From 7bb993aeb8c1f0900d485398a0a2eb363e6da8ac Mon Sep 17 00:00:00 2001 From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com> Date: Wed, 13 May 2026 16:15:07 -0500 Subject: [PATCH] Update cognitive load stack with full-stack load closure revision --- .../multi_domain_adaptive_cognitive_load.md | 793 ++++++++++++++++++ 1 file changed, 793 insertions(+) diff --git a/4-Infrastructure/shim/multi_domain_adaptive_cognitive_load.md b/4-Infrastructure/shim/multi_domain_adaptive_cognitive_load.md index 83fa6df9..9c7b7e8f 100644 --- a/4-Infrastructure/shim/multi_domain_adaptive_cognitive_load.md +++ b/4-Infrastructure/shim/multi_domain_adaptive_cognitive_load.md @@ -512,6 +512,799 @@ Individualized connectome-protective thresholds based on baseline cognitive capa ### 10. Dynamic Load Balancing Real-time shifting of cognitive load to emotional processing to prevent connectome damage. +## 2026-05-13 Full-Stack Load / Closure Revision + +This revision generalizes cognitive load from a domain response score into a boundary-and-receipt transition stack. The short intuition is: + +``` +attempting to force mountain-scale input through straw-scale assimilation +does not make the input disappear. + +It creates overflow pressure, shell stress, phase echo, residual burden, +and validation debt. +``` + +The model therefore treats load as a routed transition problem: + +``` +Boundary pressure enters; +shell sequence resists; +flux and torsion route; +Reynolds activation gates; +echoes remember; +residuals return; +receipts decide closure. +``` + +Native keeper: + +``` +No receipt, no law. No repair, no closure. +``` + +### Master Object + +``` +M_Full = + (A0, S, B, P_shell, G_T, BFTO, C16, RRTO, RRM, W, L, KOT, OECM, ECTRL) +``` + +where: +- `A0` = base admissibility layer / lawful state substrate +- `S` = typed spread network +- `B` = boundary-derived surface transform +- `P_shell` = sequential shell protection / collapse +- `G_T` = phase-coupled transport graph +- `BFTO` = boundary flux-torsion operator +- `C16` = 16-channel control manifold +- `RRTO` = Reynolds regime transition operator +- `RRM` = residual re-admission map +- `W` = state transition receipt +- `L` = loopback closure map +- `KOT` = kinetic operation receipt +- `OECM` = OmniToken entropy cost model +- `ECTRL` = extropy-compatible transition receipt layer + +Global evolution: + +``` +A0^t + -> S^t + -> B^t + -> P_shell^t + -> G_T^t + -> BFTO^t + -> RRTO^t + -> C16^t + -> RRM(epsilon^t) + -> A0^(t+1) +``` + +Closure: + +``` +A0^(t+1) ~ A0^t +``` + +Failure to close: + +``` +A0^(t+1) !~ A0^t + => new mode, quarantine, residual expansion, or model failure +``` + +### Micro-Position State + +Each local cell, node, or packet is: + +``` +m_i^t = (x_i, r_i, theta_i, q16_i, Gamma_i, s_i, g_i, Psi_i, W_i, epsilon_i) +``` + +where: +- `x_i` = position, address, coordinate, graph node, or chart point +- `r_i` = scale / refinement level +- `theta_i` = loopback phase +- `q16_i` = 16-channel controller vector +- `Gamma_i` = transition / reconstruction / braid packet +- `s_i` = shell-state vector +- `g_i` = delayed phase echo state +- `Psi_i` = local modal state +- `W_i` = transition receipt +- `epsilon_i` = residual burden + +Core local update: + +``` +m_i^(t+1) = + Gate_C16[ + Transport_G_T(m_i^t, Gamma_i, g_i) + + BFTO_i + + RRTO_i + + RRM(epsilon_i) + - SBPCM_i + ] +``` + +### Boundary-Derived Surface + +A boundary