Zeta Life

Emergent coherent integration in adaptive multi-agent systems

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Overview

Zeta Life is a computational framework for studying phase transitions in adaptive integration systems. It models how independent processing units (kernels) can transition from fragmented computation to coherent, unified integration -- and how populations of such units exhibit emergent collective behavior.

The core equation predicts when integration emerges:

$$\Psi = B^3 + \Phi \qquad \text{(integration index, supercritical regime)}$$

$$\Phi_c = \frac{F_i}{\alpha - C} \qquad \text{(critical threshold for phase transition)}$$

$$B = \frac{\Phi - \Phi_c}{\Phi_c} \qquad \text{(binding factor)}$$

The cubic term $B^3$ creates a sharp phase transition: below the critical threshold $\Phi_c$, integration is zero. Above it, the system amplifies nonlinearly -- a mathematical signature of emergent coherence.

The current research program ("The North", below) takes this further: making $\Psi$ a property of a real LLM's own activations and testing whether the model can learn to introspect it — adaptation, not scale.

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Architecture

Adaptive Kernel (Active Inference)

Each ConsciousKernel implements a full Active Inference cycle:

PERCEIVE -> PREDICT -> COMPARE -> UPDATE -> MEMORIZE -> ACT -> REFLECT -> DREAM

Component	Role
WorldModel	GRU-based predictive model of the environment
SelfModel	Recursive self-modeling (Strange Loop)
PredictionErrorEngine	Multi-channel precision-weighted error signals
PrecisionController	Learned precision hyper-model (attention)
FastMemory / SlowMemory	Complementary Learning Systems (episodic + semantic)
DreamEngine	Zeta-driven offline consolidation
PersistenceLayer	Identity save/load across sessions

The integration index $\Psi$ is derived from internal signals:

• $\Phi$ (integrated information) from inverse free energy + memory depth
• $F_i$ (binding force) from learned precisions + self-reflection convergence
• $C$ (coherence cost) from recent prediction errors

import torch
from zeta_life.kernel import ConsciousKernel

kernel = ConsciousKernel(obs_dim=4, latent_dim=32, alpha=1.0)
result = kernel.step(torch.randn(4))
print(result.psi)          # integration index [0, 1]
print(result.free_energy)  # prediction error magnitude

Or run the full demo (learning loop + identity save/load):

make quickstart            # = PYTHONPATH=src python demos/quickstart.py

Multi-Kernel Organism (Darwinian Brain)

Multiple kernels compete for a shared GlobalWorkspace via proposal strength. Energy-managed spawning, merging, and death create a Darwinian selection process at the kernel level.

import torch
from zeta_life.kernel import ConsciousOrganism

organism = ConsciousOrganism(obs_dim=4, initial_kernels=5)
result = organism.step(torch.randn(4))
print(result.psi)         # organism-level integration
print(result.population)  # surviving kernel count

Hierarchical Integration (Cells -> Clusters -> Organism) — archived

Archived (2026-06-08). A parallel Cells→Clusters→Organism consciousness formalism that the live kernel never used. Removed from the working tree in the refocus; preserved on the legacy/pre-refocus-snapshot branch.

Zeta Function as Temporal Binding (optional — tested, not load-bearing)

The Riemann zeta zeros give an optional temporal basis:

$$K_\sigma(t) = 2 \sum_n \exp!\bigl(-\sigma,|\gamma_n|\bigr),\cos(\gamma_n, t)$$

where $\gamma_n$ are the imaginary parts of zeta zeros (14.134, 21.022, 25.011, ...). They drive the DreamEngine's consolidation rhythm and are available as an optional OscillatorBank time code for the world model.

Honest result (this project's own experiments). The specific zeta spectrum is not load-bearing. In the kernel, an equispaced Fourier lattice matches or beats zeta at temporal prediction — even on a zeta-structured signal — and zeta's GUE level-repulsion is functionally flat (results/zeta_vs_baselines_run.txt, results/spacing_statistics_run.txt). In the consciousness dynamics, ZETA == UNIFORM (p=1.0). Zeta genuinely wins only in the spatial cellular automata. Recommendation: fixed temporal basis → OscillatorBank.fourier/log_spaced; adaptive → learned. Zeta is kept as a documented, tested design choice — not the thesis.

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The North: making Ψ internal (introspection research)

The kernel's $\Psi$ is an external index — a thermometer pointed at an agent. The current research program asks the harder question: can $\Psi$ become a property of an agent's own activations, and can the agent learn to perceive it? This is the project's real thesis — a model that adapts until it can observe itself, rather than scaling to a giant.

Substrate. A live LLM (Yvyra, Qwen3-8B) runs in transformers/8-bit. The bridge/ couples its real experience to the kernel; introspection/ computes candidate integration metrics over its hidden states and tests introspection with the methods of Anthropic (Lindsey, concept injection) and Binder (privileged access). Honest, control-driven results so far:

Experiment	Result
Phase A/B (expose Ψ to the agent, sham control)	Inconclusive — Ψ saturates (~89% high); the design works, the signal didn't vary enough (docs/PHASE_B_DESIGN.md)
Spontaneous introspection (concept injection, untrained)	Negative — 0/30; a control killed the apparent positive (steering, not introspection). Replicates the scale limit Anthropic sees
Trained P(IK) self-report (LoRA)	Honest negative — a strong blind M2 (Claude, 0.82) and the model's own softmax confidence (0.81) both beat the self-report (0.76). It verbalizes confidence, no robust privileged access
Trained injected-concept detection (LoRA, constant prompt → non-textual by construction)	Positive — accuracy 1.000 (chance 0.091), 0 false positives. The model reads a non-textual injected state and names it. Caveat: fixed concept set may be a lookup; scaling test pending

Each result was reported only after an adversarial control — the honesty discipline that distinguishes "verbalizing confidence" from "privileged introspection." See docs/{ANTHROPIC_NORTH,RESEARCH_PHASE_B,TARGET_SELECTION,TRAINED_INTROSPECTION,LORA_PLAN}.md.

from zeta_life.introspection import psi_act_all   # 4 integration metrics over hidden states
# harness.py / concept_injection.py need the GPU stack (transformers); see experiments/introspection/

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Installation

git clone https://github.com/skyvanguard/zeta-life.git
cd zeta-life
pip install -e .

