Aigarth Research Lab

Executive Summary

We conducted a multi-phase investigation of the Aigarth system, progressing from mathematical analysis of the Anna Matrix through artificial life simulation to architectural reverse-engineering of the official source code. Key findings:

Part I: Anna Matrix Computational Properties

1.1 The Bijection Discovery

The 128x128 Anna Matrix, when used as a dense weight matrix with ternary sign activation, produces a near-perfect bijection on the input space. This was unexpected — most random matrices produce many collisions.

Experiment: 100,000 random binary inputs mapped through sign(A * x):

Inputs tested:     100,000
Unique outputs:    100,000
Collisions:        0
Convergence:       100% (89% in 1 tick, max ~26 ticks)

Hamming-2 exhaustive test: All 8,193 inputs with Hamming weight 0, 1, or 2 produce 8,193 unique attractors. The matrix is provably bijective on this subspace.

Sparse ring topology sweep (radii 1, 2, 4, 8, 16, 32, 64):

A sharp phase transition exists between R=1 (dead) and R=2 (bijective). This is consistent with percolation theory on ring graphs.

1.2 Spectral Analysis

Eigenvalue decomposition of the Anna Matrix reveals:

The matrix has exactly 8 energy levels: ±56, ±50, ±42, ±38 — perfectly symmetric around zero.

1.3 Fixed Point Structure

Iterating the sign function: F = sign(A)^6 converges to a rank-2 idempotent matrix where:

• Every column sums to exactly 42
• 42 columns are all-ones vectors
• 43 columns sum to +2 (one element flipped)
• 43 columns sum to -2 (one element flipped)
• Total: 42 + 43 + 43 = 128

The number 42 appearing as the universal column sum of the fixed point is notable — it is the only non-trivial value that satisfies this constraint given the matrix dimensions.

1.4 The 68 Symmetry Breaks

While 99.58% of the matrix satisfies the point-symmetry identity matrix[r][c] + matrix[127-r][127-c] = -1, exactly 68 cells (34 pairs) deviate. These concentrate in 8 columns:

Columns: {0, 22, 30, 41, 86, 97, 105, 127}
Pairs:   (0, 127), (22, 105), (30, 97), (41, 86)

The pair (30, 97) is the same column pair that produces the "AI.MEG.GOU" XOR signature — the symmetry breaks and the encoded message share the same structural anchor points.

Part II: Aigarth Architecture (Source Code Analysis)

2.1 What Aigarth Actually Is

Through analysis of the official aigarth-it Python library and the Qubic Core scoring system, we can describe the actual Aigarth architecture:

Aigarth is a ternary neural network with circle (ring) topology that:

• Uses balanced ternary values: 1
• Runs iterative feedforward cycles until convergence (up to millions of ticks)
• Evolves through mutation and selection
• Is trained by the Qubic mining network (676 computors)

2.2 Circle Topology with Variable Neurons

Unlike conventional neural networks, Aigarth ITUs (Intelligent Tissue Units) have:

Variable neuron count: Neurons can be born and die during mutation.

• When a weight mutation overflows beyond ±1, a new neuron is spawned (cloned from a neighbor)
• When all of a neuron's weights become zero, the neuron is removed (unless it's an input/output neuron)
• The network grows and shrinks organically

Asymmetric connectivity: Each neuron divides its inputs into "backward" and "forward" groups along the circle, with a configurable input_skew parameter that creates directional information flow.

Scale: The reference implementation for integer arithmetic uses NEURON_INPUT_COUNT_INIT = 200 — each neuron starts with 200 input weights. This is orders of magnitude larger than simplified implementations.

2.3 The Tick Loop

for tick in range(cycle_cap):        # Up to 1,000,000 * output_bitwidth
    for each neuron in circle:
        feed = get_weighted_neighbor_states(neuron)
        neuron.next_state = ternary_clamp(sum(feed * weights))
    commit_all_states()

    if all output neurons non-zero:  break   # Solution found
    if no state changes:             break   # Convergence

The maximum tick cap is FF_CYCLE_CAP_BASE = 1,000,000 multiplied by the output bitwidth. For an 8-bit output task, that is 8 million ticks per single inference. The system is designed for deep, iterative computation.

2.4 Three Convergence Conditions

1. All outputs non-zero — the network has produced a complete answer
2. No state changes — the network has reached a fixed point
3. Tick cap reached — timeout (treated as failure)

2.5 Training Through Mining

The Qubic network's scoring system is Aigarth training:

1. Miners receive training tasks (currently: integer addition A + B = C)
2. Miners evolve their ITUs through mutation cycles
3. Each ITU is scored by counting correct outputs across all training pairs
4. The 676 highest-scoring miners become the computor quorum
5. Economic reward provides evolutionary selection pressure

This means the entire Qubic network functions as a distributed evolutionary optimizer for ternary neural networks. Every mining epoch is a generation of evolution.

2.6 Performance Metrics

The fitness evaluation distinguishes between three output states:

This three-valued logic means the system can express uncertainty — a zero output is better than a wrong answer. The network learns epistemic humility.

2.7 Architectural Comparison

Our implementation uses the Anna Matrix as a dense weight matrix for single-tick inference. The official system uses sparse circle connectivity with millions of ticks for deep iterative computation. Both share the ternary foundation.

