Formalism U \equiv I \psi_C(\rho_I)=\sum_k\alpha_k(\rho_I-\rho_I^{\mathrm{stable}})^k \rho_I^{\mathrm{stable}}=\Omega_c=0.376 \partial_t\rho_I+\nabla\!\cdot J_I=0 J_I=-D\nabla\rho_I \partial_t\rho_I=D\nabla^2\rho_I \rho(x,t)=\sum_n c_n(0)e^{-D\lambda_nt}\phi_n(x) \ker K\Rightarrow\Omega_c=\frac{47}{125}\Rightarrow R(x)\Rightarrow x^2=\Omega_c RI(x)=\lim_{n\to\infty}R^n(I(x)) \exists!\,S^\,\;R(S^\)=S^\* H(f(x))<H(x) \mathcal H=\mathcal T\otimes\mathcal F\otimes\mathcal G V=V_2\otimes V_2\otimes V_2 \dim(V)=5^3=125 C=(J_1+J_2+J_3)^2 K=(C-6I)(C-30I) E=\ker(K) \dim(E)=47 \Omega_c=\frac{\dim(E)}{\dim(V)}=\frac{47}{125}=0.376 N=pq\mapsto\hat\rho_N\in V \hat\rho_N^\dagger=\hat\rho_N,\qquad\operatorname{Tr}(\hat\rho_N)=1 E[\hat\rho]=a\,\operatorname{Tr}((D\hat\rho)^\dagger D\hat\rho)+b\,\operatorname{Tr}(\hat\rho^2)+c\,\operatorname{Tr}([L,L]^2) L=U^\dagger DU,\qquad U\in SU(2) r=\frac{78}{47} \Omega_c=\frac1{1+r}=\frac{47}{125} \mathcal B(\rho)=(1-\Omega_c)\rho+\Omega_cF(N,\rho) F(N,\rho)=\arg\min\{\operatorname{Tr}([L,L]^2)+\frac1{2\lambda}\|\sigma-\rho\|^2\} T(\psi)=\frac12\left(\psi+\frac{c}{\psi}\right) c=\phi^{-5},\qquad\phi=\frac{1+\sqrt5}{2} T(L)=L\Rightarrow L^2=c \Psi^\=\phi^{-5/2} T'(\psi)=\frac12\left(1-\frac{c}{\psi^2}\right) T'(\Psi^\)=0 e_{n+1}=O(e_n^2) e_{n+1}=\sum_{k=2}^{\infty}\frac{(-1)^ke_n^k}{2(\Psi^\)^{k-1}} e_{n+1}=\frac{e_n^2}{2\Psi^\} V=E^+\oplus E^0\oplus E^- \lambda_+=\ln2,\quad\lambda_0=0,\quad\lambda_-=-\ln2 m_+=39,\quad m_0=47,\quad m_-=39 39+47+39=125 E=\lim_{k\to\infty}\mathcal B^k(\rho) \mathcal B(E)=E z_n=(\psi_n,k_n)^T,\qquad N_n=\psi_n+k_n \Omega_n=\frac{\psi_n}{N_n} N_{n+1}=5N_n N_n=5^n \Omega_n=\frac{m}{5^n} v=(47,78)^T Mv=\lambda v \Omega_c=\frac{47}{47+78}=\frac{47}{125} \frac{m}{5^k}=\frac{47}{125} t_n=\frac{47}{125}5^n=47\cdot5^{\,n-3} p_n=\arg\min_{p\in\mathbb P}\left|\frac{p}{5^n}-\frac{47}{125}\right| \delta_n=|p_n-t_n| \frac{\delta_n}{5^n}=O(5^{-0.475n}) \lim_{n\to\infty}\frac{p_n}{5^n}=\frac{47}{125} 7750000\Omega^3-15500000\Omega^2+14947211\Omega-3840793=0 x(t)=e^{-tK}x_0 \lim_{t\to\infty}x(t)=P_Kx_0 \dot x=-K^2x x(t)=e^{-tK^2}x_0 \lim_{t\to\infty}e^{-tK^2}=P_E B=(1-\Omega_c)I+\Omega_cP_E \rho_\=I/125 \operatorname{Tr}(P_E\rho_\)=\frac{47}{125} \Phi(\rho)=\sum_iK_i\rho K_i^\dagger H_K=K^2\ge0 \ker(H_K)=E \rho_\infty=P_E\rho_0 C\rightarrow-\Delta_g (\Delta_g-6I)(\Delta_g-30I)\phi=0 g_{\mu\nu}=\langle\partial_\mu\phi,\partial_\nu\phi\rangle \phi=\Omega_c,\qquad\nabla\phi=0,\qquad\pi=0 \ker