Research-Stack/6-Documentation/docs/MATH_MODEL_MAP_classified.tsv

1	#	Model_Name	Family	Equation	Variables	Purpose	Location	Implemented	Status	Cross_Refs	Domain_Type
2	1	Intrinsic_Load_LI	Cognitive Load	L_I(x) = -Σ_{b=0}^{255} p(b|x) log₂ p(b|x)	p(b|x) = empirical byte distribution	Shannon entropy of byte distribution; irreducible complexity	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	2,71,40	LAYER_A_COMPRESSION
3	2	Extraneous_Load_LE	Cognitive Load	L_E(x) = BPB(x,w_prior) - BPB*(x) = (1/n)Σ_i log₂(P_w*(x_i)/P_wprior(x_i))	BPB=bits-per-byte, w_prior=prior weights, w*=optimal	Cost of architectural mismatch; penalty for suboptimal routing	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	1,3,6,8	LAYER_A_COMPRESSION
4	3	Germane_Load_LG	Cognitive Load	L_G(x,t) = Σ_{s=1}^{S} γ^s · ΔL_E(x_s,t+1) ≈ τ·L_E·log(S+1)/log(S_max+1)	γ=temporal discount, τ=trust, S=engram support	Productive learning effort reducing future extraneous load	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	2,6,73	LAYER_B_ROUTING
5	4	Routing_Load_LR	Cognitive Load	L_R(x) = Σ_j c_j·1[f_j computed] + Σ_{l=1}^{D(x)} log₂|M_l|	d=9 feature dims, c_j=feature cost, D=tree depth, M_l=candidates	Computational cost of classification and method selection	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	6,16-23	LAYER_B_ROUTING
6	5	Memory_Load_LM	Cognitive Load	L_M(x) = log₂|E| + α·1[hit] + β + λ·|E|/|E_max|	|E|=engram store size, α/β=retrieval/update costs, λ=eviction pressure	Burden of storing, retrieving, and updating routing memory	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	6,10,30	LAYER_B_ROUTING
7	6	Total_Cognitive_Load	Cognitive Load	L_total = λI·l̂I + λE·l̂E - λG·l̂G + λR·l̂R + λM·l̂M (Σλ=1, λG≤λE)	5 normalized load components with weighting coefficients	Aggregate processing burden; combines all load classes	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	1,2,3,4,5,7,8,9,74	LAYER_A_COMPRESSION
8	7	Cognitive_Efficiency	Cognitive Load	η(x) = l̂I(x) / (l̂I + l̂E + l̂R + l̂M + ε)	Ratio of intrinsic to total normalized load	Routing efficiency (1=perfect, 0=maximum waste)	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	6	LAYER_A_COMPRESSION
9	8	Regret_Adjusted_Load	Cognitive Load	L_ρ(x) = L_total(x) · (1 + ρ(x)/ρ_max)	ρ=BPB regret, ρ_max=max regret	Load penalized by historical performance on similar inputs	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	2,6	LAYER_A_COMPRESSION
10	9	Basin_Conditional_Load	Cognitive Load	L(x|B) = L_I(x) + L_E(x|B) + L_R^B(x)	w_B=basin-optimal weights	Load conditioned on attractor basin membership	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	1,2,4,12	LAYER_A_COMPRESSION
11	10	MoE_Predictor_Distribution	Cognitive Load	P_w(x_i|x_{<i}) = Σ_{j=1}^{k} w_j · P_{m_j}(x_i|x_{<i})	k=predictors, w∈Δ^{k-1} simplex	Combines multiple compression predictors into mixed distribution	core/intrinsic/specs/COGNITIVE_LOAD_FUNCTIONS_SPEC.md	Python	✅	1,2	LAYER_A_COMPRESSION
