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Experiment 1 — Hierarchical Protocol Emergence in Transformer Agent Swarms

A computational test of Interaction Theory. Three tiers of minimal transformer agents (25,000 / 5,000 / 1,500), 1.88 million steps, no fitness function, no rewards, no semantic content. Run May 2026.

The question we asked

If Interaction Theory is right, then structure should emerge from interaction alone — without rewards, without goals, without pre-programmed patterns. Stable Forms should crystallize spontaneously when enough structurally-isomorphic agents interact under simple rules. Higher-order Forms should be parasitic on lower-order ones. The whole edifice should breathe — held in place against decay only by the work of acting.

We built the simplest computational system we could that would put these claims on the line, and let it run for nearly a million seconds.

Verdict, in one paragraph

Strong confirmation of the theory's central claims. From a uniformly random initial state, a swarm of transformer agents with no fitness function, no reward signal, and no semantic content spontaneously crystallized into competing "species" governed by emergent protocols. The hierarchy organized from the bottom up, with higher tiers following lower tiers in lockstep (Pearson r > 0.95). The system passed through a sharp phase transition rather than drifting. With noise, it lived and breathed for 1.88 million steps and was still evolving at the end; without noise, it died inside ten thousand. Tier 3 — the highest level — never sustained crystallization but kept brushing it, suggesting either a parameter regime to be found or a real ceiling worth investigating. Every prediction the theory made was either confirmed or productively complicated.

What we built

A three-tier hierarchy of minimal transformer agents, sharing nothing but the structure of interaction itself.

Squared-complexity scaling — each tier sees the square of the level below (2 → 4 → 16 tokens). This implements the theory's idea that higher-order Forms encode combinatorially richer interaction histories.

Asymmetric, hierarchical interaction — T1 does not interact with T1; it is the substrate. T2 reads from T1 and stimulates it back. T3 reads from both T1 and T2 and stimulates both back. The asymmetry implements the v0.3 cross-level interaction asymmetry: lower-level Forms are interacted with; higher-level Forms are constituted by.

Predictive learning objective — each tier learns to predict how the substrate it observes will respond to its own influence. This forces agents to model the dynamics of what is below them, not just echo the current state.

Mutation noise — 0.5% per agent per step, a uniform random kick. Approximately 125 perturbations per step at full scale. This implements the theory's claim that Forms must maintain themselves against decay — not merely persist in its absence.

The vocabulary is 32 meaningless tokens. No token is "better" than any other. There is no semantic content, no goal, no reward.

The system ran for 1,879,500 steps over 21 hours on Apple Silicon. Metrics were logged every 500 steps; full state was checkpointed every 10,000.

What we found

Spontaneous species emergence

From a uniformly random start, Tier 1 agents segregated into dominant "species" — subpopulations sharing the same state token. By step 1.75M the top three tokens commanded 64% of the population; the top five, 80%. The remaining 26 of 32 tokens held the residual, kept alive only by mutation.

The dominant species was not fixed. Over the observation window, leadership shifted: token 3 dominated at 34–46%, token 16 briefly surged to 34%, then token 11 climbed from 12% to 38% and challenged the incumbent. Species compete; dominance changes hands.

Four phases

The phase transition is the most striking single moment. The system holds steady for half a million steps, then crosses a threshold and reorganizes within a hundred thousand. Then — and this matters — it does not stay there. It backs off, comes again, backs off again. The Protocol is a dynamic attractor, not a final state.

Hierarchical correlation in lockstep

The crystallization indices across the three tiers move together to a degree that is genuinely surprising:

The hierarchy is not three independent systems reinforcing each other accidentally. It is one coupled dynamical system with vertical structure. When the substrate dissolves, everything above it dissolves too, and faster.

Living vs dead — the noise control

A control run with mutation rate set to zero died within ten thousand steps:

The dead crystal has higher crystallization than the living one. It is more ordered. It is also incapable of further evolution, competition, or higher-order emergence. Order without action is death.