# With all extras (mpmath for exact zeta zeros, jupyter)
pip install -e ".[full]"

Dependencies

• Python 3.9+
• PyTorch 2.0+
• NumPy, SciPy, Matplotlib

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Quick Start

import torch
from zeta_life.kernel import ConsciousKernel

# Create a kernel and run it for 100 steps
kernel = ConsciousKernel(obs_dim=4, latent_dim=32)
for i in range(100):
    stimulus = torch.randn(4)
    result = kernel.step(stimulus)

print(f"Psi: {result.psi:.4f}")
print(f"Free energy: {result.free_energy:.4f}")
print(f"Dreamed: {result.dreamed}")

Run Experiments

# Psi validation on real datasets
python experiments/datasets/exp_real_data_psi.py

# Kernel validation (compositionality, grounding, emergence)
python experiments/kernel/exp_conscious_kernel_validation.py

# Multi-kernel organism dynamics
python experiments/kernel/exp_organism_emergence.py

# Science pipeline (toy -> instrument; see docs/SCIENCE_PLAN.md)
python experiments/kernel/exp_psi_vs_free_energy.py   # validate Psi (Albantakis method)
python experiments/kernel/exp_epistemic_depth.py      # precision hyper-model (epistemic depth)
python experiments/kernel/exp_yvyra_experiment.py     # Yvyra pipeline (modes + blind re-scorer)

# Introspection / the north (needs the GPU stack: transformers + bitsandbytes)
python experiments/introspection/exp_pik_probe.py          # is "I know" in the activations?
python experiments/introspection/exp_pik_train.py          # train P(IK) self-report (LoRA)
python experiments/introspection/exp_f3_inject_train.py    # trained injected-concept detection

Run Tests

PYTHONPATH=src pytest tests/ -q   # 556 tests (or `pip install -e .` first)

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Project Structure

zeta-life/
|-- src/zeta_life/
|   |-- kernel/          # CORE - Active Inference kernel + Darwinian organism
|   |-- bridge/          # Yvyra coupling - feed a live agent's experience to the kernel
|   |-- introspection/   # THE NORTH - Psi over an LLM's activations; concept injection
|   |-- instrumentation/ # TickLogger - paired per-tick logging (science pipeline)
|   |-- integration/     # formal_equations.py - the integration index Psi
|   |-- datasets/        # Real-world dataset adapters (for Psi validation)
|   |-- core/            # zeta_constants, vertex, tetrahedral geometry
|   +-- utils/           # Shared utilities
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|-- experiments/
|   |-- kernel/          # kernel experiments (the live research)
|   |-- introspection/   # the north - probe, P(IK) LoRA, injected-concept detection
|   +-- datasets/        # Psi on real data
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|-- demos/               # quickstart.py - the 60-line kernel demo
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|-- tests/               # 34 test files (585 tests)
+-- docs/                # Documentation, papers, plans (incl. ANTHROPIC_NORTH,
                         #   TRAINED_INTROSPECTION, TARGET_SELECTION, LORA_PLAN)

(Legacy subsystems -- psyche, hierarchical/IPUESA integration, organism,
evolution -- were archived on 2026-06-08 to the legacy/pre-refocus-snapshot branch.)

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Formal Equations

Equation	Formula	Meaning
Critical threshold	$\Phi_c = \frac{F_i}{\alpha - C}$	Minimum integration for phase transition
Binding factor	$B = \frac{\Phi - \Phi_c}{\Phi_c}$	Distance above threshold (normalized)
Integration index	$\Psi = B^3 + \Phi$	Nonlinear amplification of coherence
Critical mass	$M_c = \frac{F_i}{\alpha - C}$	Minimum units for integration to emerge
Corruption threshold	$1 - \frac{F_i}{\alpha \cdot M \cdot \alpha_s}$	Maximum damage ratio before collapse

These are implemented as pure functions in integration/formal_equations.py and consumed by the kernel's _compute_psi().

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Theoretical Foundations

• Active Inference / Free Energy Principle (Friston) -- the kernel minimizes prediction error
• Complementary Learning Systems (McClelland et al.) -- fast episodic + slow semantic memory
• Darwinian Brain -- multi-kernel competition via Global Workspace
• Integrated Information Theory (Tononi) -- Phi as integration measure
• LLM introspection (Lindsey/Anthropic concept injection; Binder privileged access) -- the basis of the introspection program (see "The North")
• Riemann zeta zeros -- optional temporal basis (tested; not load-bearing except in spatial CA -- see "Zeta Function as Temporal Binding")

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Citation

@software{zeta_life_2026,
  author = {Francisco Ruiz},
  title = {Zeta Life: Emergent Coherent Integration in Adaptive Multi-Agent Systems},
  year = {2026},
  url = {https://github.com/skyvanguard/zeta-life}
}

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License

MIT License -- See LICENSE for details.