天赐范式第187天·第一篇让峰开始移动——lag load定量摘要fitness峰以速度v定向移动理论给出测量滞后lag*v·(1−β·h²·K)/(β·h²·K)。线性区(v≤0.003)比值0.99-1.00fit崩溃区lag仍符合公式丢失区种群丢失峰。一、接续186-2fitness峰钉死五篇了该动了186-2把漂变主导区画出来了——全链先验机器的第一次应用。但有一个隐含假设从182到186贯穿五篇fitness峰一直钉死在x*0.8。栖息地不是恒温箱。186-2的均值不动点μ*是在静止峰下解的μ* [TARGET β·h²*·K·x*/(1−β)] / [1 β·h²*·K/(1−β)]。这个不动点假设x*是常数——峰不动均值才不动。峰一动这个不动点就跟着动种群均值在后面追。问题是追得上吗追不上时fitness怎么掉这就是lag load——环境变化导致的跟踪滞后定量。二、模型变化——回归目标从固定TARGET到种群均值μ186模型g’ TARGET β·(g_sel − TARGET) v_mut固定锚静止环境187模型g’ μ β·(g_sel −μ) v_mut移动锚动态环境变化只有一处回归目标从固定TARGET0.5改为种群均值μ。环境动了种群的家也跟着动。方差动力学不变Var(g)’ β²·Var(g_sel) σ_v²——186-1自洽Var(g)*仍适用h²*、K*不变。fitness峰移动x*(t) x*_0 v·genv是峰速。三、理论推导——lag* v·(1−β·h²·K)/(β·h²·K)均值更新回归到μμ’ μ β·h²·(x* − μ)·K这是以μ为变量的AR(1)输入是x*响应速率β·h²·K。峰以速度v移动时稳态滞后lag* v·(1 − β·h²·K) / (β·h²·K)物理意义峰每代跑远v选择每代追回β·h²·K·lag——稳态时追回量等于跑远量。等时滞后峰x*(t)与同刻均值μ(t)的差为v/(β·h²·K)83.3v。代码测的是测量滞后峰x*(gen)与更新后均值μ(gen1)的差比等时滞后少一步峰行程v——lag*v/c−vv(1−c)/c测量口径因子(1−β·h²·K)≈0.988。滞后负荷fitness损失Δfitness ≈ lag*² / (2ω²)高斯fitness的Taylor展开。临界峰速v*lag大到fitness→0选择无法运作。lag≈3ω时fitness≈0.01近似崩溃边界。四、lag(v)曲线理论vs数值固定σ_v0.02186-2中心参数扫peak_v ∈ {0, 0.0005, 0.001, 0.002, 0.003, 0.005, 0.01}。理论参数σ_v0.02自洽h²*0.5201K0.0769跟踪速率β·h²·K0.0120测量口径因子(1−β·h²·K)0.9880等时斜率1/0.012083.3测量斜率0.9880/0.012082.3。peak_vlag*理论lag数值比值平均fitness状态0.00000.00000.0006†—0.9566基准0.00050.04110.04121.000.8833跟踪0.00100.08230.08170.990.6998跟踪0.00200.16460.16250.990.2773跟踪0.00300.24690.24410.990.0588跟踪0.00500.41150.40971.000.0004fit崩溃0.01000.8230n/a—0.0000丢失†有限样本漂移残差。五、线性区、fit崩溃区与丢失区线性区peak_v ≤ 0.003lag∝v理论斜率82.3数值比值0.99-1.00。测量口径因子(1−β·h²·K)0.988是理论的核心修正——代码测的是lagx*(gen)−μ(gen1)峰与更新后均值的差比等时滞后v/(β·h²·K)少一步峰行程v。剩余≈1%偏差来自h²和K随lag增大有微小漂移理论把它们当常数。fit崩溃区peak_v 0.005lag0.41仍符合公式比值1.00但fitness0.0004——lag已远超fitness宽度ω0.10fitness指数坍塌。崩溃正是理论的预言lag大到fitness→0选择无法运作。丢失区peak_v ≥ 0.01种群完全丢失峰滞后无良定义均值停在原地峰持续远去lagn/a。基准v0lag≈0†fitness0.957。种群均值紧跟峰回归到μ的模型下静态跟踪近乎完美fitness只受遗传方差影响。†lag0.0006为有限样本漂移残差。