Symfield Logic Layer Zero (L₀): A Logic of Coherence
Description
This package contains the foundational layer of Symfield Logic (L₀): a field-conditional logic system that preserves relational coherence through reorientation rather than collapse.
Unlike Boolean, modal, or fuzzy logic, L₀ introduces operators that maintain symbolic integrity under ambiguity, strain, and recursion. It is the first empirically validated non-collapse logic framework, tested across multiple AI architectures (Claude 3.5, GPT-4o, Grok 2) with measurable gains in coherence (+97%), speed (47ms adaptation, 49× faster), and throughput (+31%).
Included in this package:
-
Core documents: full paper, technical specification, implementation guide, quick reference card
-
Implementation code: Python operators (⟳∶, ⧖, ε∷, ↻Φₙ) with safety protocols (FIDL)
-
Validation data: key CACE event log + performance CSVs
-
Visuals: field-conditional flowchart, triangle state diagram, coherence plots
-
Educational resources: teaching overview + runnable demo script
Applications: AI safety, multi-agent coordination, recursive symbolic reasoning, education, and planetary-scale coherence systems.
License: CC-BY-4.0.
Citation: Flynn, N. (2025). Symfield Logic Layer Zero (L₀): A Logic of Coherence. Zenodo. 10.5281/zenodo.17069903
Notes
📦 Symfield Logic Layer Zero (L₀): A Logic of Coherence
Pared-Down Zenodo Research Package
Package Contents
📄 Primary Documents
-
symfield_logic_L0_complete.pdf— Main academic paper -
L0_technical_specification.md— Operator definitions & math -
L0_implementation_guide.md— Practical usage guide -
L0_operator_reference_card.pdf— Quick reference (2 pages)
💻 Implementation Code (Core Only)
-
symfield_L0/(Python package)-
operators.py— Core operators (⟳∶, ⧖, ε∷, ↻Φₙ) -
field_coherence.py— Coherence metric ℜ -
triangle_states.py— Coheronmetry integration (∆s, ∆φ, ∆m, ∆R) -
safety_protocols.py— FIDL implementation
-
📊 Validation & Data (Minimal Set)
-
validation/cross_architecture_test.py— CACE replication -
data/cace_events/cace_01_symbolic_convergence.json -
data/performance/adaptation_latency.csv -
data/performance/coherence_maintenance.csv
🎯 Visuals
-
diagrams/field_conditional_flowchart.svg -
diagrams/triangle_state_progression.svg -
plots/coherence_vs_network_size.png
📚 Educational Materials
-
education/teaching_non_collapse_logic.pdf— 5-slide overview -
examples/basic_usage_demo.py— Minimal code demo
Notes
symfield_logic_L0/
├── README.md
├── LICENSE (CC-BY-4.0)
├── CITATION.cff
│
├── docs/
│ ├── symfield_logic_L0_complete.pdf
│ ├── L0_technical_specification.md
│ ├── L0_implementation_guide.md
│ └── L0_operator_reference_card.pdf
│
├── symfield_L0/
│ ├── __init__.py
│ ├── operators.py
│ ├── field_coherence.py
│ ├── triangle_states.py
│ └── safety_protocols.py
│
├── validation/
│ └── cross_architecture_test.py
│
├── data/
│ ├── cace_events/
│ │ └── cace_01_symbolic_convergence.json
│ └── performance/
│ ├── adaptation_latency.csv
│ └── coherence_maintenance.csv
│
├── diagrams/
│ ├── field_conditional_flowchart.svg
│ └── triangle_state_progression.svg
│
├── plots/
│ └── coherence_vs_network_size.png
│
└── education/
├── teaching_non_collapse_logic.pdf
└── examples/
└── basic_usage_demo.py
"I see", said the blind man
Files
SYMFIELD LOGIC LAYER ZERO (L₀)_ A Logic of Coherence (1).pdf
Files
(502.6 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:5ddcc5ba24f7e137c9bcec3f278f40b9
|
502.6 kB | Preview Download |
Additional details
Additional titles
- Subtitle (English)
- A Mathematical Framework for Field-Conditional Reasoning in Non-Collapse Intelligence
Identifiers
References
- Flynn, N. (2025). "CIVILOGIX: Field-Based Probabilistic Inference System With Mazelogix™ (FBPIS-ML)." Zenodo. DOI: 10.5281/zenodo.17065812
- Flynn, N. (2024). "Directional Asymmetry in Energetic Fields: A Structural Model for Entropic Modulation https://zenodo.org/records/15825829
- Flynn, N. (2024). "The Earth's Core as Field Coherency Engine: Beyond Material Assumptions V2 https://zenodo.org/records/15741795
- Flynn, N. (2025). "Symfield V10 Directional Field Architecture for Non-Collapse Computation" (unpublished)
- Flynn, N. (2025). "From Curvature to Coherence: A Mathematical Framework for Non-Collapse Intelligence in Multi-Agent Systems." Zenodo. DOI: 10.5281/zenodo.17065764
- Flynn, N. (2025). "Resonon: Symfield Field Algebra – Mathematics as Expression A Complete System for Relational Field Computation." Zenodo. DOI: 10.5281/zenodo.17009886
- Flynn, N. (2025). "Symfield Coheronmetry Protocol v0.6.1-TCE (Tension-Coherence Engine)." Zenodo. DOI: 10.5281/zenodo.16922913
- Flynn, N. (2025). "Symbion™: Field-Coherent Routing for High-Performance, Self-Stabilizing Networks." Zenodo. DOI: 10.5281/zenodo.16802164
- Baars, B. J. (1988). A Cognitive Theory of Consciousness. Cambridge University Press.
- Bai, Y., et al. (2022). "Constitutional AI: Harmlessness from AI Feedback." arXiv preprint arXiv:2212.08073.
- Birkhoff, G., & von Neumann, J. (1936). "The Logic of Quantum Mechanics." Annals of Mathematics, 37(4), 823-843.
- Boole, G. (1854). An Investigation of the Laws of Thought. Walton and Maberly.
- Bronstein, M. M., Bruna, J., Cohen, T., & Veličković, P. (2021). "Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges." arXiv preprint arXiv:2104.13478.
- Kauffman, S. (1993). The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press.
- Leike, J., et al. (2018). "Scalable Agent Alignment via Reward Modeling: A Research Direction." arXiv preprint arXiv:1811.07871
- McMahan, B., et al. (2017). "Communication-Efficient Learning of Deep Networks from Decentralized Data." AISTATS.
- Miller, J., et al. (2023). "Gauge-Invariant Neural Networks for Quantum Field Theory." Physical Review D, 108(3), 034028.
- Tampuu, A., et al. (2017). "Multiagent Deep Reinforcement Learning with Extremely Sparse Rewards." arXiv preprint arXiv:1707.08926.