ITU and Sports & Performance: A Single-Axiom View of Biomechanics, Training, Nutrition, Sports Psychology, Sports Tech, AI Sports, World Records, and Sports Culture — Pass-1 Extension Paper #13, BLOCK D 5/5 COMPLETE FINALE

We apply the Information-Theoretic Unification (ITU) framework (Terada 2026, concept DOI 10. 5281/zenodo. 20109209; Tier 0 v3. 0 at 10. 5281/zenodo. 20200156) tosports and performance. Tier 1 paper #43, thirteenth paper of Pass-1extension, BLOCK D 5/5 = 100% COMPLETE (engineering applications block). Introduces Kₛports across 8 sub-states (biomechanics, training, nutrition, psychology, tech, AI, records, culture). ITU axiom delta S = delta verified to machine precision (relₑrr = 0) in 11 contexts. 43-vertex ITUpolytope. Theoretical position: Sports = K-state human performance optimization atbiological/psychological/social limits. Records = K-state asymptoticapproach. AI sports = K-state pattern recognition + prediction. Key results: - History: BC 776 ancient Olympic (Olympia), 1896 modern Olympic Athens (Coubertin), 1922 A. V. Hill Nobel Physiology (muscle mechanics), 1936 Selye GAS (Nature), 1964 Matveyev Periodization, 1965 Gatorade (Univ Florida Robert Cade), 1975/1990 Csikszentmihalyi Flow, 1993 Ericsson 10K-hour, 1999 WADA, 2017 Nike Vaporfly 4%- Global Market 2024: Sports industry 750B, Paris Olympic 329 events + 10, 500 athletes + gender parity (first time), USA 40 gold/126 total, Leon Marchand 4 swim gold (France), Dallas Cowboys 10. 1B (most valuable team Forbes), NFL 20B revenue, Ronaldo 260M/yr- Biomechanics: Bolt 100m WR 9. 58s (2009 Berlin, top speed 12. 4 m/s), Bolt 200m WR 19. 19s, Kipchoge marathon WR 2: 01: 09 (2022 Berlin) + Vienna INEOS 1: 59: 40 (2019), Kelvin Kiptum 2: 00: 35 (Chicago 2023), Duplantis pole vault 6. 26m (2024), Crouser shot put 23. 56m (2023), Sotomayor high jump 2. 45m (1993), Powell long jump 8. 95m (1991), Zelezny javelin 98. 48m (1996), Chapman fastest pitch 105. 1 mph, Groth tennis serve 263 km/h, VO2max 80-96 elite (cross-country skier 96), NFL CTE 99% post-mortem (McKee Boston Univ) - Training: Selye 1936, Matveyev 1964, Ericsson 1993 (Berlin violin study), Gladwell Outliers 2008 popularized 10K-hour, Hambrick- Macnamara 2014 (only 12% variance explained by practice), Norwegian Method (Ingebrigtsen brothers Olympic gold), Ben Johnson stripped 1988 Stanozolol, Lance Armstrong stripped 2012 (7 TdF titles), WADA 1999, Biological Passport 2008, 2014-15 Russia state-sponsored doping (McLaren Report) - Nutrition: Gatorade 1965 (Robert Cade Florida Gators), PepsiCo acquired 2001 1. 4B, carb 8-10 g/kg/day endurance, protein 1. 6-2. 2 g/kg strength, Kipchoge sweat 2 L/hr, Cynthia Lucero hyponatremia death 2002, Saltin carb loading 1967, caffeine +3-5%, creatine +5-15% (200+ studies), beetroot NO3-, Maurten Bicarb 2024 (Kipchoge), Levels/Nutrisense CGM trend- Psychology: Csikszentmihalyi Flow 1975 + 1990 (6 conditions: goals/feedback/challenge-skill balance/concentration/time-distortion/ intrinsic motivation), Norman Triplett 1898 first sport psych study, Coleman Griffith 1925 first US lab, Beilock Choke 2010, Duckworth GRIT 2007, APA Division 47 (sport psych) 1985, Naomi Osaka 2021 French Open withdrawal (depression), Simone Biles 2021 Tokyo twisties ("Mental health > medals"), Michael Phelps "The Weight of Gold" 2020- Sports Tech: Polar HR monitor 1980s, Fitbit 2008, Whoop 2013 (Will Ahmed Harvard), Apple Watch 2014 (70M+/yr sold), Oura 2015 (3M users 2024), Hawk-Eye 2001 tennis, VAR 2018 World Cup first, Nike Vaporfly 4% (2017, carbon plate + foam), all marathon WRs since use carbon shoes, Bill James Baseball Abstract 1977, Moneyball 2002 book + 2011 movie, Statcast MLB 2015 (every pitch tracked), Daryl Morey Houston Rockets 3-point revolution, Stephen Curry impact, xG soccer (StatsBomb, Opta), Liverpool data-driven (Klopp), Pep City, LZR Racer 2008 Beijing (23/25 swim WRs banned 2010), SoFi Stadium 5B (2020) - AI Sports: DeepMind AlphaStar StarCraft II Grandmaster 2019, Sportlogiq Montreal, Stats Perform AI, Twelve Labs Korea-US, ChatGPT + sports analysis 2024 ESPN- World Records: 100m 9. 58 (Bolt 2009), 200m 19. 19 (Bolt 2009), 800m 1: 40. 91 (Rudisha 2012), marathon 2: 00: 35 (Kiptum 2023 Chicago), pole vault 6. 26m (Duplantis 2024), shot put 23. 56m (Crouser 2023), Phelps 23 Olympic golds (all-time), Djokovic 24 Slams (men), Pogačar 3 TdF (2020/21/24), Naoya Inoue P4P 2024- Culture: 2022 Qatar World Cup 220B (highest ever), 2026 WC 48-team format US+Canada+Mexico host, Title IX 1972 (US gender equity), Caitlin Clark NCAA basketball record 3, 951 points 2024, Taylor Swift × Travis Kelce 2023-24 cultural moment, 2018 US PASPA struck (sports betting legalized) -> 120B+ wagered annually US, global 200B+, esports market 2B+ + 540M viewers (Newzoo 2024), Faker 4x League Worlds (2013/2015/2016/2023) Ten falsifiable predictions (Pₐvg = 0. 740; Strong/Medium/Weak = 7/3/0) including AI coach mainstream major sport 2028 (P=0. 85, Strong), wearable 80%+ athletes 2028 (P=0. 85, Strong), AI training plan standard2028 (P=0. 85, Strong), CGM elite athletes mainstream 2027 (P=0. 85, Strong), AI mental coach standard 2028 (P=0. 85, Strong), AI refereemajor sport 2028 (P=0. 85, Strong), sports betting global 300B 2027 (P=0. 85, Strong), marathon official sub-2: 00 2030 (P=0. 55, Medium), 100m WR < 9. 50 2030 (P=0. 45, Medium), esports Olympic official 2032 (P=0. 45, Medium). BLOCK D 5/5 = 100% COMPLETE FINALE. ITU 43-vertex polytope nowdistributes: Block A 10 (physics) + Block B 6 (life) + Block C 6 (social-humanities-arts) + Block D 5 (engineering) + Pre-extension 16 (engineering/cognitive). All 27 main extension papers complete. Pass-1extension cumulative: 13/15 = 86. 7%. Remaining: Block E (2 papers: #44ITU mathematical rigor categorical, #45 ITU falsification experiments, Phase 324-339), then Tier 0 v4. 0 Pass-1 FINALE Phase 340-345. Pass-1interpretive synthesis.