12	11	Pressure_Piling	KDA Physics	P(i) = P₀ · χ^i (χ ≈ 1.63)	P₀=1.0 GPa, i=shock iteration, χ=Dodecahedral Piling Gain	Sequential shock pressure amplification via Mach stem focusing	core/intrinsic/formalisms/9_KDA_Equation_Manifest.md	Documented	✅	12,15	LAYER_E_VERIFICATION
13	12	Hugoniot_Temperature	KDA Physics	T_peak = T₀ · (P_peak/P₀)^0.65	T₀=293.15K, γ≈1.66, exponent=0.65	Non-isentropic temperature jump across shock fronts; predicts ~13,446K	core/intrinsic/formalisms/9_KDA_Equation_Manifest.md	Documented	✅	11,14,51	LAYER_G_ENERGY
14	13	Pressure_Ionization	KDA Physics	α(P) = 1 - exp(-k(P - P_MIT))	P_MIT≈138-155 GPa, k=rate constant	Insulator-to-metal transition via electronic band overlap	core/intrinsic/formalisms/9_KDA_Equation_Manifest.md	Documented	✅	15	LAYER_G_ENERGY
15	14	Energy_Recovery_Efficiency	KDA Physics	η_net = (W_rec - W_erasure) / W_in; W_erasure ≥ k_B·T·ln2 per bit	k_B=Boltzmann, T=T_peak=13,446K	Maxwell's Demon energy recovery after erasure cost	core/intrinsic/formalisms/9_KDA_Equation_Manifest.md	Documented	✅	12,54,55	LAYER_E_VERIFICATION
16	15	Q_Factor	KDA Physics	Q = (E_flash + E_enthalpy + E_recovered - W_demon) / (E_work + E_loss) > 1.0	Target Q≈1.05	Global energy balance; net gain threshold	core/intrinsic/formalisms/9_KDA_Equation_Manifest.md	Documented	✅	11,12,13,14	LAYER_E_VERIFICATION
17	17	Rotational_Alignment	GWL Rotation	g = cos(Δθ·2π/16) · cos(Δφ·π/8) · (1 - 2|χ_i - χ_j|)	θ∈{0..15}, φ∈{0..7}, χ∈{0,1}	Frame orientation compatibility	docs/gwl/GWL_ROTATIONAL_COUPLING_AND_LOCAL_INTERACTION_LAW_V1.md	Rust	✅	16,25	LAYER_C_TOPOLOGY
18	18	Spatial_Proximity	GWL Rotation	h = exp(-|Δp|²/(2σ²)) · 1_{|Δp|<r_max}	σ=coupling length, r_max=coupling radius	Distance decay function	docs/gwl/GWL_ROTATIONAL_COUPLING_AND_LOCAL_INTERACTION_LAW_V1.md	Rust	✅	16,25	LAYER_C_TOPOLOGY
19	19	Interaction_Force	GWL Rotation	F_ij = w_ij · (a_j - a_i) · Δp_ij / |Δp_ij|	a=activation, Δp=position delta	Activation flow between neighbors	docs/gwl/GWL_ROTATIONAL_COUPLING_AND_LOCAL_INTERACTION_LAW_V1.md	Rust	✅	16,20,21,22	LAYER_H_ALGEBRA
20	20	Energy_Function	GWL Rotation	E(f) = -½ Σ_{i,j} w_ij · a_i · a_j + Σ_i V(a_i)	V(a)=potential (e.g., λa⁴)	Frame field energy landscape	docs/gwl/GWL_ROTATIONAL_COUPLING_AND_LOCAL_INTERACTION_LAW_V1.md	Rust	✅	19,21,22,23	LAYER_G_ENERGY
21	21	Frame_Evolution_Discrete	GWL Rotation	θ_i(t+1) = θ_i(t) + α_θ·F_{i,θ} + ξ_θ	α=learning rate, ξ=noise	Discrete-time state update	docs/gwl/GWL_ROTATIONAL_COUPLING_AND_LOCAL_INTERACTION_LAW_V1.md	Rust	✅	19,22	LAYER_H_ALGEBRA
22	22	Frame_Evolution_Continuous	GWL Rotation	df_i/dt = -α ∇_{f_i} E(f) + ξ(t)	α=step size, ξ(t)=Langevin noise	Continuous dynamics; gradient descent on energy	docs/gwl/GWL_ROTATIONAL_COUPLING_AND_LOCAL_INTERACTION_LAW_V1.md	Rust	✅	20,21,23	LAYER_H_ALGEBRA
