Research Program
This page is the public entry point to a unified long-term research program on Structure Recognition — investigating how humans discover structure, assign meaning to it, and generate research questions.
The program began with specific Boolean function phenomena observed in Karnaugh maps and has expanded toward a broader meta-theoretical framework, with branches into human-AI collaboration and education.
Paper 1 — Karnaugh Map Structure Invariance
Paper 2 — Symmetric Boolean Function Visual Patterns
Paper 3 — Variable Rearrangement Invariance
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Theoretical Integration Layer
Paper 4 — Structure Recognition Theory (SRT)
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Application Domains
Human-AI Collaboration · AI Education · Structure-Based Mathematics
Repositories
KMap Structure Invariance
Visual pattern analysis of 4-variable Karnaugh maps. XOR/XNOR checkerboard structures and structural regularity under Gray code arrangements.
Status: Stable
Symmetric Boolean Functions
Symmetric Boolean functions visualized through Hamming Weight layers. Ring structures and layer-based pattern interpretation.
Status: Stable
Variable Rearrangement Invariance
Structural invariance under variable rearrangement. Equivalence classes and symmetry preservation across different map arrangements.
Status: Active
Structure Recognition Theory
Meta-theoretical framework explaining why certain structures become research-worthy. Hypotheses H1–H7 on structure discovery and research generation.
Status: Active — early-stage framework
Human-AI Research Collaboration
Methods, observations, and case studies on long-term Human-AI research collaboration. Externalized memory, AI-to-AI handover, and multi-session context continuity.
Status: Active — collecting cases
Research Portfolio
Program navigation hub. Concept genealogy, research timeline, planning documents, and cross-repository links.
Status: Active
ANTIGRAVITY
AI collaboration workspace maintaining continuity between research sessions. Handover documents and session logs.
Status: Monitoring
Concept Genealogy
The sequence below records the actual historical development of the research program — not a logical reconstruction, but a trace of discovery:
1st observation: Karnaugh map checkerboard patterns for XOR/XNOR functions
Discovery: Hamming Weight layers explain the positions of symmetric function patterns
Observation: different variable arrangements can yield the same structural pattern
Question: what exactly is preserved across variable rearrangements?
Meta-question: why do certain structures become research-worthy while others do not?
Observation: humans discover structure; AI expands the explanation space — division of cognitive labor
AI Collaboration Education · Structure-Based Elementary Mathematics