Aydın Tiryaki and Gemini 3 Pro (2025)
ABSTRACT
This paper presents the final restructuring of football pitch dimensions, replacing antiquated imperial measurements with a logical synthesis of Decimal (Base-10) and Binary (Base-2) systems. The HRSS Standards feature a “100+4+4” modular longitude, 10-cm metric lines, an “8-8-8” binary synergy, and a simplified penalty area geometry stripped of redundant markings.
1. MACRO ARCHITECTURE: MODULAR AXIS AND METRIC PRECISION
- 108-Meter Modular Longitude: Pitch length is defined by a 100-meter core “Metric Performance Corridor” flanked by two 4-meter binary corner modules (100+4+4=108).
- 64-Meter Binary Latitude: Pitch width is standardized at 64 meters (2^6), aligning the surface with digital data structures.
- 10-Centimeter Line Thickness: All boundaries are marked with a universal 10 cm (0.1\text{m}) thickness, maintaining a 1/1000 ratio with the primary 100-meter axis.
- Center Circle: The center circle is set at a 10-meter radius, representing 1/10 of the central axis.
2. BOUNDARY MANAGEMENT: FLUID TOUCHLINES AND TRIGGER LINE
- Integrated Touchlines: The 4-meter (2^2) corner curves are tactically integrated into the touchline, allowing for continuous play up to the goal line.
- 0.5-Meter Corner Trigger Line: A fine vertical marker is placed at exactly 0.5 meters (2^{-1}) along the curve to distinguish between corner kick zones and dynamic throw-in zones.
3. GEOMETRIC RESOLUTION HIERARCHY
Field resolution increases towards the goal: 4m (Outer Corners), 2m (Penalty Area), 1m (Goal Area), 0.5m (Goal Post Curves).
4. THE ACTION HUB: 8-8-8 SYNERGY AND ARC ELIMINATION
The HRSS model achieves its highest level of optimization in the goal-scoring zone.
- The 8-8-8 Synergy: Goal width is 8 meters, penalty distance is 8 meters, and penalty area depth is 16 meters.
- Elimination of the Penalty Arc (“D”): The standard wall/barrier distance is set at 8 meters (2^3). Since the penalty spot (8m) and the penalty area line (16m) have an exact 8-meter difference, the area line itself serves as the natural clearance boundary. Consequently, the Penalty Arc is removed as a redundant marking, simplifying the pitch.
- Rational Goal: Standardized at 8.00m x 2.50m, providing a net scoring area of approximately 20 m².
CONCLUSION
HRSS transforms the football pitch into a high-precision sports engineering platform. By eliminating redundant lines and imperial remnants, it provides a standardized environment that is fully compatible with digital officiating and modern gameplay.
Aydın Tiryaki and Gemini 3 Pro (2025)
ANkara, December 18, 2025
APPENDIX-1: FINAL TECHNICAL COMPARATIVE INDEX (ENGLISH)
| Feature | Traditional (Legacy) | HRSS Model | Rationale |
| Pitch Length | ~105 m | 108 m | 100m Core + 8m Mods |
| Pitch Width | ~68 m | 64 m | Binary Power (2^6) |
| Line Thickness | Variable | 10 cm | 1/1000 Metric Ratio |
| Penalty Spot | 11 m | 8 m | 1:1 Goal Symmetry (2^3) |
| Barrier Distance | 9.15 m | 8 m | Binary Standard (2^3) |
| Penalty Area Depth | 16.5 m | 16 m | Binary Power (2^4) |
| Penalty Arc (“D”) | 9.15 m Radius | REMOVED | Redundant (16-8=8m) |
| Corner Radius | 0.91 m | 4 m | Binary 2^2 / Flow Zone |
| Corner Marker | N/A | 0.5 m | Binary 2^{-1} / Trigger |
Aydın Tiryaki 