Emergent Role Differentiation in Morphable Soft-Body Robots: From Symmetry Locks to Environmental Differentiation

Correction (v11): The Computational Note in v1–v10 stated "All experiments were conducted on a single NVIDIA RTX 5080 Laptop GPU." Some early exploratory experiments may have been conducted on CPU before GPU availability. In v11, the Computational Note has been removed and the GPU Parallelization section (§2.6) has been revised to clarify that GPU execution is a capability of the framework rather than a blanket claim about all runs. All code supports both CPU and GPU execution via automatic device detection. v11 updates (March 13, 2026): • Experiment 27 (The Evolution of Deception): Replaces true energy observation with self-reported signals (an additional NN output), enabling deception. Three conditions (N=5 seeds each, α=3): HONEST—true energy + divorce (gap −0.8 ± 13.0, 4.6 divorces); DECEPTION—self-reported signal + divorce (gap −2.4 ± 6.9, 8.2 divorces); DECEPTION NO DIVORCE—signal only, no spring control (gap +12.9 ± 1.9, 0 divorces). The self-reported signal degenerates into pure noise: signal–truth correlation r ≈ 0.015 (Cheap Talk). Divorce persists because it relies on physical spring tension, not the opponent's self-report. Establishes the Signal Irrelevance Principle. • Experiment 28 (RNN Memory vs Structural Constraint): Replaces feedforward NNs with Elman RNNs (H=16, persistent hidden state) to test whether temporal memory enables tit-for-tat. Three conditions (N=5 seeds each, α=3): FFN baseline (gap +16.5 ± 2.3), RNN (gap +20.1 ± 1.3), RNN+Observable (gap +20.1 ± 3.1). Memory produces LARGER gaps than feedforward—freeriders use memory to more efficiently exploit temporal structure. Role alternation score = 0.20 across all conditions (no tit-for-tat). Establishes the Physical Irreducibility Principle. • Discussion retitled "From Parasitism to Irreducibility" with complete intervention hierarchy: information fails → memory fails → only physical sanction works → deception cannot undermine it • Added Principles 26 (Signal Irrelevance) and 27 (Physical Irreducibility) to Theme VI: Social Dynamics • Expanded from 25 to 27 principles • Paper now 42 pages, 28 experiments v10 updates (March 12, 2026): • Experiment 25 (PCA Manifold Comparison): Provides the neural-geometric proof of the Symmetry Locks Theorem. For three mass ratios (1:1, 3:1, 10:1), hidden-layer activations (32 units) are projected via PCA to visualize the neural trajectory structure. At 1:1, both bodies trace overlapping trajectories on a shared manifold (neural distance 1.51). At 3:1, trajectories partially separate into two intersecting ellipses (distance 2.40). At 10:1, bodies occupy fully distinct manifold regions (distance 2.01). Establishes the Neural Manifold Geometry Principle. • Experiment 26 (The Evolution of Divorce): Tests whether combining opponent energy observation with spring-cutting ability enables autonomous punishment. Four conditions (N=5 seeds each, α=3): Blind (gap +12.9 ± 1.9, 0 divorces), Observable only (gap +11.8 ± 2.9, 0 divorces), DIVORCE—observable + spring control (gap −2.1 ± 5.3, 10.8 divorces), Blind+Spring (gap −0.6 ± 11.5, 4.4 divorces). Evolution discovers punishment: bodies sever physical connections when partner freeloads. Information alone is insufficient (Observable: gap +11.8); capacity alone partially works (Blind+Spring: gap −0.6); the combination eliminates parasitism entirely. Establishes the Punishment Principle. • Added Principles 24 (Neural Manifold Geometry) and 25 (Punishment Principle) to Theme VI: Social Dynamics • Discussion section retitled "From Parasitism to Punishment" with complete narrative arc • Expanded from 23 to 25 principles v9 updates (March 12, 2026): • Experiment 24 (Reciprocal Altruism): Tests whether opponent energy observation enables tit-for-tat cooperation. Added opponent's cumulative energy as 8th NN input dimension. Blind (INPUT_DIM=7) vs Observable (INPUT_DIM=8) at α=3: gap +19.2 ± 2.9 vs +19.3 ± 3.9—statistically identical. At α=5, gap doubles to +36.8 ± 4.3. No temporal alternation (tit-for-tat) observed. Establishes the Structural Constraint Principle: parasitism is a structural consequence of physical coupling (Volunteer's Dilemma), not information asymmetry. • PCA Brain Analysis of Phantom Synchronization: Recorded hidden-layer activations (32 units) for all three bodies in the 5:1:5 configuration, then applied PCA. Body 0 and Body 2 (both m=5) trace identical trajectories in neural activation space. 