二重カーネル畳み込み

2つの正規化記憶カーネル、有限のHill応答、幾何学と観測量の間の明示的に未解決な橋を備えたLindgren-DKC候補経路。

DKCのFieldState較正パイプラインは実装済みで値を生成し、F1〜F9は内容ハッシュで固定された予測である。評価器は明示的な未較正感度入力も受け付ける。国別系列は技術導入時期のプロキシであって測定線量ではなく、観測量へのLindgren L2演算子は未解決である。

Publication gate: release not authorized

This is a candidate route that is not release-authorized. 0/10 critical points V1–V10 pass and the evidence-protocol audit has not passed. F1–F9 are locked candidate forecasts, not results of an authorized release artifact. The site builds with this state shown; the gate closes only with an evaluation bundle.

V1 FAIL · MISSING_EVALUATION
V2 FAIL · MISSING_EVALUATION
V3 FAIL · MISSING_EVALUATION
V4 FAIL · MISSING_EVALUATION
V5 FAIL · MISSING_EVALUATION
V6 FAIL · MISSING_EVALUATION
V7 FAIL · MISSING_EVALUATION
V8 FAIL · MISSING_EVALUATION
V9 FAIL · MISSING_EVALUATION
V10 FAIL · MISSING_EVALUATION

Rule: all(V1..V10 == PASS) AND protocolAudit.passed

1. 導出境界

L0 · LINDGREN 2025

PREMISE

g_mu_nu = eta_mu_nu + kappa A_mu A_nu

L1 · DERIVED

DERIVED

delta_g = kappa (A_bio⊗a_ext + a_ext⊗A_bio + a_ext⊗a_ext)

L1 · GEODESIC DEVIATION

DERIVED

D_u sqrt(-det g) = kappa (A·u) / sqrt(1 + kappa A^2)

L2 · LORENTZ → EUCLIDEAN/SCALAR

OPEN CHOICE

q = |A_bar| := sqrt(kappa)s [dimensionless spatial projection]

L1 · CHI ALGEBRA

DERIVED

chi_geo(q) = q / sqrt(1 + q^2); directional derivative evaluates chi_geo(|A_bar|) after the L2 reduction

L2 · OBSERVABLE BRIDGE

OPEN

O_r = integral K_r^(mu nu) delta_g_mu_nu dV

代数式χ_geo(q)はL1のままである。正のq=|Ā|をLorentz→Euclid空間・スカラー射影で選ぶ操作はL2縮約である。測定量やプロキシzには別途、明示的な無次元正規化q=N(z)が必要で、その選択と較正は未解決のL0→L2段階である。他の各成分も固有の来歴を保持する。

2. DKC計算

T4 fast: k_B(s) = s^(n_B-1) exp(-s/tau_B) / (tau_B^n_B Gamma(n_B)), n_B in 2..6

annual T4 bins: K_B[l] proportional to CDF_Erlang(l+1) - CDF_Erlang(l)

slow: k_R(s) = exp(-s/tau_R) / tau_R

T3: v(a) = 5 (a<0), 4 (a<1), 3 (a<6), 2 (a<18), else 1

BL(t) = alpha integral k_B(s)x(t-s)ds + beta integral k_R(s)v(a)x(t-s)ds; beta = 1-alpha

sigma(BL) = BL^n / (x_half^n + BL^n)

Delta endpoint(t) = -gamma sigma(BL(t))

T4は正規化Erlang高速カーネル（整数n_B=2–6）と正規化指数低速カーネルを用いる。Betaは自由ではなく beta=1−alpha、かつ tau_R>tau_B。T3のコホート重みはv(a)=5 (a<0), 4 (0≤a<1), 3 (1≤a<6), 2 (6≤a<18), その他1である。

Dual-kernel candidate explorer

Vary the candidate time scales and response shape against a synthetic annual technology-adoption curve. The chart is a sensitivity view, not an empirical country fit.

Model status

candidate calculation / national technology timing proxy / open L2 / locked F1–F9 falsification register

The registered DKC FieldState calibration pipeline is implemented and produces values; the route also publishes the locked F1–F9 register. This Explorer run deliberately uses a synthetic timing proxy, not a local physical measurement or calibrated dose.