is a collapsed disagreement surface: + +``` +partial_Omega_i = + Collapse(sum_k c_ik lambda_ik psi_ik) +``` + +Boundary activation: + +``` +B_i = + |sum_k c_ik lambda_ik psi_ik| + + a_Phi Phi_i + + a_tau tau_i + + a_g g_i + + a_epsilon ||epsilon_i|| +``` + +Quiet boundary: + +``` +B_i < Theta_partial_i +``` + +Activated boundary: + +``` +B_i >= Theta_partial_i +``` + +Boundary activation event: + +``` +BAE_i = (partial_Omega_i, B_i, Theta_partial_i, q16_i, W_i) +``` + +Native phrase: + +``` +boundary = compressed disagreement made physical +``` + +### Corrected Reynolds / Hermite Activation Bridge + +This is the repaired monotone bridge. The normalized activation and the offset physical bridge must stay distinct. + +Reynolds coordinate: + +``` +Re_i = rho_i u_i L_i / mu_i +``` + +Transition coordinate: + +``` +x_i = Clamp_[0,1]((Re_i - 2300) / 1700) +``` + +so: + +``` +Re = 2300 => x = 0 +Re = 4000 => x = 1 +``` + +Normalized activation: + +``` +A(x) = 3x^2 - 2x^3 +``` + +Properties: + +``` +A(0) = 0 +A(1) = 1 +A'(x) = 6x(1 - x) +A'(0) = 0 +A'(1) = 0 +A'(x) >= 0 for 0 <= x <= 1 +``` + +Use `A(x)` as the controller activation curve. + +Offset physical bridge: + +``` +f_A(x) = f0 + (f1 - f0) A(x) +``` + +with: + +``` +f0 = 0.0278 +f1 = 0.0398 +``` + +therefore: + +``` +f_A(x) = 0.0278 + 0.012(3x^2 - 2x^3) +``` + +and: + +``` +f_A(0) = 0.0278 +f_A(1) = 0.0398 +``` + +Use `f_A(x)` only as the offset physical bridge, not as the normalized controller activation. + +### Modal Flow State + +Flow is not binary: + +``` +Psi_flow_i = alpha_L_i psi_L + alpha_T_i psi_T + alpha_U_i psi_U +``` + +with: + +``` +alpha_L_i + alpha_T_i + alpha_U_i = 1 +``` + +Simple allocation: + +``` +alpha_U_i = A(x_i) +alpha_L_i = 1 - A(x_i) +``` + +Optional transition participation: + +``` +alpha_T_i_raw = 4 x_i (1 - x_i) +``` + +If all three modes are active: + +``` +Z_i = alpha_L_i_raw + alpha_T_i_raw + alpha_U_i_raw +alpha_k_i = alpha_k_i_raw / Z_i +``` + +### RRTO Full Activation + +``` +gamma_i = + Clamp_[0,1]( + b0 A(x_i) + + b1 |omega_i| + + b2 Q_i + + b3 h_i + + b4 Phi_E_i + + b5 g_i + + b6 ||epsilon_i|| + ) +``` + +where: +- `A(x_i)` = smooth Reynolds transition activation +- `omega_i = curl(u_i)` = vorticity +- `Q_i` = Q-criterion / vortex criterion +- `h_i = u_i dot omega_i` = helicity +- `Phi_E_i` = local energy / flux activation +- `g_i` = delayed phase echo +- `epsilon_i` = residual burden + +``` +RRTO_i = + (Re_i, x_i, A(x_i), f_A(x_i), gamma_i, alpha_L_i, alpha_T_i, alpha_U_i) +``` + +### Sequential Boundary Protection / Collapse + +Generalized boundary pressure: + +``` +Pi_i = + a_E E_chem_i + + a_Phi Phi_partial_i + + a_sigma sigma_i + + a_sigmadot sigmadot_i + + a_grad |grad Pi_i| + + a_tau tau_i + + a_T T_i + + a_C C_i +``` + +Each shell state: + +``` +s_ij(t) in [0,1] +``` + +Total shell protection: + +``` +P_shell_i(t) = sum_j A_ij s_ij(t) +``` + +Shell dynamics: + +``` +ds_ij/dt = + alpha_ij sigma_k(Pi_i - Theta_ij_on)(1 - s_ij) + - beta_ij sigma_k(Pi_i - Theta_ij_fail)s_ij + + eta_ij RRM(epsilon_i) +``` + +with: + +``` +sigma_k(z) = 1 / (1 + exp(-kz)) +``` + +Safe discrete update: + +``` +s_ij^(t+1) = Clamp_[0,1](s_ij^t + Delta_t ds_ij/dt) +``` + +Static envelope: + +``` +P_shell_i(Pi) = + sum_j A_ij sigma_k(Pi_i - Theta_ij_on) + [1 - sigma_k(Pi_i - Theta_ij_fail)] +``` + +Native phrase: + +``` +boundary survives by admitting shell class before failure +``` + +### Boundary Flux-Torsion Operator + +Classical projected flux: + +``` +S_i = E_i x H_i +``` + +or: + +``` +S_i = (1 / mu_0) E_i x B_i +``` + +Boundary flux: + +``` +Phi_partial_i = integral_partial_Omega_i S dot n dA +``` + +Discrete: + +``` +Phi_partial_i ~= sum_(ell in partial_Omega_i) (S_ell dot n_ell) Delta_A_ell +``` + +Torsion: + +``` +tau_i = + b1 kappa_i + + b2 dGamma_i/dt + + b3 g_i + + b4 ||epsilon_i|| +``` + +Boundary flux-torsion operator: + +``` +BFTO16_i = Gate_C16[Phi_partial_i xor tau_i xor Gamma_i xor g_i xor epsilon_i] +``` + +Loopback phase: + +``` +theta_i^(t+1) = + theta_i^t + Omega(Phi_partial_i, tau_i, Gamma_i, g_i, epsilon_i) +``` + +### Delayed Phase Echo + +Complex form: + +``` +g_i(t) = sum_(j in N(i)) alpha_ij S_j(t - Delta_ij) exp(i phi_ij) +``` + +Real controller form: + +``` +g_i(t) = sum_(j in N(i)) alpha_ij cos(phi_ij) S_j(t - Delta_ij) +``` + +Echo edge: + +``` +e_ij_echo = (Delta_ij, phi_ij, alpha_ij, kappa_ij, epsilon_ij, W_ij) +``` + +Bounded echo: + +``` +sum_j |alpha_ij| <= A_max < 1 +Delta_ij <= Delta_max +N_echo <= N_max +``` + +Phase-coupled transport graph: + +``` +G_T = (V, E_transport, E_phase, E_echo, q, W, epsilon) +``` + +### Cutting / Collapse + +Complete cutting score: + +``` +K_partial_Omega_i = + Gate_C16[ + Norm(Pi_i) + + lambda1 Norm(Pi_dot_i) + + lambda2 Norm(|grad Pi_i|) + - Norm(K_mat_i) + - Norm(P_shell_i) + + lambda3 Norm(tau_i) + + lambda4 Norm(g_i) + + lambda5 Norm(epsilon_i) + ] +``` + +Cut: + +``` +K_partial_Omega_i > Theta_cut_i +``` + +Survival: + +``` +K_partial_Omega_i <= Theta_cut_i +``` + +Explosive branch: + +``` +dPi_i/dt > dP_shell_i/dt + K_rate_i +``` + +Native phrase: + +``` +explosive cut = outrun shell admission +``` + +Implosive branch: + +``` +|grad Pi_i| > |grad P_shell_i| + K_grad_i +``` + +Native phrase: + +``` +implosive cut = collapse shell geometry +``` + +Corrosive branch: + +``` +Pi_i > Theta_N_fail and s_iN -> 0 +``` + +Native phrase: + +``` +corrosive cut = exhaust shell sequence +``` + +Fatigue / pulsed branch: + +``` +D_i^(t+1) = + D_i^t + + zeta1 Norm(Pi_i) + + zeta2 Norm(g_i) + - zeta3 Norm(P_shell_i) +``` + +Failure: + +``` +D_i > D_max +``` + +Native phrase: + +``` +fatigue cut = echo-assisted residual accumulation +``` + +### Residual Re-Admission + +Prediction error: + +``` +epsilon_i = D_i - D_hat_i +``` + +Residual classifier: + +``` +r_i = Classify(epsilon_i, q16_i, W_i) +``` + +Residual re-admission: + +``` +RRM(epsilon_i) = + 0 if ||epsilon_i|| < Theta0 + compress if Theta0 <= ||epsilon_i|| < Theta1 + new mode if Theta1 <= ||epsilon_i|| < Theta2 + quarantine if ||epsilon_i|| >= Theta2 +``` + +Admissibility update: + +``` +A0^(t+1) = L(C16^t, RRM(epsilon^t), W^t) +``` + +Native phrase: + +``` +residual is pullback, not garbage +``` + +### 16-Channel Control Manifold + +``` +q16_i = [q0_i, q1_i, ..., q15_i] +``` + +Current integrated layout: + +| Channel | Meaning | +|---|---| +| `q0` | normalized boundary pressure `Norm(Pi)` | +| `q1` | pressure rate `Pi_dot` | +| `q2` | pressure gradient `Norm(|grad Pi|)` | +| `q3` | total shell protection `Norm(P_shell)` | +| `q4` | active shell occupancy / shell index | +| `q5` | material cohesion `Norm(K_mat)` | +| `q6` | boundary flux `Norm(Phi_partial)` | +| `q7` | torsion `Norm(tau)` | +| `q8` | delayed phase echo `Norm(g)` | +| `q9` | residual burden `Norm(||epsilon||)` | +| `q10` | normalized Reynolds activation `A(x)` | +| `q11` | offset physical bridge `f_A(x)` | +| `q12` | entropy reduction `Delta_S_minus` | +| `q13` | entropy generated / cost `Delta_S_plus` | +| `q14` | witness confidence `W` | +| `q15` | final admissibility / halt / loopback gate | + +Controller update: + +``` +q16_i^(t+1) = + Clamp_Q0.16( + q16_i^t + + F_q[ + Norm(Pi), + Pi_dot, + grad Pi, + Norm(P_shell), + Norm(Phi_partial), + Norm(tau), + Norm(g), + Norm(epsilon), + A(x), + f_A(x), + W + ] + ) +``` + +Gate output: + +``` +G_i = Gate_q16(m_i) + in {ADMIT, REFINE, MERGE, BRAID, PATCH, QUARANTINE, HALT, LOOPBACK} +``` + +### Kinetic Operation Receipt + +Every accepted transition emits: + +``` +KOT_i = + (m_i, m_i+1, Delta_S_i_minus, Delta_S_i_plus, + E_i, C_i, T_i, B_i, epsilon_i, W_i, DAG_i) +``` + +Validity: + +``` +KOT_i valid + iff W_i >= Theta_W + and B_i <= B_max + and ||epsilon_i|| <= epsilon_max +``` + +### OmniToken Entropy Cost Model + +``` +O_i = OECM(KOT_i) +``` + +Signed entropy-cost form: + +``` +O_i = + a Delta_S_i_minus + - b Delta_S_i_plus + - c E_i + - d C_i + - e T_i + - f ||epsilon_i|| + + g W_i +``` + +Interpretation: + +``` +useful transformation = entropy reduction - cost of achieving it +``` + +Claim aggregation: + +``` +O_claim = sum_i O_i +``` + +### Extropy-Compatible Transition Receipt Layer + +Transition receipt: + +``` +ECTRL(m_i -> m_i+1) = + (Delta_S_i, D_i, I_i, B_i, Falsify_i, Vc_i, DAG_i) +``` + +Acceptance: + +``` +Vc_i >= Theta_V +and Delta_S_i > 0 +and Falsify_i != empty +and DAG_i != empty +``` + +Extropy-native settlement: + +``` +XP_j = R_j F_j Delta_S_j (w_j dot E_j) (1 / T_s_j) +``` + +OmniToken-adapted settlement: + +``` +XP_j = R_j F_j O_claim (w_j dot E_j) (1 / T_s_j) +``` + +Goodhart isolation invariant: + +``` +Value(KOT_i) != f(actor reputation) +``` + +Reputation may route validators, but must not alter transition value. + +### Receipt / Attack-Repair Validation + +Complete state transition receipt: + +``` +STR_i = + (m_i, m_i+1, Norm(K_i), q16_i, s_i, g_i, + epsilon_i, W_i, KOT_i, DAG_i, A_i) +``` + +Attack / repair audit: + +``` +A_i = { + STR_units, + STR_shell_bounds, + STR_echo_safe, + STR_residual, + STR_smooth_activation, + STR_Goodhart, + STR_falsifiable +} +``` + +Justified transition: + +``` +m_i -> m_i+1 justified + iff every STR_a in A_i is PASS +``` + +Failed receipt: + +``` +m_i -> m_i+1 = UNJUSTIFIED + => RRM(epsilon_i) or QUARANTINE +``` + +### Compressed Master Equation + +``` +m_i^(t+1) = + Gate_C16[ + Transport_G_T(m_i^t, Gamma_i, g_i) + + BFTO(Phi_partial_i, tau_i, Gamma_i, g_i, epsilon_i) + + RRTO(Re_i, A(x_i), f_A(x_i), Psi_flow_i) + + RRM(epsilon_i) + - SBPCM(Pi_i, s_i, Theta_i) + ] +``` + +with: + +``` +x_i = Clamp_[0,1]((Re_i - 2300) / 1700) +A(x_i) = 3x_i^2 - 2x_i^3 +f_A(x_i) = 0.0278 + 0.012 A(x_i) + +SBPCM = + K_mat_i + + sum_j A_ij s_ij(t) + - lambda1 Pi_dot_i + - lambda2 |grad Pi_i| + +KOT_i = + Receipt(m_i, m_i+1, Delta_S_minus, Delta_S_plus, + E, C, T, B, epsilon, W, DAG) + +O_i = + a Delta_S_i_minus + - b Delta_S_i_plus + - c E_i + - d C_i + - e T_i + - f ||epsilon_i|| + + g W_i + +A0^(t+1) = L(C16^t, RRM(epsilon^t), {STR_i}) +``` + +Claim boundary: + +``` +This is a control / compression / transition-receipt model. +It is not a proven biological, fluid-mechanical, psychological, +or economic law without calibrated domain instruments and receipts. +``` + ## Implementation Requirements ### Data Collection