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Non-Abelian Stratified Quantum Normative Dynamics (NA-SQND)

Research repository for the Stratified Quantum Normative Dynamics framework - a novel approach to AI ethics and alignment using gauge-theoretic principles.

Repository Structure

non-abelian-sqnd/
├── papers/           # Academic papers (TeX, PDF)
├── experiments/      # Python research scripts and notebooks
├── docs/             # Documentation and whitepapers
├── data/             # Experimental data and results
└── personal/         # Personal documents (CV, presentations)

Related Repositories

Repository Description
ahb-sjsu/erisml-lib ErisML/DEME production library implementing these theoretical frameworks
ahb-sjsu/sqnd-probe Dear Ethicist - advice column game for measuring moral reasoning structure

DEME V3 Implementation Status (as of January 2026)

Phase Sprints Status Features
Foundation 1-3 Complete MoralTensor, tensor ops, V2/V3 compat
Distributional 4-6 Complete Per-party facts, fairness metrics, V3 EMs
Multi-Agent 7-10 Complete Temporal, coalitions, Shapley, strategic layer
Acceleration 11-13 Complete CPU/CUDA/Jetson backends
Advanced 14-15 Complete Uncertainty (rank-5), full context (rank-6)
Hardening 16-18 In Progress Decision proofs, testing, docs

Key Papers

Core Theory

  • Non-Abelian Stratified Quantum Normative Dynamics - Core theoretical framework establishing gauge-theoretic foundations for AI ethics
  • Stratified Geometric Ethics - Foundational paper on differential geometry applied to moral alignment
  • Tensorial Ethics - Mathematical framework for multi-dimensional ethical reasoning

Empirical Work

  • Dear Abby Ground Truth Paper - Empirical validation using 20K letters (1985-2017) as ethical ground truth
  • Bond Index Calibration - Representational coherence metrics for AI evaluators

Experiments

Core SQND Experiments

Script Description Status
quantum_bell_test.py Bell inequality tests for ethical alignment Active
quantum_bell_test_v2.py Enhanced Bell test with DEME integration Active
hysteresis_double_blind.py Double-blind hysteresis experiments Active
hysteresis_v2.py Updated hysteresis with V3 tensors Active
protocol1_claude_aita.py Protocol 1 AITA corpus experiments Active
protocol2_holonomy.py Holonomy measurement protocols Active
contextuality_experiment.py Contextuality detection in LLMs Active

Algebraic Topology

Script Description
algebraic_topology_of_self.py Self-referential topology experiments
stratified_gauge_exploration.py Gauge structure exploration
sqnd_phase_transition_v2.py Phase transition detection
sqnd_fuzzer.py Bond Index fuzzing tests

Data Collection

Script Description
comprehensive_fetcher_v2.py Multi-source ethical corpus fetcher
baseline_em.py Baseline Ethics Module generator
full_baseline_generator.py Complete baseline EM with Dear Abby weights

Notebooks

  • Protocol1_NASQND_Experiment.ipynb - Interactive Protocol 1 experiments

Documentation

Vision Papers

  • Non_Abelian_SQND_Bond_2026_v4_1.md - Latest SQND paper draft
  • NASQND_Experimental_Protocols_v1.md - Experimental protocols specification
  • sqnd_paper_v3_5_with_results.md - Paper with experimental results

Technical Guides

  • sqnd_ethics_desk_specification_v2.md - Ethics Desk tool specification
  • sqnd_interactive_probe_specification.md - Interactive probe design
  • structural_fuzzing_whitepaper.md - Bond Index fuzzing methodology

Analysis

  • interim_results_paper.md - Interim experimental results
  • protocol1_results_analysis.md - Protocol 1 analysis
  • new_section_9_experimental_results.md - Section 9 experimental data

Integration with ErisML/DEME V3

The experimental scripts in this repository now leverage the DEME V3 tensor framework:

from erisml.ethics import (
    MoralTensor, MoralVector,
    TuckerDecomposition, TensorTrainDecomposition,
    generate_samples, cvar, stochastic_dominance,
    get_dispatcher, JetsonConfig,
)

# Create rank-4 ethical assessment tensor
tensor = MoralTensor.from_dense(
    data,  # shape: (9, n_parties, n_timesteps, n_actions)
    axis_names=("k", "n", "tau", "a"),
)

# Uncertainty quantification
samples = generate_samples(mean=0.7, std=0.1, n_samples=1000)
risk = cvar(samples, alpha=0.05)

# Hardware acceleration
dispatcher = get_dispatcher()
backend = dispatcher.get_best_backend()

Author

Andrew H. Bond San Jose State University andrew.bond@sjsu.edu

License

Copyright (c) 2025-2026 Andrew H. Bond. All rights reserved.

This research is provided for academic and educational purposes.

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Papers, Research Experiments and Results on Non-Abelian Gauge Structure in Stratified Quantum Normative Dynamics

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