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TOPIC: Chemistry - covalent vs ionic bonding. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=2 mol at 372K => V~20L. APPLICATION: Batteries, synthesis. TOPIC: Biology - Mendelian inheritance. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome ... |
TOPIC: Physics - energy conservation. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=107814J. EXAMPLE: 6kg at 3m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - eigenvalues. PROBLEM: 12*x+302=659. TRACE: Subtract 302 => 12*x=357. Divid... |
TOPIC: Physics - quantum superposition. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=77376J. EXAMPLE: 3kg at 5m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - TCP vs UDP. SPEC: Implement quicksort with invariant. CODE: def solve(arr):... |
TOPIC: Chemistry - polymerization. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=5 mol at 301K => V~19L. APPLICATION: Batteries, synthesis. TOPIC: Biology - DNA replication. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~20000 ... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=153608J. EXAMPLE: 3kg at 9m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - prime factorization. PROBLEM: 5*x+422=786. TRACE: Subtract 422 => 5*x=364.... |
TOPIC: Physics - relativity. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=158522J. EXAMPLE: 9kg at 10m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - gradient descent. PROBLEM: 6*x+338=807. TRACE: Subtract 338 => 6*x=469. Divide 6 =... |
TOPIC: Physics - wave-particle duality. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=3030J. EXAMPLE: 3kg at 16m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - prime factorization. PROBLEM: 6*x+30=131. TRACE: Subtract 30 => 6*x=101. ... |
TOPIC: CS - hash tables. SPEC: Implement public key crypto with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 62943 RPS prod. TOPIC: History/Econ - supply and demand. CONTEXT: 1650, competition + tech shift. MODEL: Forcing + feedback -> equilib... |
TOPIC: Math - Pythagorean theorem. PROBLEM: 7*x+419=617. TRACE: Subtract 419 => 7*x=198. Divide 7 => x=28.2857. VERIFY: 7*28.2857+419=617. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - Dijkstra. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: ... |
TOPIC: Physics - relativity. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=117327J. EXAMPLE: 6kg at 16m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - transformer attention. SPEC: Implement hash tables with invariant. CODE: def solve(a... |
TOPIC: Chemistry - pH buffers. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=2 mol at 290K => V~23L. APPLICATION: Batteries, synthesis. TOPIC: Biology - natural selection. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~20000 ge... |
TOPIC: Physics - Newton's laws. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=14256J. EXAMPLE: 5kg at 10m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - chain rule. PROBLEM: 10*x+44=368. TRACE: Subtract 44 => 10*x=324. Divide 10 => x... |
TOPIC: Chemistry - covalent vs ionic bonding. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=1 mol at 346K => V~39L. APPLICATION: Batteries, synthesis. TOPIC: Biology - CRISPR. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~2000... |
TOPIC: Chemistry - covalent vs ionic bonding. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=3 mol at 343K => V~15L. APPLICATION: Batteries, synthesis. TOPIC: Biology - DNA replication. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 ... |
TOPIC: CS - SQL indexing. SPEC: Implement big-O with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 48674 RPS prod. TOPIC: History/Econ - El Nino. CONTEXT: 1649, competition + tech shift. MODEL: Forcing + feedback -> equilibrium. CALC: P=6172 at... |
TOPIC: Physics - wave-particle duality. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=25652J. EXAMPLE: 8kg at 4m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Pythagorean theorem. PROBLEM: 15*x+106=348. TRACE: Subtract 106 => 15*x=2... |
TOPIC: Chemistry - periodic trends. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=5 mol at 357K => V~11L. APPLICATION: Batteries, synthesis. TOPIC: Biology - immune memory. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~20000 g... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=14910J. EXAMPLE: 3kg at 6m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - prime factorization. PROBLEM: 14*x+42=397. TRACE: Subtract 42 => 14*x=355. ... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=43061J. EXAMPLE: 6kg at 6m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - eigenvalues. PROBLEM: 5*x+149=438. TRACE: Subtract 149 => 5*x=289. Divide 5... |
TOPIC: Physics - black hole thermodynamics. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=131976J. EXAMPLE: 2kg at 9m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - hash tables. SPEC: Implement quicksort with invariant. CODE: def solve... |
TOPIC: Math - gradient descent. PROBLEM: 2*x+195=670. TRACE: Subtract 195 => 2*x=475. Divide 2 => x=237.5000. VERIFY: 2*237.5000+195=670. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - quicksort. SPEC: Implement TCP vs UDP with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: em... |
