About
I am an independent researcher and a graduate of Inha Technical College, conducting a long-term research program on Structure Recognition — the study of how humans discover structure, assign meaning to it, and generate new research questions from what they observe.
My research began with a simple observation: certain patterns in 4-variable Karnaugh maps — like the checkerboard formed by XOR/XNOR functions — feel visually different from other Boolean function patterns. That intuition grew into a series of connected studies on structural invariance, equivalence under variable rearrangement, and the cognitive mechanisms behind pattern recognition.
A Starting Insight
The 4-variable Boolean function space contains exactly 216 = 65,536 distinct functions. Under axis-swap symmetry — where F(A,B,C,D) = F(C,D,A,B) — these functions are not all structurally independent. Some are symmetric under the swap, some form pairs, and some form larger orbits.
Research question: When the 65,536 functions are classified by axis-swap symmetry, how many distinct equivalence classes result? This question — bridging group theory and combinatorics — is one of the active directions in the newest branch of this research program.
My research philosophy: humans discover structure through visual and spatial intuition; AI expands the explanation space. The collaboration between human structural insight and AI's capacity for systematic exploration is itself a research object — not just a method.
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 Boolean function space theory.
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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Applied Research Layer
Paper 5 — Human-AI Research Collaboration (HARCT)
Paper 6 — Boolean Function Space Theory (NEW)
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Application Domains
AI Collaboration Education · Structure-Based Mathematics
Central Hub Documents
This repository (inha20) is the central hub of the research program.
Research documentation, theory summaries, and AI collaboration files are maintained here.
⚠️ 2026-06-21 구조 통합 (Session 33): 이전의 program/, theory/, ai-workspace/ 하위 폴더 문서들이 아래 루트 파일들로 통합되었습니다.
SESSION_START.md
- AI 단일 진입점 (v5.4) — 프로그램 전체 구조 & AI 운영 원칙
- Active Queue & Repository Health 표 (작업 현황 통합)
- Critical Workflow Rules & Four-Paper Architecture (B)
- Session History (Sessions 45–50+)
StructureRecognitionTheory_Unified.md
- Formal Definitions 3.1–3.3 (Structure · Attention · Explanatory Significance)
- H1–H10 Hypotheses — Research Generation + Concept Evolution
- Q1–Q15 Question Hierarchy (Level 0–8), OP-01–OP-09
Full theory documents → 4StructureRecognitionTheory
HumanAICollaborationProposal_Outline.md
- Human-AI 협업 연구 제안서 개요
- 협업 모델 · 연구 질문 생성 구조 · 장기 프로그램 설계
Repositories
KMap Structure Invariance
Visual pattern analysis of 4-variable Karnaugh maps. XOR/XNOR checkerboard structures and structural regularity under Gray code arrangements. D₄ group theory and equivalence class theory applied to pattern classification.
Status: Stable — submission ready
Symmetric Boolean Functions
Symmetric Boolean functions visualized through Hamming Weight layers. Ring structures and layer-based pattern interpretation of all 65,536 four-variable Boolean functions.
Status: Stable
Variable Rearrangement Invariance
Structural invariance under variable rearrangement. Equivalence classes and symmetry preservation across different map arrangements.
Status: Stable
Structure Recognition Theory
Meta-theoretical framework explaining why certain structures become research-worthy. Hypotheses H1–H10 on structure discovery, research generation, and concept evolution.
Status: Stable
Human-AI Research Collaboration
Methods, observations, and case studies on long-term Human-AI research collaboration. HARCT framework, externalized memory, AI-to-AI handover, and multi-session context continuity.
Status: Complete
Boolean Function Space Theory
Complete S₄ orbit classification of 65,536 four-variable Boolean functions: Space(XOR) 10 orbits, Space(AND) 30 orbits, Space(NOT) 32 orbits. Unified paper (paper.md) complete. Connection to SRT established.
Status: Phase 1·2·5 Complete — §6 personal narrative pending
Research Portfolio
Archived program hub repository. Core content consolidated into this central hub (inha20).
Status: Archived
ANTIGRAVITY
AI collaboration workspace origin repository. Operational content consolidated into SESSION_START.md in this hub.
Status: Archived
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
New direction: gate-generated function spaces as the mathematical domain for structural classification
AI Collaboration Education · Structure-Based Elementary Mathematics · Post Lattice × Karnaugh Map Geometry