23	23	Energy_Monotonicity_Theorem	GWL Rotation	dE/dt = -α Σ_i |∇_{f_i} E|² ≤ 0	—	Proves energy decreases monotonically; convergence guarantee	docs/gwl/GWL_ROTATIONAL_COUPLING_AND_LOCAL_INTERACTION_LAW_V1.md	Rust	✅	20,22	LAYER_H_ALGEBRA
24	24	Temporal_Weight	GWL Temporal	w_ij^(τ) = cos(2π(τ_j - τ_i)/16)	τ∈{0..15} (4 bits)	Temporal phase coupling strength	docs/gwl/GWL_TEMPORAL_DIMENSION_AND_T_VARIABLE_FORMALISM_V1.md	Documented	✅	16,25,26	LAYER_F_CONTROL
25	25	Complete_Weight_5Factor	GWL Temporal	w_ij = cos(Δθ·22.5°)·cos(Δφ·22.5°)·cos(2πΔτ/16)·(1-2|Δχ|)·exp(-|Δp|²/2σ²)	θ,φ,τ,χ,Δp combined	Full spatial+temporal+rotational+chiral+proximity coupling	docs/gwl/GWL_TEMPORAL_DIMENSION_AND_T_VARIABLE_FORMALISM_V1.md	Documented	✅	16,17,18,24,26	LAYER_C_TOPOLOGY
26	26	Temporal_Force	GWL Temporal	F_ij^(τ) = w_ij^(τ) · (a_j - a_i) · sgn(τ_j - τ_i)	—	Information flow from past to future	docs/gwl/GWL_TEMPORAL_DIMENSION_AND_T_VARIABLE_FORMALISM_V1.md	Documented	✅	24,25,27	LAYER_F_CONTROL
27	27	Temporal_Evolution	GWL Temporal	τ_i(t+1) = τ_i(t) + α_τ·F_{i,τ} + ω₀	ω₀=intrinsic temporal frequency	Temporal phase evolution with intrinsic oscillator	docs/gwl/GWL_TEMPORAL_DIMENSION_AND_T_VARIABLE_FORMALISM_V1.md	Documented	✅	26,28	LAYER_F_CONTROL
28	28	Temporal_Stability	GWL Temporal	d/dt(τ_j - τ_i) = 0 for all i,j	—	Locked temporal attractor condition	docs/gwl/GWL_TEMPORAL_DIMENSION_AND_T_VARIABLE_FORMALISM_V1.md	Documented	✅	27,29	LAYER_D_INVARIANTS
29	29	Temporal_Entropy	GWL Temporal	H_τ = -Σ_{k=0}^{15} p(τ=k) log₂ p(τ=k)	0≤H_τ≤4 bits	Measure of temporal disorder (0=synchronized, 4=max)	docs/gwl/GWL_TEMPORAL_DIMENSION_AND_T_VARIABLE_FORMALISM_V1.md	Documented	✅	28	LAYER_F_CONTROL
30	30	Mu_Seed_Cardinality	GWL State Space	|S_μ| = 8×8×16×16×8×8×2×16×8×4 = 8,589,934,592 ≈ 2^33	10 independent fields	Complete enumeration of local mu-seed configuration space	docs/gwl/GWL_TOTAL_STATE_SPACE_AND_CARDINALITY_LEDGER_V1.md	Documented	✅	31,32	LAYER_D_INVARIANTS
31	31	Fractal_Occupancy	GWL State Space	|P_occ| = ρ_occ · N^{d_H} (d_H ≈ 2.7268)	N=64 → |P_occ|≈84,000 vs 262,144 raw	Effective addressable positions in Menger sponge lattice	docs/gwl/GWL_TOTAL_STATE_SPACE_AND_CARDINALITY_LEDGER_V1.md	Documented	✅	30,32,49	LAYER_D_INVARIANTS
32	32	Total_Formal_State_Space	GWL State Space	|S_total| ≈ 2^{5,900,000}	μ-seed: 2,772,000 bits + edges: 2,016,000 + rotation: 924,000 + boot: 8,000 + registers: 133,000	Upper bound on all possible GWPL configurations	docs/gwl/GWL_TOTAL_STATE_SPACE_AND_CARDINALITY_LEDGER_V1.md	Documented	✅	30,31,33,5	LAYER_B_ROUTING
33	33	Reachable_State_Space	GWL State Space	|S_reachable| ≈ |S_total| / 10^{29}	Constraints: geometric 10^6, convergence 10^{12}, energy 10^3, chirality 10^2, TTM 10^6	State space satisfying all physical and computational constraints	docs/gwl/GWL_TOTAL_STATE_SPACE_AND_CARDINALITY_LEDGER_V1.md	Documented	✅	32,59	LAYER_A_COMPRESSION