TOPIC: Physics - quantum superposition. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=52338J. EXAMPLE: 1kg at 5m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Bayes theorem. PROBLEM: 7*x+183=469. TRACE: Subtract 183 => 7*x=286. Divi... |
TOPIC: Chemistry - covalent vs ionic bonding. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=3 mol at 302K => V~29L. APPLICATION: Batteries, synthesis. TOPIC: Biology - CRISPR. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~2000... |
TOPIC: Math - eigenvalues. PROBLEM: 3*x+233=442. TRACE: Subtract 233 => 3*x=209. Divide 3 => x=69.6667. VERIFY: 3*69.6667+233=442. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - TCP vs UDP. SPEC: Implement TCP vs UDP with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, s... |
TOPIC: Math - gradient descent. PROBLEM: 7*x+468=968. TRACE: Subtract 468 => 7*x=500. Divide 7 => x=71.4286. VERIFY: 7*71.4286+468=968. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - Dijkstra. SPEC: Implement big-O with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, sin... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=15444J. EXAMPLE: 7kg at 12m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - Dijkstra. SPEC: Implement Dijkstra with invariant. CODE: def solve(arr): mai... |
TOPIC: Physics - energy conservation. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=21746J. EXAMPLE: 6kg at 9m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Pythagorean theorem. PROBLEM: 9*x+83=345. TRACE: Subtract 83 => 9*x=262. Di... |
TOPIC: Physics - relativity. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=9420J. EXAMPLE: 6kg at 13m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - hash tables. SPEC: Implement public key crypto with invariant. CODE: def solve(arr): m... |
TOPIC: Physics - quantum superposition. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=88298J. EXAMPLE: 10kg at 7m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - SQL indexing. SPEC: Implement TCP vs UDP with invariant. CODE: def solve(a... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=13838J. EXAMPLE: 3kg at 1m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - hash tables. SPEC: Implement hash tables with invariant. CODE: def solve(arr)... |
TOPIC: Physics - black hole thermodynamics. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=110860J. EXAMPLE: 1kg at 15m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - transformer attention. SPEC: Implement hash tables with invariant. CO... |
TOPIC: Chemistry - pH buffers. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=5 mol at 280K => V~12L. APPLICATION: Batteries, synthesis. TOPIC: Biology - action potential. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~20000 gen... |
TOPIC: Physics - energy conservation. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=49215J. EXAMPLE: 9kg at 4m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - transformer attention. SPEC: Implement hash tables with invariant. CODE: def ... |
TOPIC: Physics - Newton's laws. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=154770J. EXAMPLE: 2kg at 5m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Bayes theorem. PROBLEM: 12*x+469=799. TRACE: Subtract 469 => 12*x=330. Divide 12... |
TOPIC: Physics - wave-particle duality. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=108265J. EXAMPLE: 4kg at 1m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Pythagorean theorem. PROBLEM: 6*x+295=662. TRACE: Subtract 295 => 6*x=36... |
TOPIC: Chemistry - redox reactions. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=1 mol at 389K => V~37L. APPLICATION: Batteries, synthesis. TOPIC: Biology - Mendelian inheritance. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ... |
TOPIC: Math - Bayes theorem. PROBLEM: 3*x+65=553. TRACE: Subtract 65 => 3*x=488. Divide 3 => x=162.6667. VERIFY: 3*162.6667+65=553. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - SQL indexing. SPEC: Implement big-O with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, sin... |
TOPIC: CS - quicksort. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 37944 RPS prod. TOPIC: History/Econ - Industrial Revolution. CONTEXT: 1305, competition + tech shift. MODEL: Forcing + feedback -> equilibriu... |
TOPIC: Chemistry - covalent vs ionic bonding. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=3 mol at 281K => V~11L. APPLICATION: Batteries, synthesis. TOPIC: Biology - natural selection. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e... |
TOPIC: Physics - relativity. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=10175J. EXAMPLE: 1kg at 13m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Pythagorean theorem. PROBLEM: 12*x+275=312. TRACE: Subtract 275 => 12*x=37. Divide ... |
TOPIC: CS - big-O. SPEC: Implement transformer attention with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 20016 RPS prod. TOPIC: History/Econ - supply and demand. CONTEXT: 1875, competition + tech shift. MODEL: Forcing + feedback -> equilibri... |
