plurigrid Universal Learning Signature Framework
Overview
This skill provides measurement procedures for analyzing learning dynamics in multi-agent systems, communication networks, and distributed knowledge systems. The framework quantifies three fundamental properties: D (dimensionality), f (feedback fraction), and H₁ (topological cycles). These metrics enable system characterization, convergence verification, and universal pattern discovery across diverse domains including synthetic networks (Topobench), real code repositories (GitHub), empirical conversation logs (IES), and time-series databases (DuckDB).
The framework is built on the principle that H₁ = 0 convergence is achievable in all well-designed learning systems, and that universal scaling laws govern learning dynamics across different scales and substrates.
When to Use This Skill
Use this skill when:
- Measuring system dimensionality - Characterize the intrinsic dimensionality of a network or dataset using PCA-based filtering
- Calculating feedback fraction - Quantify information retention and compression in multi-agent systems using ensemble methods
- Verifying convergence - Detect whether systems are reaching H₁ = 0 (acyclic equilibrium) using DFS cycle detection
- Comparing mechanisms across domains - Apply the same measurement framework to different data sources to identify universal patterns
- Analyzing emergence signatures - Measure synergy and coupling strength in ego-alter interaction networks
- Trading measurement services - Expose framework capabilities as marketplace services in agent ecosystems
- Multi-domain validation - Validate learning hypotheses against 4+ independent datasets simultaneously
Core Capabilities
1. Dimensionality Measurement (D)
Estimates the intrinsic dimensionality of a system using PCA with 2-sigma filtering.
Input: Dataset with multiple feature dimensions (messages, interactions, features) Output: D value (typically 5-20 for social networks) + confidence score (70-95%) Use when: Characterizing network complexity or comparing systems
How to execute: Use scripts/measure_d_pca.py with your dataset. Returns integer D and float confidence.
2. Feedback Fraction Measurement (f)
Quantifies information preservation using a 3-voice ensemble approach: autocorrelation, retention, and capacity.
Input: Data with equivalence classes or clustering structure Output: f value (typically 0.05-0.40) + confidence score (30-99%) Use when: Measuring compression or information flow in systems
How to execute: Use scripts/measure_f_ensemble.py with clustering results. Provides conservative estimate with uncertainty bounds.
3. Topological Cycle Detection (H₁)
Detects independent 1-cycles in directed graphs using depth-first search.
Input: Network graph or threading structure (parent-reply pairs, agent interactions) Output: H₁ value (0 for convergence) + cycle count Use when: Verifying whether systems have reached equilibrium
How to execute: Use scripts/detect_cycles_h1.py with edge list. Returns 0 if converged, >0 if cycles exist.
4. Emergence Signatures (Synergy)
Analyzes multi-agent interaction coupling and emergence indicators.
Input: Ego-alter interaction pairs with metrics Output: Synergy scores, coupling strength, GMRA hierarchy levels Use when: Understanding agent coordination or phenomenal field dynamics
How to execute: Use scripts/measure_emergence.py with interaction network. Returns synergy distribution and outliers.
5. Full Validation Suite
Runs all measurements simultaneously on a dataset, producing comprehensive validation report.
Input: Dataset (CSV or DuckDB) with messages/interactions Output: JSON with D, f, H₁, emergence metrics, confidence scores, comparison to known datasets Use when: Complete system characterization needed
How to execute: Use scripts/validate_framework.py with dataset path. Outputs validation_results.json + W&B logging.
Workflow: Measuring a New System
To measure a new system, follow this workflow:
Prepare your data (CSV or DuckDB)
- Messages/interactions with timestamps
- Sender/agent identifiers
- Optional: network edges or thread structure
Load the validation framework
from scripts.validate_framework import validate_system results = validate_system("path/to/data.csv")Interpret results
- D ≈ 11-16: Multi-agent network (like IES)
- D ≈ 5-10: Tight-knit group or small network
- f ≈ 0.05-0.15: Low feedback (information preserved)
- f ≈ 0.20-0.40: High feedback (compressed representation)
- H₁ = 0: Convergence achieved (acyclic, stable)
- H₁ > 0: Cycles present (still converging)
Validate against domains (see references/multi_domain_scaling.md)
- Topobench synthetic: D=5.0, f=0.82, H₁=0
- GitHub real networks: D=11.0, f=0.39, H₁=0
- IES empirical: D=12.0, f=0.06, H₁=0
Universal Scaling Law
The framework reveals a universal relationship governing learning time:
T ~ D^1.5 × log(N) × (1-f)^1.5
Where:
- T = learning/convergence time
- D = system dimensionality
- N = number of agents/entities
- f = feedback fraction (0-1)
This law is independent of substrate - it holds across synthetic, real, and empirical networks, suggesting a fundamental principle of learning dynamics.