K\Rightarrow\Omega_c\Rightarrow\hat O\Psi=\Omega_c\Psi \frac{d^2y}{d\tau^2}+\Gamma_{yyy}\left(\frac{dy}{d\tau}\right)^2+F=0 y=\rho_I-\Omega_c C^2=A Q_n=\operatorname{Tr}(P\rho_n) Q_{n+1}=\frac{Q_n^2+Q_k^2}{2Q_n} G(Q) \delta S=0 G'(Q_k)=125 \lim_{n\to\infty}L_{\rm op}^nR_{\rm op}^n(C_{\rm op}(I_{\rm op}(x))) T=\int\Lambda(t)\,dC_{\rm op}(t) \Psi_C(\nabla_C(\rho_I^{\rm stable})) K(\Phi)=\frac{\delta S_{\rm UMVP}}{\delta\Phi}=0 T_{\mu\nu}=g_{\mu\nu}-\frac12g_{\mu\nu}(g^{\alpha\beta}g_{\alpha\beta}) T_{\mu\nu}=-g_{\mu\nu} G_{\mu\nu}+\Lambda g_{\mu\nu}=0 \Lambda=8\pi G Kx=0\Longleftrightarrow(\Delta_g-6)(\Delta_g-30)\phi=0\Longleftrightarrow T_{\mu\nu}=-g_{\mu\nu}\Longleftrightarrow G_{\mu\nu}+\Lambda g_{\mu\nu}=0 \Psi=\rho^{1/2}e^{iS/\hbar} Q=-\frac{\hbar^2}{2m}\frac{\nabla^2\rho^{1/2}}{\rho^{1/2}} S=k\log\Omega \Omega=\dim(\ker K)=47 K=(H-\lambda_1)(H-\lambda_2) K=\frac{\delta S}{\delta g_{\mu\nu}} Kx=0\Longleftrightarrow G_{\mu\nu}+\Lambda g_{\mu\nu}=0 \nabla\times v=0 E(k)\sim k^{-5/3} S(n)=S_0e^{-2\Delta En} \frac{dV}{dt}=0 V=\operatorname{tr}(H\Pi_{\rm total}) \mathrm{Key}=\{\Pi_1,\dots,\Pi_{13}\} \Pi_1\Pi_2\cdots\Pi_{13}\neq0 \mathrm{Ciphertext}=\langle\Psi|O|\Psi(\tau)\rangle \operatorname{Enc}(m)=P_E(m+Kc) K=(C-aI)(C-bI) \Pi_k^{-1}\Rightarrow\mathcal B(\rho)\rightarrow E V\rightarrow\text{vacuum noise} \lambda_{\rm crit}=\frac{\hbar}{mv_s} V(r)=D_e\left(1-e^{-a(r-r_e)}\right)^2 \psi_{\rm local}=\frac{E_0}{D_e} i\hbar\partial_t\Psi=\left[-\frac{\hbar^2}{2m}\nabla^2+V_{\rm fractal}\right]\Psi V_{\rm fractal}(x)=\sum_nS^{-nH}\cos(S^nx) D=2-H S=2 H_{\rm cl}=\frac{p^2}{2}+F(x) \lambda_+=\ln2 P(s)=\frac{\pi s}{2}e^{-\pi s^2/4} Z_q(\varepsilon)=\sum_ip_i^q\sim\varepsilon^{\tau(q)} D_q=\frac{\tau(q)}{q-1} \tau(q)=(q-1)\left(3-\frac{39}{125}q^2\right) f(\alpha)=q\alpha-\tau(q) \rho_I\ge\Omega_c \phi^5=SU(3)\times SU(2)\times U(1) \alpha^{-1}=137.0359\ldots V_{125}\rightarrow E_{47}\rightarrow\phi^{12.5}\rightarrow\phi^5\rightarrow\alpha V\cong\mathbb C^{125},\qquad\rho\in\mathcal D(V) \rho^\dagger=\rho,\qquad\operatorname{Tr}(\rho)=1 v_N=\frac1{\sqrt Z}[N\bmod p_i] Z=\sum_i(N\bmod p_i)^2 \rho_0=v_Nv_N^\top D_N=\operatorname{diag}\!\left(\frac1{1+|N\bmod p_i|}\right) \mathcal M_\varepsilon(\rho)=(1-\varepsilon)\rho+\varepsilon I/125 \rho=\sum_i\lambda_i|e_i\rangle\langle e_i| \Pi_{47}(\rho)=\sum_{i=1}^{47}\lambda_i|e_i\rangle\langle e_i| F(N,\rho)=\Pi_{47}\!