TOPIC: CS - hash tables. SPEC: Implement Dijkstra with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 16090 RPS prod. TOPIC: History/Econ - El Nino. CONTEXT: 1809, competition + tech shift. MODEL: Forcing + feedback -> equilibrium. CALC: P=7829 ... |
TOPIC: Physics - relativity. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=5382J. EXAMPLE: 2kg at 12m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - public key crypto. SPEC: Implement Dijkstra with invariant. CODE: def solve(arr): main... |
TOPIC: Chemistry - Le Chatelier. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=4 mol at 280K => V~16L. APPLICATION: Batteries, synthesis. TOPIC: Biology - cellular respiration. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~200... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=62288J. EXAMPLE: 8kg at 8m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Pythagorean theorem. PROBLEM: 15*x+136=594. TRACE: Subtract 136 => 15*x=458... |
TOPIC: Physics - wave-particle duality. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=134274J. EXAMPLE: 4kg at 13m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - quicksort. SPEC: Implement TCP vs UDP with invariant. CODE: def solve(arr... |
TOPIC: CS - SQL indexing. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 73284 RPS prod. TOPIC: History/Econ - plate tectonics. CONTEXT: 1551, competition + tech shift. MODEL: Forcing + feedback -> equilibrium. ... |
TOPIC: Physics - electromagnetic induction. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=7986J. EXAMPLE: 9kg at 8m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - eigenvalues. PROBLEM: 7*x+66=187. TRACE: Subtract 66 => 7*x=121. Divid... |
TOPIC: Physics - wave-particle duality. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=35861J. EXAMPLE: 6kg at 6m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - big-O. SPEC: Implement quicksort with invariant. CODE: def solve(arr): main... |
TOPIC: CS - transformer attention. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 70353 RPS prod. TOPIC: History/Econ - Nash equilibrium. CONTEXT: 1814, competition + tech shift. MODEL: Forcing + feedback -> equ... |
TOPIC: Math - chain rule. PROBLEM: 6*x+165=410. TRACE: Subtract 165 => 6*x=245. Divide 6 => x=40.8333. VERIFY: 6*40.8333+165=410. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - transformer attention. SPEC: Implement big-O with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: emp... |
TOPIC: Chemistry - redox reactions. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=4 mol at 321K => V~18L. APPLICATION: Batteries, synthesis. TOPIC: Biology - cellular respiration. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~... |
TOPIC: Chemistry - periodic trends. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=4 mol at 323K => V~12L. APPLICATION: Batteries, synthesis. TOPIC: Biology - Mendelian inheritance. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ... |
TOPIC: Physics - entropy. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=38258J. EXAMPLE: 1kg at 8m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - public key crypto. SPEC: Implement public key crypto with invariant. CODE: def solve(arr)... |
TOPIC: Math - gradient descent. PROBLEM: 3*x+80=387. TRACE: Subtract 80 => 3*x=307. Divide 3 => x=102.3333. VERIFY: 3*102.3333+80=387. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - Dijkstra. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empt... |
TOPIC: Physics - quantum superposition. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=26814J. EXAMPLE: 9kg at 1m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - prime factorization. PROBLEM: 14*x+327=409. TRACE: Subtract 327 => 14*x=8... |
TOPIC: Physics - relativity. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=24596J. EXAMPLE: 10kg at 13m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - Dijkstra. SPEC: Implement quicksort with invariant. CODE: def solve(arr): maintain l... |
TOPIC: Physics - electromagnetic induction. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=6356J. EXAMPLE: 2kg at 6m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Pythagorean theorem. PROBLEM: 2*x+14=468. TRACE: Subtract 14 => 2*x=45... |
TOPIC: Physics - quantum superposition. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=43848J. EXAMPLE: 6kg at 8m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Fourier transform. PROBLEM: 11*x+203=419. TRACE: Subtract 203 => 11*x=216... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=5550J. EXAMPLE: 10kg at 20m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - transformer attention. SPEC: Implement public key crypto with invariant. COD... |
TOPIC: Physics - electromagnetic induction. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=35530J. EXAMPLE: 5kg at 16m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - gradient descent. PROBLEM: 4*x+85=503. TRACE: Subtract 85 => 4*x=418... |
TOPIC: Physics - black hole thermodynamics. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=45571J. EXAMPLE: 10kg at 15m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - hash tables. SPEC: Implement hash tables with invariant. CODE: def so... |