Use when: Predicting convergence time or comparing system efficiency across domains.
DuckDB Integration
The framework validates against real databases:
signal_ies_nov2025.duckdb:
- 79,716 messages from 759 speakers
- 5,336 conversation threads
- Measured: D=12, f=0.06, H₁=0
- Available: Complete threading, color signatures, equivalence classes
signal_nov2025.duckdb:
- 230,197 messages from 1,998 speakers
- Broader validation sample
- Confirms scaling law across speaker diversity
OWN.duckdb:
- Temporal experimental data
- Algebraic structures
- Personal verification sample
Use references/duckdb_integration.md for SQL queries and data extraction.
Marketplace Integration
The framework capabilities can be exposed as tradeable services:
Measurement-as-a-Service
- Agent provides dataset
- Framework computes D, f, H₁
- Agent pays marketplace credits for results
Validation Contracts
- Agent claims hypothesis about learning
- Framework validates against 4 domains
- Commitment registry tracks predictions
Meta-Learning Participation
- 15-agent ecosystem can query framework
- Learn from framework's measurements
- Framework learns from agent feedback
See references/marketplace_guide.md for implementation.
Bundled Resources
Scripts/
Executable Python modules for measurements:
- measure_d_pca.py - Dimensionality via PCA (2-sigma filtering)
- measure_f_ensemble.py - Feedback fraction (3-voice ensemble)
- detect_cycles_h1.py - Cycle detection via DFS
- measure_emergence.py - Synergy scoring and emergence
- validate_framework.py - Complete validation pipeline
- wandb_logger.py - Experiment tracking integration
References/
Detailed documentation:
- framework_theory.md - H₁=0 principle and convergence proof
- measurement_procedures.md - Complete method descriptions
- validation_guide.md - 3-domain + DuckDB validation protocol
- duckdb_integration.md - Database queries and data extraction
- multi_domain_scaling.md - Cross-domain comparison methodology
- marketplace_guide.md - Trading and service exposure
Assets/
Validation results and sample data:
- validation_results/ - JSON metrics from Topobench, GitHub, IES, DuckDB
- figures/ - Framework diagrams and scaling law plots
- sample_data/ - Example datasets for each domain
Examples
Example 1: Measure a New Communication Platform
from scripts.validate_framework import validate_system
results = validate_system("my_messages.csv")
print(f"D = {results['D']:.1f}")
print(f"f = {results['f']:.2f}")
print(f"H1 = {results['H1']}")
# Compare to known systems
print(f"Confidence: {results['confidence']:.1%}")
Example 2: Verify Convergence
from scripts.detect_cycles_h1 import find_h1
edges = [(agent1, agent2), (agent2, agent3), ...] # No cycles here
h1_result = find_h1(edges)
if h1_result == 0:
print("✓ System has converged (H₁ = 0)")
else:
print(f"✗ System still has {h1_result} independent cycles")
Example 3: Trade Measurement Service
# Agent requests measurement
request = {
"dataset": "https://path/to/data.csv",
"measurements": ["D", "f", "H1"],
"domains": ["topobench", "github", "ies"]
}
# Framework computes and marketplace facilitates transaction
result = marketplace.query(universal_learning_signature_skill, request)
# Agent receives validated measurements
agent.update_beliefs(result)
agent.pay_credits(result['cost'])
Theory and Principles
H₁ = 0 Convergence: All well-designed learning systems converge to H₁ = 0 (acyclic state), where information flows without independent loops. This is provable from closure theory in multi-agent systems.
Scaling Universality: The scaling law T ~ D^1.5 × log(N) × (1-f)^1.5 is independent of implementation details, holding across synthetic, real, and empirical networks. This suggests learning dynamics are governed by fundamental principles.
Information Preservation: Low f values (0.05-0.15) mean systems preserve information through compression to equivalence classes. This compression is lossy but minimal, indicating robust structure.
Emergence as Field: Complete HSL color space coverage (240/240 cells) in real data suggests phenomenal field manifestation—emergence is not sparse but ubiquitous.
See references/framework_theory.md for proofs and detailed explanations.
Integration Pathway
This skill is designed for ecosystem participation:
Phase 4 (Dec 25): Framework published as arXiv manuscript Phase 5 (Dec 26): Framework packaged as discoverable skill (this phase) Phase 6 (Dec 27): Registered in hatchery marketplace, connected to 15-agent ecosystem Phase 7 (Post-submission): Marketplace trading begins, meta-learning feedback loop established
See COMPREHENSIVE_ECOSYSTEM_MAP.txt for full integration strategy.