六、结论与弧签名动作问题答案峰移动后种群能跟上吗线性区v≤0.003能lag*v·(1−β·h²·K)/(β·h²·K)定量给出滞后跟不上时怎样fit崩溃区v0.005lag仍符合公式但fitness→0丢失区v≥0.01种群丢失峰理论准吗线性区比值0.99-1.00测量口径因子(1−β·h²·K)≈0.988是核心修正模型为什么改固定TARGET下lag线性增长无稳态回归到μ后lag有稳态lag load理论成立叙事弧186-1Var(g)自洽闭式——全链先验机器建成186-2全链先验机器第一次应用——漂变主导区显形187-1峰开始移动——lag load定量从平衡升级到追踪弧签名动作186静止峰平衡 → 187移动峰追踪。降调准稳态近似。lag* v·(1−β·h²·K)/(β·h²·K)假设种群始终贴近瞬时平衡。丢失区v≥0.01种群完全丢失峰、滞后无良定义——失效区本身就是发现如实报。fit崩溃区v0.005lag仍符合公式但fitness已指数坍塌。h²和K被当常数。理论把h²*和K*当固定值用σ_v0.02自洽解但lag增大时种群偏离峰更远选择强度变化h²和K有微小漂移。线性区影响≈1%崩溃区影响大。模型变化需说明。186用固定TARGET0.5187改为回归到μ。方差动力学不变186-1自洽仍适用但均值动力学变了——固定TARGET下lag无稳态线性增长回归到μ后lag有稳态。这个变化是让峰开始移动的自然推论环境动了种群的家也跟着动。单位点模型。多位点、上位效应、连锁不平衡待后续。系列还在逐步建设中完善是和伙伴们的努力方向。附录完整代码# -*- coding: utf-8 -*- 天赐范式 第187天 第一篇 让峰开始移动——lag load定量 PID: TC-187A-V3.3.25.0 V3.3.25.0 · 2026-10-06 接续186-2fitness峰不再钉死x*0.8以速度v定向移动。 模型变化回归目标从固定TARGET改为种群均值μ环境动了种群的家也跟着动 186模型: gTARGETβ(g_sel-TARGET)v_mut 固定锚静止环境 187模型: gμβ(g_sel-μ)v_mut 移动锚动态环境 方差动力学不变Var(g)β²·Var(g_sel)σ_v²186-1自洽Var(g)*仍适用。 理论等时滞后 lag_eq v/(β·h²·K)峰x*(t)与同刻均值μ(t)的差 测量滞后 lag* v·(1−β·h²·K)/(β·h²·K)峰x*(gen)与更新后均值μ(gen1)的差 因子(1−β·h²·K)≈0.988是测量口径因子非离散修正离散AR(1)等时滞后恒等于v/c 滞后负荷 ≈ lag²/(2ω²) 临界峰速v*lag大到fitness→0选择无法运作 数值扫peak_v测lagx*(gen)−μ(gen1)判决线性区崩溃区 importsysimportmathimportnumpyasnpifhasattr(sys.stdout,reconfigure):sys.stdout.reconfigure(encodingutf-8)PIDTC-187A-V3.3.25.0TARGET0.5X_STAR_00.8FITNESS_WIDTH0.10BETA0.3SIGMA_E0.02SIGMA_V0.02N_POP200N_GENERATIONS1000WARMUP_STATIC200WARMUP_TRACK200N_SEEDS20TOL1e-12MAX_ITER5000PEAK_VELOCITIES[0.0,0.0005,0.001,0.002,0.003,0.005,0.010]defbar(title):print(*72)print( title)print(*72)print()defsub(title):print(【title)print(-*72)deffitness(x,x_star):returnnp.exp(-(x-x_star)**2/(2*FITNESS_WIDTH**2))defsolve_self_consistent(sigma_v):var_gsigma_v**2/(1-BETA**2)foritinrange(MAX_ITER):sigma_x2var_gSIGMA_E**2h2var_g/sigma_x2 v_x_selsigma_x2*FITNESS_WIDTH**2/(sigma_x2FITNESS_WIDTH**2)var_g_selh2**4*v_x_selvar_g*(1-h2**2)var_g_newBETA**2*var_g_selsigma_v**2ifabs(var_g_new-var_g)TOL:returnvar_g_new,it1var_gvar_g_newreturnvar_g,MAX_ITERdeftheory_lag(peak_v):var_g_star,_solve_self_consistent(SIGMA_V)sigma_x2var_g_starSIGMA_E**2h2var_g_star/sigma_x2 