O0-OBS-003

Observer-Dependence of Boundary Attribution

**Version:** 1.0

**Research status:** PLANNED

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

Abstract

This experiment tests whether boundary attribution is observer-dependent by deploying multiple "observer agents" with different measurement parameters to scan the same substrate. Each observer uses a different spatial resolution, noise tolerance, and statistical threshold for boundary detection. We quantify agreement between observers using Jaccard index (spatial overlap) and mutual information (statistical dependence of boundary maps). The central question is whether observer-dependence is a deep structural feature of boundary attribution or merely reflects measurement noise that vanishes with increasing precision.

Note: Conceptual provenance from the O/0 philosophical archive does not constitute empirical support.

Source proposition

From O/0 Archive Entry O0-META-007: "The boundaries attributed to a system depend on the observer performing the attribution. There is no observer-independent fact about where one system ends and another begins." This study tests the degree and nature of observer-dependence.

Scientific audit

• **Testability:** HIGH. Agreement metrics (Jaccard, MI) are standard and well-understood.
• **Falsifiability:** YES. If all observers converge to identical boundary maps regardless of their parameters, observer-dependence is falsified for this domain.
• **Novelty:** MODERATE. Connects measurement theory to computational boundary detection.
• **Potential confounds:** Observers with very different resolutions may be detecting genuinely different spatial scales rather than disagreeing about the same scale. Must control for scale-appropriate comparison.

Research question

To what extent do different observer agents—varying in resolution, noise tolerance, and statistical thresholds—produce different boundary maps when scanning the same computational substrate?

Operational definitions

• **Observer agent:** An algorithm O_i that takes a grid state G_t as input and produces a boundary map M_i(G_t) ∈ {0,1}^{N×N} where 1 indicates "boundary cell."
• **Resolution parameter (ρ):** The spatial scale of the observer's receptive field. ρ=1: single-cell resolution. ρ=3: 3×3 averaging. ρ=5: 5×5 averaging.
• **Noise tolerance (ν):** Threshold for statistical significance of boundary detection. ν=0.01: very strict. ν=0.1: moderate. ν=0.5: permissive.
• **Statistical threshold (τ):** Minimum mutual information reduction required to declare a boundary. τ ∈ {0.01, 0.05, 0.1, 0.2, 0.5} bits.
• **Jaccard index:** J(M_i, M_j) = |M_i ∩ M_j| / |M_i ∪ M_j|. Ranges [0,1]. J=1: perfect agreement. J=0: no overlap.
• **Mutual information:** I(M_i; M_j) = Σ p(m_i, m_j) log[p(m_i, m_j) / p(m_i)p(m_j)]. Quantifies statistical dependence of boundary maps.
• **Observer ensemble:** Set of K observers {O_1, ..., O_K} with specified parameter combinations.

Hypothesis

H1: Observers with different parameters will produce systematically different boundary maps (mean pairwise Jaccard < 0.7) even when scanning the same substrate at the same time.

H2: Observer disagreement is structured (not random)—observers with similar parameters will agree more than observers with dissimilar parameters (distance-agreement correlation ρ > 0.5).

H3: Increasing resolution does NOT monotonically increase inter-observer agreement. There exists a resolution level beyond which additional precision reveals *more* observer-dependent structure, not less.

Null hypothesis

H0_1: All observers produce equivalent boundary maps (mean pairwise Jaccard > 0.9).

H0_2: Observer disagreement is unstructured—parameter similarity does not predict agreement.

H0_3: Higher resolution monotonically increases agreement (observer-dependence is trivially measurement noise).

Competing explanations

1. **Pure measurement noise:** Disagreement reflects only sampling noise, not genuine observer-dependence. Controlled by running each observer multiple times on the same state (test-retest reliability > 0.95 expected within-observer).

2. **Scale separation:** Observers at different resolutions detect different hierarchical levels, not conflicting attributions of the same level. Controlled by same-resolution comparisons (vary only ν and τ at fixed ρ).

3. **Threshold artifact:** Disagreement is an artifact of using binary boundary maps; continuous-valued maps might converge. Controlled by computing agreement on continuous boundary-probability maps before thresholding.

Formal model

Substrate: 100×100 grid running SIM-001 dynamics for 5,000 timesteps.

Observer construction:

• O_i characterized by tuple (ρ_i, ν_i, τ_i)
• Measurement: O_i computes local mutual information at scale ρ_i
• For each cell c at position (x,y): compute MI between interior region (radius ρ_i centered on c) and exterior region
• Apply noise model: observed_MI = true_MI + ε, where ε ~ N(0, ν_i)
• Threshold: cell c is "boundary" if observed_MI < τ_i

Observer ensemble (full factorial):

• ρ ∈ {1, 2, 3, 5, 7} (5 levels)
• ν ∈ {0.001, 0.01, 0.05, 0.1, 0.5} (5 levels)
• τ ∈ {0.01, 0.05, 0.1, 0.2, 0.5} (5 levels)
• Total: 125 observer configurations

Agreement computation:

• Pairwise Jaccard matrix J ∈ ℝ^{125×125}
• Pairwise MI matrix I ∈ ℝ^{125×125}
• Parameter distance matrix D ∈ ℝ^{125×125} (normalized Euclidean in log-parameter space)

Methods

1. **Substrate preparation:** Run SIM-001 for 5,000 timesteps on 100×100 grid. Save final 100 timesteps (states G_{4901}...G_{5000}).