\left(\frac{D_N\mathcal M_\varepsilon(\rho)D_N}{\operatorname{Tr}(D_N\mathcal M_\varepsilon(\rho)D_N)}\right) B(\rho)=(1-\Omega_c)\rho+\Omega_cF(N,\rho) \rho_{k+1}=B(\rho_k) E=\lim_{k\to\infty}\rho_k E=F(N,E) \operatorname{rank}(E)\le47 E=\sum_{i=1}^{47}\lambda_i|e_i\rangle\langle e_i| s_i=\langle e_i|D_N|e_i\rangle i^\=\arg\max_i s_i p=\gcd\!\left(N,\lfloor s_{i^\}^{-1}\rfloor\right) \rho\xrightarrow{\mathcal M_\varepsilon}D_N\xrightarrow{\mathrm{normalize}}\Pi_{47} \rho_{k+1}=(1-\Omega_c)\rho_k+\Omega_c\Pi_{47}\!\left(\frac{D_N[(1-\varepsilon)\rho_k+\varepsilon I/125]D_N}{\operatorname{Tr}(\cdot)}\right) \rho_0\rightarrow B^k(\rho_0)\rightarrow E\rightarrow(p,q) F(\omega,\rho)=\Pi_{47}\!\left(\frac{D_\omega\mathcal M_\varepsilon(\rho)D_\omega}{\operatorname{Tr}(D_\omega\mathcal M_\varepsilon(\rho)D_\omega)}\right) \boxed{\Sigma\rightarrow K\rightarrow E_{47}\rightarrow P_E\rightarrow\Omega_c\rightarrow\mathcal B\rightarrow\rho_\infty} 153. \Sigma = V_2^{\otimes3} 154. \dim(\Sigma)=125 155. \Sigma=\Psi\oplus\Psi^\perp 156. \dim(\Psi)=47 157. \dim(\Psi^\perp)=78 158. 125=47+78 159. \Omega_c=\frac{47}{125} 160. r=\frac{78}{47} 161. \Omega_c=\frac{1}{1+r} 162. C=(J^{(1)}+J^{(2)}+J^{(3)})^2 163. \sigma(C)=\{0,2,6,12,20,30,42\} 164. K=(C-6I)(C-30I) 165. \ker(K)=E_{47} 166. \operatorname{rank}(K)=78 167. \operatorname{im}(K)=E_{78} 168. P_E=\lim_{n\to\infty}(I-\varepsilon K)^n 169. P_E^2=P_E 170. P_E^\dagger=P_E 171. KP_E=0 172. P_EK=0 173. I=P_E+P_\perp 174. P_EP_\perp=0 175. P_\perp^2=P_\perp 176. \Gamma=I-\varepsilon K 177. \Gamma^n=(I-\varepsilon K)^n 178. \Lambda=\lim_{n\to\infty}\Gamma^n 179. \Lambda=P_E 180. \Gamma P_E=P_E 181. P_E\Gamma=P_E 182. \Gamma x\rightarrow P_Ex 183. x_{n+1}=(I-\varepsilon K)x_n 184. x_{n+1}=(I-\varepsilon K^2)x_n 185. |\psi_{n+1}\rangle=\operatorname{normalize}\!\left((I-\varepsilon K^2)|\psi_n\rangle\right) 186. \Omega(x)=\frac{\|P_Ex\|^2}{\|x\|^2} 187. 0\le\Omega(x)\le1 188. \Omega(n)\rightarrow1 189. \Omega(0)\approx0.33 190. \Omega(\infty)=1 191. d(E_{47},x_n)\rightarrow0 192. \|x_n-P_Ex_n\|\rightarrow0 193. F[\rho]=\intf(\rho,\nabla\rho)\,dx 194. \mu=\frac{\delta F}{\delta\rho} 195. \partial_t\rho=\nabla\cdot(D\rho\nabla\mu) 196. \frac{dF}{dt}\le0 197. \rho_{n+1}=\operatorname*{arg\,min}\left[F(\rho)+\frac1{2\tau}W_2^2(\rho,\rho_n)\right] 198. \dot x=-Kx 199. x(t)=e^{-Kt}x_0 200. \lim_{t\to\infty}x(t)=P_Ex_0 201. L(x)=x^TKx 202. \frac{dL}{dt}=-\|Kx\|^2 203. \Psi=\ker(K)=V_2\oplusV_5 204. \dim(V_2)=25 205. \dim(V_5)=22 206. 