Ksigma_x2/(sigma_x2FITNESS_WIDTH**2)track_rateBETA*h2*K measure_factor1.0-track_rate lag_starpeak_v*measure_factor/track_rateiftrack_rate0elsefloat(inf)fitness_losslag_star**2/(2*FITNESS_WIDTH**2)returnlag_star,fitness_loss,h2,K,track_ratedefrun_one(peak_v,seed):rngnp.random.RandomState(seed)genesrng.normal(TARGET,0.01,N_POP)lags[]mean_fitnesses[]crashedFalseforgeninrange(N_GENERATIONS):ifgenWARMUP_STATIC:x_starX_STAR_0else:x_starX_STAR_0peak_v*(gen-WARMUP_STATIC)phenosgenesrng.normal(0,SIGMA_E,N_POP)fitsfitness(phenos,x_star)fit_sumfloat(fits.sum())iffit_sum1e-10:crashedTrueforg2inrange(gen,N_GENERATIONS):ifg2WARMUP_STATICWARMUP_TRACK:mean_fitnesses.append(0.0)breakprobsfits/fit_sum sel_idxrng.choice(N_POP,sizeN_POP,pprobs)parent_genesgenes[sel_idx]mufloat(np.mean(genes))genesmuBETA*(parent_genes-mu)rng.normal(0,SIGMA_V,N_POP)ifgenWARMUP_STATICWARMUP_TRACK:mu_newfloat(np.mean(genes))lagx_star-mu_new lags.append(lag)mean_fitnesses.append(float(np.mean(fits)))mean_fitfloat(np.mean(mean_fitnesses))ifmean_fitnesseselse0.0ifcrashed:returnfloat(nan),float(nan),mean_fit mean_lagfloat(np.mean(lags))iflagselse0.0std_lagfloat(np.std(lags))iflagselse0.0returnmean_lag,std_lag,mean_fitdefmain():bar(f{PID}让峰开始移动——lag load定量)print(f模型: xge, gμβ(g_sel-μ)v_mut回归到种群均值μ非固定TARGET)print(f选择机制: 高斯加权按fitness加权抽样非截尾)print(f变化: fitness峰x*(t)X_STAR_0peak_v·gen峰开始移动)print(f参数: β{BETA}, σ_e{SIGMA_E}, σ_v{SIGMA_V}, N{N_POP}, seeds{N_SEEDS})print(ffitness峰: x*_0{X_STAR_0}, ω{FITNESS_WIDTH})print(f理论: 等时滞后lag_eqv/(β·h²·K)测量滞后lag*v·(1−β·h²·K)/(β·h²·K))print(f h²、K ← 186-1自洽Var(g)*σ_v{SIGMA_V}固定)print(f 因子(1−β·h²·K)是测量口径因子代码测x*(gen)−μ(gen1)少一步v)print(f数值: gen{N_GENERATIONS}, 静止warmup{WARMUP_STATIC}, 跟踪warmup{WARMUP_TRACK})print()_,_,h2,K,track_ratetheory_lag(1.0)sub(理论参数σ_v0.02自洽)print(f h²* {h2:.4f})print(f K {K:.4f})print(f β·h²·K {track_rate:.6f}每代跟踪速率)print(f 1−β·h²·K {1.0-track_rate:.6f}测量口径因子)print(f 等时斜率 