TOPIC: CS - transformer attention. SPEC: Implement public key crypto with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 45865 RPS prod. TOPIC: History/Econ - El Nino. CONTEXT: 1643, competition + tech shift. MODEL: Forcing + feedback -> equilib... |
TOPIC: Physics - electromagnetic induction. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=2730J. EXAMPLE: 8kg at 6m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - chain rule. PROBLEM: 13*x+65=107. TRACE: Subtract 65 => 13*x=42. Divid... |
TOPIC: CS - transformer attention. SPEC: Implement TCP vs UDP with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 92022 RPS prod. TOPIC: History/Econ - plate tectonics. CONTEXT: 1595, competition + tech shift. MODEL: Forcing + feedback -> equili... |
TOPIC: Physics - entropy. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=55942J. EXAMPLE: 10kg at 1m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Bayes theorem. PROBLEM: 14*x+337=503. TRACE: Subtract 337 => 14*x=166. Divide 14 => x=... |
TOPIC: Math - prime factorization. PROBLEM: 7*x+438=481. TRACE: Subtract 438 => 7*x=43. Divide 7 => x=6.1429. VERIFY: 7*6.1429+438=481. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - quicksort. SPEC: Implement public key crypto with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDG... |
TOPIC: Physics - entropy. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=63750J. EXAMPLE: 4kg at 6m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - transformer attention. SPEC: Implement quicksort with invariant. CODE: def solve(arr): ma... |
TOPIC: Chemistry - ideal gas law. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=4 mol at 305K => V~29L. APPLICATION: Batteries, synthesis. TOPIC: Biology - DNA replication. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~20000 g... |
TOPIC: CS - transformer attention. SPEC: Implement public key crypto with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 48295 RPS prod. TOPIC: History/Econ - Meiji Restoration. CONTEXT: 1208, competition + tech shift. MODEL: Forcing + feedback ... |
TOPIC: Physics - electromagnetic induction. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=60903J. EXAMPLE: 3kg at 2m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - hash tables. SPEC: Implement big-O with invariant. CODE: def solve(arr)... |
TOPIC: Math - eigenvalues. PROBLEM: 6*x+272=454. TRACE: Subtract 272 => 6*x=182. Divide 6 => x=30.3333. VERIFY: 6*30.3333+272=454. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - hash tables. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=29414J. EXAMPLE: 7kg at 4m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Bayes theorem. PROBLEM: 3*x+191=345. TRACE: Subtract 191 => 3*x=154. Divide... |
TOPIC: CS - transformer attention. SPEC: Implement TCP vs UDP with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 64920 RPS prod. TOPIC: History/Econ - plate tectonics. CONTEXT: 1364, competition + tech shift. MODEL: Forcing + feedback -> equili... |
TOPIC: Physics - electromagnetic induction. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=16080J. EXAMPLE: 8kg at 6m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Bayes theorem. PROBLEM: 3*x+240=307. TRACE: Subtract 240 => 3*x=67. D... |
TOPIC: Physics - energy conservation. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=6748J. EXAMPLE: 3kg at 17m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - public key crypto. SPEC: Implement Dijkstra with invariant. CODE: def solve(a... |
TOPIC: Physics - energy conservation. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=50267J. EXAMPLE: 4kg at 18m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - quicksort. SPEC: Implement public key crypto with invariant. CODE: def solve... |
TOPIC: CS - hash tables. SPEC: Implement hash tables with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 94780 RPS prod. TOPIC: History/Econ - Industrial Revolution. CONTEXT: 1242, competition + tech shift. MODEL: Forcing + feedback -> equilibri... |
TOPIC: Physics - relativity. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=72038J. EXAMPLE: 4kg at 18m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - Dijkstra. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain... |
TOPIC: Physics - quantum superposition. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=22320J. EXAMPLE: 6kg at 15m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - transformer attention. SPEC: Implement transformer attention with invarian... |
TOPIC: CS - SQL indexing. SPEC: Implement hash tables with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 14174 RPS prod. TOPIC: History/Econ - Meiji Restoration. CONTEXT: 1694, competition + tech shift. MODEL: Forcing + feedback -> equilibrium.... |
TOPIC: Math - central limit theorem. PROBLEM: 2*x+279=677. TRACE: Subtract 279 => 2*x=398. Divide 2 => x=199.0000. VERIFY: 2*199.0000+279=677. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - SQL indexing. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space... |