25+22=47 207. \Psi=E_6\oplusE_{30} 208. m_6=25 209. m_{30}=22 210. m_6+m_{30}=47 211. \Omega_c=\frac{m_6+m_{30}}{125} 212. \alpha^{-1}=4\pi\,\mathcal G(\Omega_c) 213. \phi=\frac{1+\sqrt5}{2} 214. \psi=\phi^{-2} 215. \psi\approx0.381966 216. \Omega_c\approx\psi 217. \Sigma\rightarrow\Gamma\rightarrow\Lambda\rightarrow\Psi\rightarrow\Omega\rightarrow\mathcal I 218. \mathcal I=\Omega\!\left(\Lambda(\Gamma^n(K(\Sigma)))\right) 219. \mathcal M=id_\Psi 220. \Sigma'=\mathcal M\circ\mathcal I\circ\Lambda:\Sigma\rightarrow\Sigma' 221. \mathcal M:\Psi\rightarrow\Psi 222. \mathcal I:\Psi\rightarrow\mathcal J 223. \mathcal J=f(\Psi) 224. \Sigma'=\mathcal M(\mathcal J) 225. \Sigma\rightarrowK\rightarrow\Psi\rightarrow\Gamma^n\rightarrow\Lambda\rightarrow\Omega\rightarrow\mathcal J\rightarrow\mathcal M\rightarrow\Sigma' 226. \mathcal J=\operatorname{Inv}(\Psi) 227. \mathcal M=id_\Psi 228. \mathcal J\neq\mathcal M 229. \mathcal M\circ\mathcal J=\Sigma' 230. \Sigma'\longrightarrowK\longrightarrow\Psi 231. \Sigma_n\rightarrow\Sigma_{n+1} 232. \Sigma_{n+1}=\mathcal M(\mathcal J(\Sigma_n)) 233. \Omega(\Sigma_{n+1})\ge\Omega(\Sigma_n) 234. \Omega\rightarrow1 235. \ker(K)=\operatorname{Fix}(\Gamma) 236. \operatorname{Fix}(\Gamma)=E_{47} 237. \Gamma|{E{47}}=I 238. \Gamma|{E{78}}<I 239. E_{47}=\lambda_0(\Gamma) 240. E_{78}=\{\lambda_i<1\} 241. \mathcal L_{\mathrm{IG}}=(\mathcal A,\mathcal N,\mathcal P,\mathcal S,\llbracket\cdot\rrbracket) 242. \mathcal A=\{\Sigma,K,\Xi,\Psi,\Gamma^n,\Lambda,\Omega,J,M,X,H,\Theta,I,\bullet,:,\Delta,\Pi,\varnothing,\alpha,\phi,\infty\} 243. \mathcal N=\{\langle\mathrm{Sentence}\rangle,\langle\mathrm{Input}\rangle,\langle\mathrm{Filter}\rangle,\langle\mathrm{Core}\rangle,\langle\mathrm{Iterate}\rangle,\langle\mathrm{Project}\rangle,\langle\mathrm{Interpret}\rangle\} 244. \langle\mathrm{Sentence}\rangle::=\langle\mathrm{Input}\rangle\langle\mathrm{Filter}\rangle\langle\mathrm{Core}\rangle\langle\mathrm{Iterate}\rangle\langle\mathrm{Project}\rangle\langle\mathrm{Interpret}\rangle 245. \langle\mathrm{Input}\rangle::=\Sigma\midX\Sigma 246. \langle\mathrm{Filter}\rangle::=K\mid\Xi\mid\Theta 247. \langle\mathrm{Core}\rangle::=\Psi 248. \langle\mathrm{Iterate}\rangle::=\Gamma^n\mid\Gamma^{I}\mid\Gamma^{II}\mid\Gamma^{III} 249. \langle\mathrm{Project}\rangle::=\Lambda 250. \langle\mathrm{Interpret}\rangle::=\Omega J 251. \mathcal S=\langle\mathrm{Sentence}\rangle 252. \Sigma\to K\to\Psi\to\Gamma^n\to\Lambda\to\Omega\to J 253. \llbracket\Sigma K\Psi\Gamma^n\Lambda\Omega J\rrbracket=\Omega\!