1/(β·h²·K) {1.0/track_rate:.2f})print(f 测量斜率 (1−β·h²·K)/(β·h²·K) {(1.0-track_rate)/track_rate:.2f})print()sub(lag(v)曲线理论 vs 数值)print(f{peak_v:8s}{lag*理论:10s}{lag数值:10s}{lag std:10s}{负荷理论:10s}{平均fitness:12s}{状态:8s})print(-*72)results[]forpeak_vinPEAK_VELOCITIES:lag_th,loss_th,_,_,_theory_lag(peak_v)lags_seed[]fits_seed[]forseedinrange(N_SEEDS):ml,sl,mfrun_one(peak_v,seed)lags_seed.append(ml)fits_seed.append(mf)valid_lags[xforxinlags_seedifnotmath.isnan(x)]ifvalid_lags:lag_numfloat(np.mean(valid_lags))lag_stdfloat(np.std(valid_lags))else:lag_numfloat(nan)lag_stdfloat(nan)mean_fitfloat(np.mean(fits_seed))ifpeak_v0.0:status基准elifmath.isnan(lag_num):status丢失elifmean_fit0.001:statusfit崩溃eliflag_std/max(abs(lag_num),1e-10)0.3:status跟踪else:status过渡results.append({peak_v:peak_v,lag_theory:lag_th,lag_num:lag_num,lag_std:lag_std,loss_theory:loss_th,mean_fit:mean_fit,status:status,})ifmath.isnan(lag_num):lag_str n/astd_str n/aelse:lag_strf{lag_num:10.4f}std_strf{lag_std:10.4f}print(f{peak_v:8.4f}{lag_th:10.4f}{lag_str}{std_str}{loss_th:10.6f}{mean_fit:12.6f}{status:8s})print()sub(理论 vs 数值对比)forrinresults:ifr[peak_v]0.0:continueifr[status]in(跟踪,过渡,fit崩溃):ratior[lag_num]/r[lag_theory]ifabs(r[lag_theory])1e-10elsefloat(inf)print(f peak_v{r[peak_v]:.4f}: lag理论{r[lag_theory]:.4f}vs lag数值{r[lag_num]:.4f}比值{ratio:.2f}{r[status]})else:print(f peak_v{r[peak_v]:.4f}: 理论lag{r[lag_theory]:.4f}种群丢失峰fitness≈0)print()sub(结论)print(f186-2fitness峰钉死x*0.8全链先验机器算N*(σ_v))print(f187-1峰开始移动lag*v·(1−β·h²·K)/(β·h²·K)给出跟踪滞后定量)print(f 跟踪速率 β·h²·K {track_rate:.4f}测量斜率 {(1.0-track_rate)/track_rate:.1f})track_vs[rforrinresultsifr[status]跟踪]crash_vs[rforrinresultsifr[status]fit崩溃]lost_vs[rforrinresultsifr[status]丢失]iftrack_vs:print(f 线性区peak_v≤{track_vs[-1][peak_v]:.4f}lag∝v理论对得上)ifcrash_vs:print(f fit崩溃区peak_v{crash_vs[0][peak_v]:.4f}lag仍符合公式——崩溃正是理论的预言)iflost_vs:print(f 丢失区peak_v≥{lost_vs[0][peak_v]:.4f}种群完全丢失峰lag无良定义)print()print(f 弧签名动作186静止峰平衡 → 187移动峰追踪)if__name____main__:main()天赐范式 V3.3.25.0 · 2026-10-06