':iu#ddlZddlZddlZddlZddlmZdbdZ dcdZ e dejddd Z e d jjj!Zej%Ze d eed e d eddej+ZeezZe de de de eddZe de dedde dede dede dedezde dedezd e d!ed"d#e d$e ede%ezZej2d&d&d'(\ZZed)Zeed*D]2\ZZeDcgc]}|d" c}Z ejCe d+d,edz-4ejEd.ejGd/ejId0ejKd1ejMed2Zeed*D]2\ZZeDcgc]}|d3 c}Z'ejCe'd+d,edz-4ejQedd4d5d6ed7ejGd8ejId0ejKd9ejMed:ZejReeZ*ejReeeedzZ+ejCe*ed;dd?d&=ejYe+ed@zedAzdBd4Cej[eedz dDdEdFGejGdHejIdIejKdJejMedKZej]dLdMedddNZ/ej_dOd@e/ej`ddPdQe1dRdSdTUVejdejfe de dWe de dIdXdYdZd[dYd\d]e d^d_D]#Z4e4eekse e4dXd`ee4dz da%e dycc}wcc}w)dN(c |d}d}tjt|d}d}td}g} t|D]z} tjdt j |zdz } | jj} tjj| g| } g} td D]}| j|| |\}}|j| jtj5| jd ddd| j!|| j#|j#|j#d |j#|ks|j#}| j#}| j!| |dks{n|t j$|sd }tt'|}|dzd|zz}tt)j t+|d }t+||z dz d }t+||zdz d }|||||| dS#1swY(xYw)uU BTC forecasting via gradient descent on the price gap. Key Insight: - Treat BTC price P as having a "hidden factorization" structure - Find the "gap" d between price and market equilibrium - The loss L(d) = sin²(π·s) where s = √(d² + 4P) - Gradient descent collapses d to find the true price manifold ctj|dzd|zz}tjtj|zdz}||fS)u d = gap between price and equilibrium P_val = current BTC price s = √(d² + 4P) is the "market invariant" that should be integer-like g@)torchsqrtsinpi)dP_valslosss btc_factorization.pyloss_fnz*cct_btc_gradient_forecast..loss_fnsE JJq!tcEk) *yyA&!+QwF) requires_gradNinf )lrig)min)stepr rrg|=rg@)d_starr base_factorsentiment_factorr trajectories)rtensorfloatrangerandnnpr detachrequires_grad_optimAdam zero_gradbackwardrno_gradclamp_appenditemisfiniteroundmathmax)prices days_aheadr num_restartsPrP_tbest_d best_lossall_trajectoriesrestartr optimizer trajectoryrrrrs_sqbase sentiments rcct_btc_gradient_forecastr@s r A  ,,uQxu 5C Fe I& KKNRWWQZ '" , HHJ % % 'KK$$aSR$0  #J "D    !aoGD! MMO NN  "S! "   VVX VVX  yy{Y& IIK % "(  + u  =B~R[[0 5= !F 19q1u D diiD#'(A F c!3 'DQZ3&,I %(  ? " "s II cg}|j}t|D]}|d}t|dd}tt |dd}|tddt j jzzdz}|j|t j||}td |dzd ||zd d ||zd d |d|zd d|d t j|S)z CCT-ODE Multi-Step Forecast: Each future day is predicted by gradient descent on the current state. This creates a "chain of collapses" - each day collapses independently. rrr3r4rg-q=g{Gz?gư>zDay z: P=.2fu → Predicted=z | Base Factor=z, Gap d=r) copyr!r@r1r r#randomr"r,printarray) r2r3 price_scale forecastscurrent_pricesdayr5resultpredicted_prices rpredict_multi_steprOfs I[[]NZ b 2 +>aVWXeF=$9:EB 3q4"))//*;#;;TBB)>?C SUG4K4OOVaDabeCfg#M2[@EXfU]N^M_a b#b( 88I rzDownloading BTC data...zBTC-USD6mo1d)periodintervalClosezLoaded z days of BTC datazCurrent price: $rz,.2fz= ============================================================zCCT-GRADIENT BTC FORECASTz<============================================================rrrCz CCT Analysis of Current Price:z Current Price P: $z Optimal Gap d*: rz Market Invariant s: rz Base Factor (Fundamental): $rz Sentiment Factor: rrDz Loss (Collapsed): rz.2ez Generating 40-day forecast...)r3rIr)r)figsize)rrrgffffff?zRestart )alphalabellogz&CCT Gradient Descent: Loss ConvergenceStepu Loss (sin²))rrr redz--z Final d*=)ycolor linestylerXz'CCT Gradient Descent: Gap d ConvergencezGap d)rrzb- Historical)rX linewidthzr-z CCT Forecastg?g?g?)rWr]gray:Today)xr]r^rXz)BTC-USD: Historical + 40-Day CCT ForecastDayz Price (USD))rroffu CCT-GRADIENT STRUCTURE ═══════════════════════════════════════════ BTC Price P = Base Factor × Sentiment Factor Current Price: $uF ┌─────────────────────────────────────────────┐ │ Loss: L(d) = sin²(π·s) │ │ where s = √(d² + 4P) │ │ │ │ Gradient: ∂L/∂d = π·sin(2πs)·d/s │ │ │ │ Converges when s → integer (stable state) │ └─────────────────────────────────────────────┘ Analogy to Factorization: • Factorization: c = p × q, find gap d = q - p • BTC: P = B × S, find gap d = S - B Both use: s² = d² + 4c (or 4P) The "integer constraint" forces collapse to the true factor structure. g?top monospacer/wheatg?)boxstyle facecolorrW) transformfontsizeverticalalignment fontfamilybboxz"40-Day BTC Forecast (CCT-Gradient)z<6 Forecastz<20z Base Factorz<15z<------------------------------------------------------------)rrrz $z>15,.2f)rg?rs)rg?)5numpyr#yfinanceyfrr0matplotlib.pyplotpyplotpltr@rOrGdownloadbtcdropnavaluesflattencloserE close_rawlenr1 close_scalerMforecastsubplotsfigaxesax enumerateitrajlossesplot set_yscale set_title set_xlabel set_ylabellegenddsaxhlinearange days_histdays_fc fill_betweenaxvlineaxistext transAxesdict tight_layoutshowr )ts0rrs TnF bkk)ED9 G $$,,. JJL E |,-.2t,-.iik  m!"f  #5QR H(*Yr]40126(+,-.vc{m,-&}(= (KT&RSTV$67+EcJKLVF^C012') e L{ Z CLLAx 0 T $Z/07GAt!% &Aai &FGGF#x!u%5G67 e 56 f n  $Z/03GAt Q!C& BGGBc8AaC5!1G23 VH UdIfU]N^M_B` a 67 f g  $Z BIIc%j ! "))CJE R 0 9d,!D4~CCCs%P S^A Vs' J 89 e m  $Z  2t$% 4S$",,K 7gS AC m*+f r !Js#1]3$789f 2ACM 2b!A#w/012f a' s > Q Q"