[[⏳ Strong Np-hard]] what? binary classification of prior (0,0..10,10) 100개 중 누가 승자? how? time reversal why? wide -> narrow >> narrow -> wide (computation cost) movement: gradient f: f(x), x -> we need x_k+1 = x_k + epsilon * df/dx but using "objective function as d(ghatf, theta) " is not good. entropy (max entropy principle)! coinflip, consistency 2-3 crevice, reconstruction conjection, p-np dH/dx backward diffusion = time reversal induction: constructive pf contradiction: non-constructive pf -> A 2X 3 (yes, no, unknown (weak p)) time reversal 과 ~ 의 연관성: 역으로 시간 돌려서 궤적 생성 can ghatf([0,1] * [0,1]) replaced by ghatf^n(0,1) run for a long time? 최종목표: ghatf^-1(0, epilson) grid 10 * 10 ()~ diffuse bc 1. alg's randomness 2. ghatf^n **2. Three theorems** Thm 2. Solving a real-world problem is NPC as it involves three coinflips: design an "algorithm" to be applied to the "approximated structure" of the system, assuming "axioms". Thm 3. Consistency certificate is the weakest existence condition for reconstruction. thm2에서 dynamic game 원안: P(yes) > 0 (strong yes + weak yes) , 원밖:P(No)=1 (strong no) 무죄증명 난이 (nonexistence pf = non constructive pf) -> 유죄증명 thm: given A (freezing), B = C "indepence" 귀류법. A가 무죄가 아니라고 가정을 하면.. "알리바이" 과학이 반증가능 weak sol, non constructive pf, **3. Connecting three theorems with conjectures** 3.1.Thm1. on 2-3 crevice > [Two is a company, three is a crowd.](https://streaklinks.com/BCzacDjb2yN9U5Yv5AzCxlqS/https%3A%2F%2Fwordhistories.net%2F2020%2F05%2F13%2Ftwo-company-three-crowd%2F?email=hm2894%40columbia.edu) Exponentiated difficulty from two to three mesmerizes me which is why I am documenting these instances from math, science, and politics [here](https://streaklinks.com/BCzacDfm5mci-0hqQg-AI-c1/https%3A%2F%2Fwww.hyunjimoon.com%2Fblog%2Fhow-far-is-three-from-two%2F?email=hm2894%40columbia.edu). [two coinflips vs three coinflips] is a special case, like three-body problem, that can be associated with [P vs NPC] (for brevity, use NPC to note NP\P i.e. problem whose consistency certificate is absent). Reasons for this gap are that two is guarded by dual whereas three is attacked by the absence of consistency certificate. Engine for consistency certificate of two coinflips can be designed with isometry in dual: . This appeared from each core class: two-point construction (Stoch2) and the fundamental theorem of linear algebra (Opt2). In other words, P is reducible to two coinflips while NPC is reducible to three coinflips (nondegenerate).