34	34	Wave_Packet_State	GWL Throat	P = (ΔV, Δt, π, τ, χ, C, A)	7-tuple: volume, time, rotation, temporal, chirality, confidence, activation	Complete state of computational packet traversing throat	docs/gwl/GWL_WAVE_PACKET_THROAT_ARCHITECTURE_V1.md	Documented	✅	35,36	LAYER_C_TOPOLOGY
35	35	Throat_Condition	GWL Throat	T_throat = {(i,j) | Φ_topo(i,j) >> Φ_metric(i,j)}	topological adjacency >> metric distance	Defines non-local transport corridor	docs/gwl/GWL_WAVE_PACKET_THROAT_ARCHITECTURE_V1.md	Documented	✅	34,36,37	LAYER_C_BRAID
36	36	Multi_Factor_Coupling_Weight	GWL Throat	w_ij = w_p · w_π · w_τ · w_χ · w_topo · w_σ	6 coupling factors (spatial, rotational, temporal, chirality, topological, stress)	Comprehensive coupling evaluation during packet propagation	docs/gwl/GWL_WAVE_PACKET_THROAT_ARCHITECTURE_V1.md	Documented	✅	25,34,35	LAYER_C_BRAID
37	37	Holonomy_Accumulation	GWL Throat	Hol(γ_loop) = ∮_γ T(p) dp	T(p)=torsion tensor, γ=closed loop	Phase accumulated when transporting vector around closed loop	docs/gwl/GWL_WAVE_PACKET_THROAT_ARCHITECTURE_V1.md	Documented	✅	38,78	LAYER_C_BRAID
38	38	Non_Euclidean_Distance	GWL Throat	d_N = path_length(γ_ij) + curvature_penalty(κ) + torsion_cost(T); d_T = d_E + λ_N·d_N	Euclidean + topological combined	Topology-aware distance for routing through multi-manifold structures	docs/gwl/GWL_MANIFOLD_INTERSECTION_JOIN_AND_TOPOLOGICAL_ADDRESSING_V1.md	Documented	✅	37,63	LAYER_C_TOPOLOGY
39	39	Trixal_Axes	Thermodynamic	TrixalAxes = (thermal, work, irreversibility), each ∈ [0,1]; |axes| = √(th² + w² + ir²)	3D thermodynamic phase space	Phase space coordinates for process tracking	core/gwl-vm/src/thermo/mod.rs	Rust	✅	40,42,50	LAYER_G_ENERGY
40	40	Shannon_Entropy	Thermodynamic	H = -Σ_b p(b) log₂ p(b), where p(b)=count(b)/len	Byte distribution, H ∈ [0,8] bits/byte	Information content measurement	core/gwl-vm/src/thermo/entropy_engine.rs	Rust	✅	1,39,41,42,43	LAYER_G_ENERGY
41	41	Kolmogorov_Estimate	Thermodynamic	K_est = (8 - H) / 8	From Shannon entropy	Rough estimate of structure via compressibility	core/gwl-vm/src/thermo/entropy_engine.rs	Rust	✅	40,42	LAYER_G_ENERGY
42	42	Thermodynamic_Entropy	Thermodynamic	S_thermo = H + K_est · 0.1	Shannon + Kolmogorov contribution	Combined information thermodynamics	core/gwl-vm/src/thermo/entropy_engine.rs	Rust	✅	40,41,43,55	LAYER_G_ENERGY
43	43	Entropy_Gradient	Thermodynamic	dS/dt = (S_current - S_previous) / Δt	Time derivative	Tracks rate of entropy change over time	core/gwl-vm/src/thermo/entropy_engine.rs	Rust	✅	42,55	LAYER_H_ALGEBRA
44	44	Mutual_Information_Extracted	Thermodynamic	MI = H_initial - H_current	Difference in Shannon entropy	Work performed by compression; information extracted	core/gwl-vm/src/thermo/entropy_engine.rs	Rust	✅	40,71	LAYER_A_COMPRESSION