\left(\Lambda\!\left(\Gamma^n(K(\Sigma))\right)\right) 254. \Gamma\vdash s:T 255. 125\to47 256. \operatorname{Ob}=\{\Sigma,\Sigma\times\Sigma,\Sigma\times\Psi,\Psi\times[0,1]\} 257. \operatorname{Mor}=\{\Delta,\operatorname{id}\times P_\Psi,J\} 258. \mathcal I=J\circ(\operatorname{id}\Sigma\times P\Psi)\circ\Delta 259. \operatorname{id}\Sigma:\Sigma\to\Sigma 260. \Delta:\Sigma\to\Sigma\times\Sigma 261. \Delta(x)=(x,x) 262. (\operatorname{id}\times P\Psi)\circ\Delta(x)=(x,P_\Psi x) 263. J(x,p)=\left(p,\frac{\|p\|^2}{\|x\|^2}\right) 264. \mathcal I(x)=\left(P_\Psi x,\frac{\|P_\Psi x\|^2}{\|x\|^2}\right) 265. \Omega(x)=\frac{\|P_\Psi x\|^2}{\|x\|^2}\in[0,1] 266. \mathbb E[\Omega]=\frac{\operatorname{tr}(P_\Psi)}{\dim\Sigma} 267. \mathbb E[\Omega]=\frac{47}{125} 268. \Omega^{-1}(1)=\Psi 269. \Omega^{-1}(0)=\Psi^\perp 270. \Psi^\perp=\operatorname{im}K 271. x\in\Psi\Rightarrow\mathcal I(x)=(x,1) 272. x\in\Psi^\perp\Rightarrow\mathcal I(x)=(0,0) 273. P_\Psi K=0 274. KP_\Psi=0 275. \Gamma^\infty=P_\Psi 276. \Psi=\operatorname{Fix}(\Gamma)=\ker K 277. \Lambda\Sigma=\Psi 278. \mathcal I=\Omega(\Psi) 279. c:S\to F(S) 280. F=K\circ\Gamma 281. \mathrm{Exec}(s)=\Gamma^n(s) 282. \rho_\perp(\Gamma)<1 283. \rho_\perp=0.9375 284. \|K\psi_{250}\|=5.42\times10^{-6} 285. \|\Psi^\perp\|^2=2.51\times10^{-15} 286. \|P^2-P\|=0 287. \|KP\|=0 288. \Sigma\to K\to\Psi\to\Gamma^n\to\Lambda\to\Omega\to J\to M\to\Sigma' 289. J(x)=(P_\Psi x,\Omega(x)) 290. M:J\to\Sigma' 291. \Sigma_{n+1}=M(J(\Sigma_n)) 292. \Sigma'=M\circ J\circ\Lambda\circ K:\Sigma\to\Sigma' 293. \Sigma\xrightarrow{\Delta}\Sigma\times\Sigma\xrightarrow{\operatorname{id}\times\Gamma^\infty}\Sigma\times\Psi\xrightarrow{J}\Psi\times[0,1] 294. \Gamma^\infty=P_\Psi 295. \Psi=5V_2\oplus2V_5 296. \Omega_c=\frac{\operatorname{tr}(P_\Psi)}{125}=\frac{47}{125} 297. \mathcal M=M^4\times\mathcal P 298. \mathbb G_{AB}=\begin{pmatrix}G_{\mu\nu}(x) & \mathcal C_{\mu\beta}(x,p)\\\mathcal C_{\alpha\nu}(x,p) & h_{\alpha\beta}(p)\end{pmatrix} 299. \mathcal C_{\mu\beta}:M^4\times\mathcal P\to T^\ast M\otimes T^\ast\mathcal P 300. \mathcal C_{\alpha\nu}:\mathcal P\times M^4\to T^\ast\mathcal P\otimes T^\ast M 301. \Phi=\frac{\nabla_A\mathcal C^{A}{}{B}}{J_D}=\mathrm{constant} 302. \square\Phi^i=-2\lambda\xi^i\exp(2\xi\cdot\Phi) 303. \mathcal R{AB}-\frac12\mathbb G_{AB}\mathcal R=\kappa\mathcal T_{AB}\,\delta(\sigma-1) 304. G_{\mathrm{inv}}[A,B]:=R_{\mathrm{inv}}[A,B]-\frac12\,\mathrm{Metric}[A,B]\,\mathrm{Scal}{\mathrm{inv}} 