2 PCs capture 77.1% of variance. L2 neural distance between Body 0 and Body 2 unchanged after spring cutting (2.36 pre-cut vs 2.55 post-cut, ratio 1.08). Proves Phantom Sync is a deterministic consequence of input identity. • Added Principle 23 (Structural Constraint) to Theme VI • Expanded from 22 to 23 principles v8 updates (March 12, 2026): • Multi-seed statistical validation confirms robustness of three key findings: – Phantom Synchronization (N=20): Mirror sync r₀₂ = 0.942 ± 0.058 (no cut) vs 0.924 ± 0.076 (cut@300). Difference Δ = 0.018 is negligible. – No-Cost Environmental Differentiation (N=20): Friction asymmetry reliably produces differentiation (r = 0.305 ± 0.111) while improving fitness (+179 ± 2). – Parasitic Phase Transition (N=10, α=3): Fitness gap = +19.5 ± 3.8. Freeloader fitness variance extremely low (±0.8). • All single-seed results fall within one standard deviation of multi-seed means. v7 updates (March 11, 2026): • Experiment 21 (Parasite's Dilemma): 7-point α dose-response sweep reveals nonlinear freerider phase transition at α ≈ 2, fitness gap 0 → +70. Body 0 evolves as unconditional worker; no reciprocal altruism. Parasite × Mass factorial confirms initial position determines worker/freeloader role. • Experiment 22 (Independent NNs × Friction): Highest fitness (+189) but weaker differentiation (r = 0.430) than shared NNs (r = −0.032). • Experiment 23 (Topology Control): Evolution discovers 31-cycle separation/recombination pulsation without fitness loss. • Added Theme VI: Social Dynamics (Principles 20–22) • Expanded from 19 to 22 principles Key findings (27 principles in 6 themes): Theme I — Symmetry & Differentiation: Symmetry Locks Theorem: Symmetric bodies cannot differentiate (r = 0.742); invariant to body count, physical coupling, and controller architecture. Inertial Asymmetry Principle: Only mass asymmetry breaks synchronization (F = ma). Transient Differentiation: Role specialization peaks early then is partially reabsorbed. Reward Paradox: Multi-phase fitness can mask poor locomotion via reward hacking. Symmetry Optimality: Evolution chooses symmetric masses when free to evolve. Theme II — Efficiency–Specialization Trade-offs: 6. The Sweet Spot: Mass ratio 3:1 maximizes differentiation per unit fitness cost. 7. DoF Trap: Per-particle control catastrophically collapses fitness (+175 → −81). 8. Environmental Differentiation: Asymmetric friction induces differentiation at superior fitness (+181). Theme III — Environmental Control: 9. No-Cost Differentiation: Friction asymmetry differentiates without fitness cost (Diff×Fit = 171.0). 10. Asymmetry Interference: Combining body + environment asymmetry produces destructive interference. Theme IV — Dimensional Compression: 11. Muscle Synergy: 1D center-of-mass shift overcomes DoF Trap (+210). 12. Adaptive Robustness: Reversal-trained controllers maintain +171. 13. Synergy Dimension Optimality: 2–3D synergy achieves all-time record +216. 14. Dynamic Resonance: Synergy bypasses Interference (+211 under asymmetric env). Theme V — Architectural Invariance: 15. N-Body Selective Differentiation: Only mass-different pairs differentiate; mirror sync r = 0.996. 16. Neural Synchronization: Mirror sync persists after physical decoupling (r₀₂ ≥ 0.977). PCA confirms identical neural manifold trajectories (77.1% variance in 2 PCs). 17. Convergent Strategy: Independent NNs synchronize (r = 0.952) without weight sharing. 18. Physical Inevitability: Independent NNs differentiate more strongly (r = −0.301) than shared NNs (r = 0.571). 19. Parasitic Drag Cost: One body dragging dead weight costs 61% fitness; cooperation = 2.6× solo. Theme VI — Social Dynamics: 20. Parasitic Phase Transition: Co-evolutionary energy costs produce freeriders with nonlinear dose-response (gap 0 → +70, critical α ≈ 2). Unconditional worker emerges; no reciprocal altruism. 21. Architecture–Environment Interaction: Independent NNs + friction = highest fitness (+189) but weaker differentiation (r = 0.430). 22. Topology Pulsation: Evolution discovers 31-cycle separation/recombination without fitness loss. 23. Structural Constraint: Opponent energy observation does not reduce freeriding (gap +19.3 ± 3.9 vs blind +19.2 ± 2.9). Parasitism is structural, not informational. 24. Neural Manifold Geometry: Symmetry Locks Theorem = trajectory overlap in low-dimensional neural manifold. Symmetric bodies share a single orbit (distance 1.51); asymmetric bodies occupy separated submanifolds (distance 2.40 at 3:1). 25. Punishment Principle: When agents have both opponent observation AND physical disconnection ability ("divorce"), evolution discovers autonomous punishment, collapsing freeriding gap from +12.9 to −2.1 with 10.8 divorces per simulation. 26. Signal Irrelevance: Self-reported communication channels degenerate into uninformative noise (signal–truth r ≈ 0.015, Cheap Talk). Punishment mechanisms that rely on physical observables (spring tension) are robust to deception. 27. Physical Irreducibility: The Structural Constraint persists under RNN controllers with temporal memory (gap +20.1 ± 1.3 vs FFN +16.5 ± 2.3). Memory amplifies parasitism rather than enabling tit-for-tat; the constraint is physically irreducible.