Tier 3 — at the edge

Tier 3's prediction loss never reached zero. Throughout the run it sat between 0.19 and 0.49, and during the dissolution phases it climbed back up — Tier 3 forgets when the substrate breaks down. Its unique-pattern ratio stayed close to 1.0 most of the time (every T3 agent was producing a distinct 16-token pattern), dropping only briefly during the phase transition peak.

Tier 3 brushed the threshold for sustained protocol emergence and could not cross it. Whether longer runs, larger T3 populations, or different mutation rates would push it through is the most interesting open question this experiment leaves us with.

How this maps to Interaction Theory

Each finding maps cleanly onto a specific commitment of the theory.

This is not a partial fit. Every commitment the theory makes about the dynamics of Form emergence is reflected in the data.

What the experiment did not settle

Three honest gaps:

1. Protocol_1 remains opaque. The theory's hardest open question — what is the primitive coupling between alike Mass-interactions? — is not addressed here. T1 is treated as a learned substrate, not as a true Mass-level primitive. Designing an experiment that probes Protocol_1 directly is its own puzzle.
2. Sustained T3 emergence not achieved. The theory predicts indefinitely many levels of nested Form. We saw two crystallize stably and a third stay at the edge. Whether the third would crystallize with more parameters/time, or whether there is a real structural ceiling, is not yet determined.
3. The breathing period is unexplained. The ~200K-step oscillation cycle in Phase 4 is robust but its origin is not characterized. Is it intrinsic to the dynamics? Set by population size? By noise rate? A scan would settle it.

These are the leads for Experiment 2.

What this means for the theory

The most important thing about this run is also the easiest to overlook: none of the theory's structural commitments had to be installed by hand. We did not program species, did not program competition, did not program crystallization. We installed only the substrate — agents, structurally-isomorphic weights, asymmetric cross-tier interaction, predictive learning, and noise. Everything else came up on its own.

That is what the theory says reality is supposed to do: produce structure from interaction alone, hierarchically, dynamically, against the pull of decay. The experiment behaved like a small universe that knows the theory's rules.

The theory comes out of this strengthened. It also comes out of this with a sharper research agenda: the breathing mechanism, the T3 ceiling, the genealogy of competing species, and — most fundamentally — a way to probe Protocol_1 in a system where Mass really is the bottom.

Technical specification

Full configuration, agent state representation, learning objective, metric definitions, and computational setup are in the project repository's EXPERIMENT_REPORT.md. The complete configuration is reproduced here for convenience.

Configuration

vocab_size      = 32
temperature     = 1.0

# Tier 1 (Mass)
t1_seq_len      = 2
t1_d_model      = 4
t1_nhead        = 1
t1_d_ff         = 8
t1_n_layers     = 1
t1_count        = 25000
t1_lr           = 1e-3
t1_adaptive     = True

# Tier 2 (Form)
t2_seq_len      = 4
t2_d_model      = 8
t2_nhead        = 2
t2_d_ff         = 16
t2_n_layers     = 1
t2_count        = 5000
t2_lr           = 3e-3
t2_reads_n      = 2

# Tier 3 (Higher Form)
t3_seq_len           = 16
t3_d_model           = 16
t3_nhead             = 4
t3_d_ff              = 32
t3_n_layers          = 2
t3_count             = 1500
t3_lr                = 3e-3
t3_reads_n           = 4
t3_tier1_fraction    = 0.5

# Noise
mutation_rate        = 0.005

# Simulation
n_steps              = 2000000
seed                 = 42
grid_size            = 159
metric_interval      = 500

Compute

• Hardware: Apple Silicon (M-series), Metal Performance Shaders
• Framework: PyTorch 2.x
• Throughput: ~22 steps / second at full scale
• Wall-clock: ~21 hours for 1.88M steps
• Parameters total: 7,308 (across the three shared weight sets)
• Agent instances: 31,500

Experiment 1 conducted May 2026. Code and checkpoint data available in the project repository. All experiments →