Scenario parameters

Fast scale τB0.50 years

Slow scale τR12 years

Fast share α0.60

Derived slow share β

0.40

Hill coefficient n2.50

Erlang shape nB3

T4 uses the selected Erlang nB = 2–6 for the fast arm and a normalized exponential for the slow arm. β is constrained to 1 − α.

T3 cohort vulnerability (shown explicitly; not applied to this period-only curve): v(a)=5 for a<0, 4 for 0≤a<1, 3 for 1≤a<6, 2 for 6≤a<18, otherwise 1. Supply a cohort birth year to the evaluator to apply it to the slow input.

Candidate load and Hill saturation, 1990–2030

Four annual curves show the weighted fast arm, weighted slow arm, their total, and the normalized Hill saturation.

Fast armSlow armTotal loadHill saturation

Example construction: a midpoint-2013 sigmoid with 0.5/year steepness, multiplied by the continuous 0.33–1.00 duty-cycle scenario. A longer prehistory is calculated before the displayed window to avoid an artificial start-edge effect.

2030 scenario snapshot

Synthetic proxy: 1.000
Duty cycle: 1.000
Fast arm: 0.600
Slow arm: 0.292
Total load: 0.892
Hill saturation: 0.809
Seasonal CV: 0.000

3. T1–T12精緻化レジスター

T1L3_IMPORTED

country-specific continuous duty cycle

d(t,c)=0.33+0.67/(1+exp(-k_s(t-t_mid(c))))

Stage 2 · free parameters: 0

T2L3_PHENOMENOLOGICAL

Hill response exponent

sigma(x)=x^n/(x_half^n+x^n)

Stage 3 · free parameters: 1

T3L3_IMPORTED

birth-cohort vulnerability

v(a)={5:a<0,4:0<=a<1,3:1<=a<6,2:6<=a<18,1:a>=18}

Stage 2 · free parameters: 0

T4L3_PHENOMENOLOGICAL

Erlang behavioural kernel

k_B(s)=s^(n_B-1) exp(-s/tau_B)/(tau_B^n_B Gamma(n_B))

Stage 3 · free parameters: 1

T5L3_IMPORTED

endpoint-specific testicular SAR multiplier

w_fertility(f)=SAR_testicular(f) coupling(f) modulation(f)

Stage 2 · free parameters: 0

T6L3_PHENOMENOLOGICAL

separate indoor Wi-Fi proxy

wifi(t)=w_wifi BB(t) D_wifi(t)

Stage 4 · free parameters: 0-1

T7L3_PHENOMENOLOGICAL

handset power-control correction

personal_eff=P_tx_max(1-eta ambient_norm)

Stage 4 · free parameters: 1

T8L3_PHENOMENOLOGICAL

network-density saturation

P_ambient=P_max N/(N_half+N)

Stage 4 · free parameters: 1

T9L3_PHENOMENOLOGICAL

spectral-complexity multiplier

H=-sum(p_f log2 p_f); multiplier=1+lambda_H H

Stage 4 · free parameters: 1

T10L3_PHENOMENOLOGICAL

seasonal-variation prediction

CV_seasonal=CV_0(1-duty_cycle)

Stage 2 · free parameters: 0

T11L3_PHENOMENOLOGICAL

melatonin-redox synergy

BL_syn=BL(1+epsilon_syn d_night chi_pineal)

Stage 2 · free parameters: 0

T12L3_PHENOMENOLOGICAL

explicit parental epigenetic carry-over

BL_final=BL_syn+epsilon_epi BL_parent_at_conception

Stage 4 · free parameters: 1

4. 現在利用できるもの

Layer	Current state	Allowed interpretation
Geometry	2025 Weyl ansatz + exact tensor perturbation	Premise / derived algebra
L2	OPEN	No geometry-to-observable claim
National series	World Bank mobile, broadband, urban	TECHNOLOGY_TIMING_PROXY
FieldState	calibration pipeline implemented and producing values; uncalibrated sensitivity inputs also supported	Calibration output, proxy class and execution capability kept separate
DKC parameters	tau_B, tau_R, alpha and Hill parameters carry L3 provenance	They do not relabel L1-derived components
Predictions	F1–F9 content-addressed and locked	LOCKED_FALSIFIABLE_FORECAST

続ける

Frequency weights Model comparison Falsification registry