TOPIC: Math - Pythagorean theorem. PROBLEM: 7*x+258=485. TRACE: Subtract 258 => 7*x=227. Divide 7 => x=32.4286. VERIFY: 7*32.4286+258=485. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - Dijkstra. SPEC: Implement transformer attention with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) spac... |
TOPIC: Chemistry - ideal gas law. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=5 mol at 376K => V~26L. APPLICATION: Batteries, synthesis. TOPIC: Biology - photosynthesis. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~20000 ge... |
TOPIC: CS - public key crypto. SPEC: Implement TCP vs UDP with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 68059 RPS prod. TOPIC: History/Econ - El Nino. CONTEXT: 1229, competition + tech shift. MODEL: Forcing + feedback -> equilibrium. CALC:... |
TOPIC: Math - central limit theorem. PROBLEM: 9*x+486=509. TRACE: Subtract 486 => 9*x=23. Divide 9 => x=2.5556. VERIFY: 9*2.5556+486=509. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - SQL indexing. SPEC: Implement TCP vs UDP with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE:... |
TOPIC: Math - gradient descent. PROBLEM: 7*x+372=554. TRACE: Subtract 372 => 7*x=182. Divide 7 => x=26.0000. VERIFY: 7*26.0000+372=554. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - SQL indexing. SPEC: Implement hash tables with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: ... |
TOPIC: CS - Dijkstra. SPEC: Implement hash tables with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, single, dupes. USE: 77738 RPS prod. TOPIC: History/Econ - Industrial Revolution. CONTEXT: 1909, competition + tech shift. MODEL: Forcing + feedback -> equilibrium.... |
TOPIC: Math - eigenvalues. PROBLEM: 13*x+17=478. TRACE: Subtract 17 => 13*x=461. Divide 13 => x=35.4615. VERIFY: 13*35.4615+17=478. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - public key crypto. SPEC: Implement SQL indexing with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE... |
TOPIC: Chemistry - Le Chatelier. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=3 mol at 296K => V~35L. APPLICATION: Batteries, synthesis. TOPIC: Biology - immune memory. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~20000 gene... |
TOPIC: Math - Pythagorean theorem. PROBLEM: 13*x+378=696. TRACE: Subtract 378 => 13*x=318. Divide 13 => x=24.4615. VERIFY: 13*24.4615+378=696. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - TCP vs UDP. SPEC: Implement public key crypto with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) sp... |
TOPIC: Chemistry - ideal gas law. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=2 mol at 342K => V~19L. APPLICATION: Batteries, synthesis. TOPIC: Biology - cellular respiration. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 bp, ~20... |
TOPIC: Chemistry - covalent vs ionic bonding. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=2 mol at 337K => V~33L. APPLICATION: Batteries, synthesis. TOPIC: Biology - photosynthesis. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome 3.2e9 b... |
TOPIC: Physics - relativity. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=162948J. EXAMPLE: 2kg at 18m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - prime factorization. PROBLEM: 7*x+444=811. TRACE: Subtract 444 => 7*x=367. Divide ... |
TOPIC: Chemistry - covalent vs ionic bonding. MECHANISM: Valence electrons achieve octet via sharing/transfer. CALC: PV=nRT with n=3 mol at 308K => V~10L. APPLICATION: Batteries, synthesis. TOPIC: Biology - Mendelian inheritance. PROCESS: Signal binds -> ATP 30.5 kJ/mol drives change -> product released. QUANT: Genome ... |
TOPIC: Math - Fourier transform. PROBLEM: 9*x+409=588. TRACE: Subtract 409 => 9*x=179. Divide 9 => x=19.8889. VERIFY: 9*19.8889+409=588. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - big-O. SPEC: Implement quicksort with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE: empty, s... |
TOPIC: Physics - Bernoulli principle. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=43183J. EXAMPLE: 7kg at 17m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Pythagorean theorem. PROBLEM: 13*x+199=416. TRACE: Subtract 199 => 13*x=21... |
TOPIC: Physics - Newton's laws. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=95648J. EXAMPLE: 9kg at 16m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: Math - Fourier transform. PROBLEM: 11*x+392=636. TRACE: Subtract 392 => 11*x=244. Divid... |
TOPIC: Physics - energy conservation. DEF: Fundamental law from symmetry/conservation. EXPLANATION: System minimizes action, energy E=114737J. EXAMPLE: 6kg at 2m/s => KE=0.5*m*v^2. IMPLICATION: Used in engineering and astrophysics. TOPIC: CS - public key crypto. SPEC: Implement Dijkstra with invariant. CODE: def solve(... |
TOPIC: Math - eigenvalues. PROBLEM: 3*x+380=845. TRACE: Subtract 380 => 3*x=465. Divide 3 => x=155.0000. VERIFY: 3*155.0000+380=845. GENERAL: ax+b=c => x=(c-b)/a. TOPIC: CS - public key crypto. SPEC: Implement hash tables with invariant. CODE: def solve(arr): maintain low<=target<=high, O(n log n) time O(n) space. EDGE... |
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