45	45	Carnot_Efficiency	Thermodynamic	η_Carnot = 1 - T_cold / T_hot	Absolute temperatures	Maximum theoretical thermodynamic efficiency	core/gwl-vm/src/thermo/mod.rs	Rust	✅	46,51,54	LAYER_B_ROUTING
46	46	Work_Extraction	Thermodynamic	W_actual = Q_absorbed · η_Carnot · 0.7	70% of Carnot limit	Model computation as thermodynamic work extraction cycle	core/gwl-vm/src/thermo/heat_engine.rs	Rust	✅	45,55	LAYER_C_TOPOLOGY
47	47	Irreversibility_Metric	Thermodynamic	score = (entropy_production + path_asymmetry + time_reversal_violation) / 3	Three irreversibility components	Quantifies thermodynamic irreversibility of process trajectory	core/gwl-vm/src/thermo/process_shape.rs	Rust	✅	48,49	LAYER_G_ENERGY
48	48	Thermodynamic_Length	Thermodynamic	L_thermo = Σ_i distance_i · (1 + irreversibility_i)	Weighted by dissipation	Dissipative trajectory length accounting for thermodynamic cost	core/gwl-vm/src/thermo/process_shape.rs	Rust	✅	47,49	LAYER_B_ROUTING
49	49	Thermodynamic_Depth	Thermodynamic	depth = entropy_production · ln(time_steps)	Combined dissipation × trajectory length	Complexity measure	core/gwl-vm/src/thermo/mod.rs	Rust	✅	31,47,48	LAYER_F_CONTROL
50	50	Stamp_Code	Thermodynamic	SHA256(axes || traj_hash || hardware_entropy || timing_jitter || process_nonce)	Cryptographic hash of thermodynamic state	Unique non-reproducible process fingerprint	core/gwl-vm/src/thermo/trixalating_stamp.rs	Rust	✅	39,42	LAYER_B_ROUTING
51	51	Arrhenius_Temperature_Factor	Informatic Stress	AF = exp(E_a / (k_B · T))	E_a=activation energy (eV), k_B=8.617e-5 eV/K	Failure rate temperature acceleration	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	12,45,52,59	LAYER_G_ENERGY
52	52	Blacks_Equation_EM	Informatic Stress	EM_risk = J^n · exp(E_a / (k_B · T)) / 10^{12}	J=current density, n=exponent (2.0)	Electromigration failure risk	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	51,59	LAYER_G_ENERGY
53	53	Coffin_Manson_Fatigue	Informatic Stress	CM_damage = (ΔT / ΔT_threshold)^m · 10^{-8}, m≈1.9	Solder/interconnect fatigue exponent	Accumulates damage from thermal cycling	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	56,59	LAYER_G_ENERGY
54	54	Landauer_Limit	Informatic Stress	W_erasure ≥ k_B · T · ln(2) ≈ 2.87e-21 J/bit at 300K	Minimum energy per bit erased	Thermodynamic lower bound on computation	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	14,45,55	LAYER_A_COMPRESSION
55	55	Entropy_Generation_Rate	Informatic Stress	dS/dt = power_dissipation / (k_B · T · ln 2) [bits/s]	Power dissipation rate	Rate of entropy generation from computational dissipation	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	14,42,43,46,54	LAYER_E_VERIFICATION