305. \mathrm{FieldEq}:=G{\mathrm{inv}}[A,B]=\kappa T_{\mathrm{inv}}[A,B]\Delta[\sigma-1] 306. \operatorname{Tr}(K)=\sum_\lambdaM_\lambda(\lambda-6)(\lambda-30) 307. \operatorname{Tr}(K)=180+1008+0-3024-3780+0+5616=0 308. \Sigma=\rho(\operatorname{Diff}(M)) 309. K_{\mathrm{GR}}=G_{\mu\nu}-\frac{8\pi G}{c^4}T_{\mu\nu} 310. \Psi_{\mathrm{GR}}=\ker K_{\mathrm{GR}} 311. \Psi_{\mathrm{GR}}=\left\{g\in\operatorname{Lor}(M)\midG_{\mu\nu}(g)=\frac{8\pi G}{c^4}T_{\mu\nu}\right\} 312. \Gamma_{\mathrm{GR}}=I-\varepsilon K_{\mathrm{GR}} 313. \nabla^\mu T_{\mu\nu}=0 314. J_{\mathrm{GR}}=\operatorname{Inv}(\operatorname{Diff}(M)) 315. \mathrm{GR}=\frac{\ker\!\left(G_{\mu\nu}+\Lambda g_{\mu\nu}-\frac{8\pi G}{c^4}T_{\mu\nu}\right)}{\operatorname{Diff}(M)} 316. R:=\lim_{n\to\infty}f^n(x)+\int\Lambda(t)\,dC(t)+\Psi_C(\nabla C(\rho_I^{\mathrm{stable}})) 317. \phi_{ij}(x)=\sin(\theta(r))\left(\hat r_i\hat r_j-\frac13\delta_{ij}\right) 318. Q_{\mathrm{top}}=1 319. E_{\mathrm{Bog}}=\frac{\pi^2}{3} 320. r^2\theta''+2r\theta'-3\sin\theta\cos\theta+\frac{\sin^2\theta}{r^2}\left(2\sin^2\theta+4r^2(\theta')^2\right)=0 321. \theta(0)=\pi 322. \theta(\infty)=0 323. \Sigma\text{ separable Hilbert space} 324. \sigma\in\Sigma 325. \Gamma:\Sigma\to\Sigma 326. \sigma_{n+1}=\Gamma(\sigma_n) 327. \Gamma(\sigma_n)=F(\sigma_n,\sigma_{n-1},\ldots) 328. \Omega(\sigma_n)=1-\frac{\|\Gamma(\sigma_n)-\sigma_n\|}{\|\sigma_n\|} 329. \Psi=\Lambda\circ\Gamma^\infty(\sigma_0):=\lim_{n\to\infty}\sigma_n 330. \Lambda\circ\Gamma=\Gamma\circ\Lambda 331. F(\sigma)=\|\Gamma(\sigma)-\sigma\|^2 332. F(\sigma_{n+1})\leF(\sigma_n) 333. \frac{d\Psi}{dt}=\Gamma(\Psi)-\Psi 334. \lim_{t\to\infty}\frac{d\Psi}{dt}=0 335. v_n=\sigma_{n+1}-\sigma_n=\Gamma(\sigma_n)-\sigma_n 336. \|v_n\|^2=F(\sigma_n) 337. \frac{d\sigma}{dt}=\Gamma(\sigma)-\sigma 338. 1-\Omega(\sigma_{n+1})\leL\bigl(1-\Omega(\sigma_n)\bigr) 339. L<1 340. \Theta_C:=\sup\{\Omega(\sigma):L(\sigma)\ge1\} 341. \Omega(\sigma)>\Theta_C\Longleftrightarrow\sigma\to\Psi^\\in\Psi 342. \Omega(\sigma)\le\Theta_C\Longleftrightarrow\sigma\not\to\Psi^\ 343. \exists!\,\Psi^\\in\Psi 344. \sigma_0\mapsto\Psi^\ 345. \varphi:\Sigma\to\Sigma' 346. \Gamma'=\varphi\circ\Gamma\circ\varphi^{-1} 347. \varphi(\Psi^\)=\Psi'^\ 348. I:\Sigma\to\mathbb R 349. I(\sigma):=-F(\sigma) 350. I|\Psi=\mathrm{constant} 351. \nabla\Omega I>0 352. \Theta_C\approx0.376 353. \Omega_c=\Theta_C
attachment:bd2b3220-770a-490e-a867-19293d24d031:Formalism.pdf