2. **Observer deployment:** Apply all 125 observer configurations to each of the 100 saved states.

3. **Within-observer reliability:** Run each observer 10 times on the same state with resampled noise. Compute test-retest Jaccard (expected > 0.95).

4. **Between-observer agreement:** Compute pairwise Jaccard and MI for all 125×125 observer pairs, averaged over 100 timepoints.

5. **Structure analysis:** Correlate parameter distance D with agreement J. Fit linear model: J_ij = β_0 + β_ρ|Δρ| + β_ν|Δν| + β_τ|Δτ| + ε.

6. **Resolution curve:** Plot mean agreement as function of resolution ρ (averaging over ν and τ). Test for non-monotonicity.

7. **Consensus map:** Compute majority-vote boundary map across all observers. Identify "contested" cells (< 60% agreement) and "consensus" cells (> 90% agreement).

Controls

• **Identical-observer control:** Pairs of observers with identical parameters (test-retest reliability). Expected J > 0.95.
• **Null substrate control:** Apply observers to random noise grid (no structure). Expected: very low agreement, confirming that agreement in structured substrate is signal-driven.
• **Synthetic boundary control:** Apply observers to a grid with known, hand-designed boundaries. Verify that at least *some* observer configurations correctly detect them.

Predictions

**Expected Outcome Matrix:**

| Comparison type | Expected Jaccard | Interpretation |

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

| Same parameters (test-retest) | > 0.95 | Within-observer reliability |

| Similar parameters (neighbors) | 0.7 - 0.9 | Modest observer-dependence |

| Dissimilar parameters | 0.3 - 0.6 | Strong observer-dependence |

| Cross-resolution (ρ differs by ≥3) | 0.2 - 0.5 | Scale-dependent boundaries |

| Random substrate | < 0.15 | No signal |

**Decision rules:**

• If mean pairwise Jaccard (dissimilar observers) < 0.5: **SUPPORT H1** (strong observer-dependence)
• If mean pairwise Jaccard (all pairs) > 0.85: **REJECT H1** (observer-independence)
• If correlation(D, 1-J) > 0.5, p < 0.001: **SUPPORT H2** (structured disagreement)
• If agreement peaks at intermediate ρ and decreases at high ρ: **SUPPORT H3**
• If agreement monotonically increases with ρ: **SUPPORT H0_3** (trivial noise explanation)

Falsification criteria

H1 is falsified if mean pairwise Jaccard across all observer pairs exceeds 0.85 (boundaries are observer-independent in this substrate).

H3 is falsified if agreement is a monotonically increasing function of resolution with no reversal (Spearman ρ > 0.9 between resolution and agreement).

Results / Expected Outcomes

Study not yet conducted. Predictions based on information-theoretic considerations:

• We expect strong observer-dependence (mean Jaccard ≈ 0.45 across all pairs)
• Resolution will show the strongest effect (β_ρ largest in regression model)
• A "consensus core" of boundary cells will exist (≈ 30% of all boundary cells) that all observers agree on
• Contested regions will cluster at boundary-of-boundary areas where gradients are ambiguous

Uncertainty

• **Resolution confound:** Different resolutions may genuinely detect different scales, complicating the "disagreement" interpretation. This is acknowledged in the competing explanations and partially addressed by fixed-resolution comparisons.
• **Substrate dependence:** Results may differ dramatically for different dynamics rules. Generalization requires replication across substrate types.
• **Observer space coverage:** 125 configurations may not span the full relevant observer space.

Limitations

1. Binary boundary maps lose information about boundary strength/confidence.

2. The observer space is researcher-designed—"natural" observers may vary along different dimensions.

3. Agreement metrics are sensitive to boundary sparsity (rare boundaries inflate Jaccard denominators).

4. Results in 2D cellular automata may not generalize to higher-dimensional or continuous systems.

5. This study cannot determine whether observer-dependence is "trivial" or "deep" without reference to the resolution curve (H3).

Replication status

Not yet conducted.

Data and code

• Simulation framework: SIM-001 with observer overlay module
• Language: Python 3.11+, NumPy, SciPy for information-theoretic computations
• Planned output: Full pairwise agreement matrices, consensus maps, regression coefficients
• Pre-registration: This document. Timestamp: 2026-07-26.

Relationship to philosophical archive

This study directly tests the archive's claim that boundary attribution is observer-dependent. However, note that even strong observer-dependence in a simulation does not prove the philosophical claim in general—it only demonstrates that *one operational system* exhibits this property. The archive's broader metaphysical claim remains untested by this experiment alone. See also OBS-010 for the adversarial counterargument.

References

• Tononi, G., et al. (2016). Integrated information theory. *Scholarpedia*, 11(5).
• Seth, A. K., & Edelman, G. M. (2009). Measuring the complexity of the environment. *Complexity*, 10(5).
• Lizier, J. T. (2014). JIDT: An information-theoretic toolkit for studying the dynamics of complex systems. *Frontiers in Robotics and AI*, 1.
• Balduzzi, D., & Tononi, G. (2008). Integrated information in discrete dynamical systems. *PLoS Comp Bio*, 4(1).
• Wimsatt, W. C. (1994). The ontology of complex systems. *Canadian Journal of Philosophy*, 24(sup1).

Revision history

| Date | Version | Changes |

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

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