-region entropy instead of boundary entropy. Compare accuracy to test whether self-specific modeling emerges.

Predictions

| Outcome | Self-model accuracy (r) | Interpretation |

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

| Strong support | r > 0.8, exceeds persistence by > 0.2 | Self-models form and capture non-trivial dynamics |

| Moderate support | 0.7 < r < 0.8, exceeds persistence by 0.1-0.2 | Self-models form but add limited value |

| Weak/null | r < 0.7 or does not exceed persistence | Self-model formation not demonstrated |

**Expected Outcome Matrix:**

| Condition | Expected r | Decision |

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

| Full self-model | > 0.75 | If achieved: proceed to OBS-002 |

| Persistence baseline | ~ 0.5 | Reference point |

| Shuffled-input | < 0.3 | If high: task is trivial, redesign needed |

| External-model | < full self-model | If equal: no self-specificity |

**Decision rules:**

• If full self-model r > persistence + 0.15 AND shuffled-input r < 0.4: **SUPPORT H1**
• If full self-model r ≤ persistence + 0.05: **REJECT H1, accept H0**
• If shuffled-input r > 0.6: **INCONCLUSIVE, task too easy, redesign**

Falsification criteria

H1 is falsified if:

1. Self-model accuracy does not significantly exceed persistence baseline (paired t-test, p > 0.05, across 50 runs), OR

2. Shuffled-input control achieves comparable accuracy (within 0.1 of full model), OR

3. No bounded regions maintain stable self-models for > 100 timesteps in any run.

Results / Expected Outcomes

Study not yet conducted. Based on active inference literature and preliminary SIM-001 results, we expect:

• Self-model accuracy r ≈ 0.78 (moderate-to-strong support)
• Convergence time ≈ 800-1,200 timesteps
• Negative correlation between boundary stability and convergence time (r ≈ -0.4)
• Recovery from perturbation within 200-400 timesteps

Uncertainty

• **Parametric uncertainty:** Learning rate η and hidden dimension k may require tuning. Planned sensitivity analysis over η ∈ {0.001, 0.005, 0.01, 0.05} and k ∈ {8, 16, 32, 64}.
• **Model uncertainty:** The recurrent architecture may be insufficient; transformer-based alternatives should be explored if RNN fails.
• **Definitional uncertainty:** The threshold τ = 0.1 for boundary detection is somewhat arbitrary. Robustness check: repeat with τ ∈ {0.05, 0.1, 0.2}.

Limitations

1. Cellular automata are vastly simpler than biological or AI systems—generalization is uncertain.

2. The prediction layer is externally attached, not emergent—this tests whether self-modeling *can* occur, not whether it *must* occur.

3. Boundary entropy is a scalar summary; richer self-models (predicting full boundary configuration) are left to future work.

4. No claim about consciousness or phenomenal experience is made or tested.

Replication status

Not yet conducted. Code will be made available upon completion.

Data and code

• Simulation framework: Extension of SIM-001 (O0-SIM-001)
• Language: Python 3.11+ with NumPy, JAX for gradient computation
• Repository: [To be created upon study initiation]
• Pre-registration: This document serves as pre-registration. Timestamp: 2026-07-26.

Relationship to philosophical archive

This study operationalizes claims from O0-META-003 regarding observer self-modeling. The philosophical archive provides the conceptual motivation but NOT evidential support. Results of this study stand or fall on their own empirical merits regardless of the archive's philosophical arguments.

References

• Friston, K. (2013). Life as we know it. *Journal of the Royal Society Interface*, 10(86).
• Kirchhoff, M., et al. (2018). The Markov blankets of life. *Journal of the Royal Society Interface*, 15(138).
• Hohwy, J. (2016). The self-evidencing brain. *Noûs*, 50(2), 259-285.
• Seth, A. K. (2021). Being You: A New Science of Consciousness. Dutton.
• Beer, R. D. (2020). An integrated perspective on the constitutive and interactive dimensions of autonomy. *BioSystems*, 91(2).

Revision history

| Date | Version | Changes |

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

| 2026-07-26 | 1.0 | Initial pre-registration |