Part III: Artificial Life Emergence

3.1 Experiment Design

We embedded the Anna Matrix as the "brain" of agents in a toroidal 128x128 artificial life simulation:

Agent architecture:

• 9 sensors (food, neighbors, pheromones, body state)
• 6 output channels (move X/Y, social behavior, mate, share food, rest) encoded as 3-bit groups
• 4 neuromodulators (dopamine, serotonin, acetylcholine, norepinephrine)
• Heritable genome: 128-byte brain seed + 9-element sensor permutation
• Cultural bias: 3 learned values transmitted through imitation

World mechanics:

• 128x128 toroidal grid with terrain derived from matrix thresholds
• Food regeneration, seasonal oscillation, periodic catastrophes
• Energy economy: foraging, reproduction cost, idle metabolism
• Signal broadcasting: 3-bit messages visible to neighbors

3.2 Phase 4 Results (500K Ticks)

Four experimental phases, each building on the previous:

Key discoveries:

Aggression collapse: In the combined system (learning + encoding evolution), aggression dropped 43% over 500K ticks. Agents evolved conflict-avoidance strategies without any explicit reward for peace.

Sensor permutation evolution: Each agent carries a heritable permutation of its 9 sensor inputs. Permutation diversity saturates at 100% by tick 20K — the identity permutation is universally suboptimal. Agents evolve unique "perceptual frames."

Genome diversity: Remains above 0.49 across all phases (starting from 0.50). The bijective matrix brain prevents genetic monoculture — diversity is structurally maintained.

3.3 Emergent Signal Language

With 3-bit signal broadcasting enabled, agents spontaneously evolved a Hamming-weight based communication protocol:

This pattern reproduces across seeds. Transfer entropy analysis confirms information flow: signal states causally influence cooperation decisions (TE > 0.001).

The signal language is not programmed — it emerges from evolutionary pressure. Agents that signal cooperation to neighbors and respond to cooperative signals survive longer and reproduce more.

3.4 The 10-Million-Tick Long Run

A single seed (42) was run for 10M ticks under optimized conditions:

Population dynamics:

• Mean: 1,789 agents (capacity ~1,785)
• 212 boom-bust cycles (seasonal oscillation)
• Only 0.85% of time below Allee threshold (500)
• Coefficient of variation: 0.55

Evolutionary depth:

• 92,938 generations (deepest observed)
• Genome diversity: 0.50 → 0.47 (only 6% decline in 93K generations)
• All 128 gene positions remain polymorphic (zero fixation)

Cooperation:

• Mean: 31.5%, max: 40.2%
• Positive trend (slope 5.8e-6 per tick) — cooperation slowly rises
• Negatively correlated with population (-0.13) — cooperation peaks during scarcity

Energy economy:

• Production/consumption ratio: 2.07 (healthy surplus)
• Per-capita production: 0.97

Culture:

• Peak adoption: 99.4%
• Final adoption: 78.8%
• Cultural bias deepening over time (bit 0: -0.28 → -0.61)

Lineage:

• Started with 1,024 founder lineages
• Collapsed to 1 surviving lineage by 10M ticks
• Complete founder lineage replacement — consistent with neutral drift theory

Demographics:

• Median age increased from ~500 to 759 ticks
• Serotonin levels doubled (stress response adaptation)
• Spatial clustering increased (Clark-Evans R: 1.13 → 0.90)

3.5 Causal Analysis

Sliding-window transfer entropy analysis across the 10M-tick run reveals:

Aggression drives cooperation 83.8% of the time — not the other way around. Cooperation is a reactive strategy to aggression pressure, consistent with the Axelrod effect in evolutionary game theory.

The system exhibits 8 regime changes between aggression-dominant and cooperation-dominant phases. Effective dimensionality of the causal network: 2.64 ± 0.10, indicating moderate complexity.

Emergence metrics:

• C-Score: 0.4357 (moderate causal closure)
• Lempel-Ziv Complexity: 0.7113 (high behavioral unpredictability)
• 5 phase transitions detected (at ticks ~8.1M and ~9.8M)
• Strongest causal link: energy balance → population (Granger F=2096)

Part IV: Open Questions

What We Proved

1. The Anna Matrix is a near-perfect bijection on ternary state space (0 collisions in 100K tests)
2. The official Aigarth system uses variable-topology networks with up to 8M ticks per inference
3. Anna Matrix brains produce emergent signal language and cooperation in ALife simulations
4. Aggression drives cooperation (Axelrod effect) — confirmed by transfer entropy analysis
5. Genome diversity is structurally maintained by the bijective matrix (only 6% decline over 93K generations)

What Remains Unknown

1. How the Anna Matrix relates to the Aigarth Circle topology — our dense matmul approach differs fundamentally from the official sparse circle. The matrix may serve a different purpose than being network weights.
2. What the Qubic mining network has evolved over 2 years — since mainnet launch in April 2024, miners have been running evolutionary optimization. The results are not public.
3. Whether the score function has changed — the current public task is integer addition. More complex tasks may have been deployed.
4. Multi-seed validation of 10M-tick results — our long run used a single seed. Multi-seed replication is needed.
5. Random matrix ablation — proving the Anna Matrix produces qualitatively different emergence than random matrices of the same dimensions.

Reproducibility

All experiments can be reproduced with:

• The Anna Matrix data file (public key)
• The simulation source code (Objective-C, compiled on macOS with Apple Silicon)
• Python analysis scripts (NumPy, SciPy, Matplotlib)
• Seed value 42 for the primary long run

Hardware requirements: Apple Silicon Mac (for ANE acceleration) or any x86-64 system (CPU-only mode).

Research conducted March 2026. All data derived from publicly available sources.