56	56	BitFlip_Gradient_5D	Informatic Stress	|G| = (D1/120 + D2/5000 + D3/1000 + D4/100 + D5/5000) / 5	D1=T_ambient, D2=V_jitter(nV), D3=φ_leak(μA), D4=ε_SEU(Hz), D5=dt_clock(ppm)	Normalized 5D hardware stress gradient	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	53,57,59	LAYER_D_INVARIANTS
57	57	SEU_BitFlip_Rate	Informatic Stress	BFR = ε_SEU · 2^{(T-25)/10} · (1 + V_jitter/1000) · 3600 [flips/hr]	SEU rate, temperature, voltage jitter	Estimated bit-flips per hour from hardware conditions	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	56,59	LAYER_G_ENERGY
58	58	Stress_Decay	Informatic Stress	stress(t) = stress_0 · e^{-t/300} + intensity · (1 - e^{-t/300})	5-minute half-life	Stress accumulation with exponential decay	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	59	LAYER_G_ENERGY
59	59	Remaining_Useful_Life	Informatic Stress	RUL = MTBF / (AF · (1 + fatigue·0.01 + thermal_fatigue·0.1))	MTBF=10^9/FIT_rate, AF=acceleration factor	Hardware lifetime prediction under current stress	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	33,51,52,53,56,57,58	LAYER_G_ENERGY
60	60	Homeostatic_Stress_Injection	Informatic Stress	surprise = -ln(margin), margin = 1 - stress_magnitude; regret = max(0, stress - 0.5)	Optimal stress ≈ 0.5	Converts stress margin to surprise/regret for homeostatic controller	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	58,73	LAYER_E_VERIFICATION
61	61	Exact_Int_to_FP_Cast	Informatic Stress	int_bits ≤ fp_mantissa_bits + 1 (signed) or ≤ fp_mantissa_bits + 1 (unsigned)	fp_mantissa=23 (f32) or 52 (f64)	Proves safe integer-to-floating-point conversion	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	62,63	LAYER_D_INVARIANTS
62	62	Safe_Narrowing_Proof	Informatic Stress	can_safely_narrow(src_bits, signed, dst_mantissa) → bool	Delegates to exact cast check	Proves double→single precision narrowing is safe	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	61,63	LAYER_D_INVARIANTS
63	63	RISCV_Instruction_Latency	Informatic Stress	fdiv.d=33, fdiv.s=19 → penalty=0.737; fadd.d=4, fadd.s=4 → penalty=0.0	SiFive P550 measurements	Per-instruction latency for dispatch scoring	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	61,62	LAYER_D_INVARIANTS
64	64	Photon_Energy	QCL Energy	E = hc/λ = 1.2398 / λ_μm [eV]	λ in μm	Wavelength-to-energy conversion	core/gwl-vm/src/thermo/qcl_energy_model.rs	Rust+Python	✅	65,70	LAYER_G_ENERGY
65	65	Subband_Spacing	QCL Energy	ΔE = E_upper - E_lower; E_upper=hc/λ_min, E_lower=hc/λ_max	QCL emission range [λ_min, λ_max]	Energy difference between subbands in conduction band	core/gwl-vm/src/thermo/qcl_energy_model.rs	Rust+Python	✅	64,66,67	LAYER_G_ENERGY
66	66	Cascade_Gain	QCL Energy	G = photons_per_e⁻ × n_wells; photons_per_e⁻ = ⌊E_electron / ΔE⌋	E_electron=1.0 eV, n_wells=50	Total photon amplification per cascading electron	core/gwl-vm/src/thermo/qcl_energy_model.rs	Rust+Python	✅	65,67,68	LAYER_G_ENERGY
67	67	Temperature_Tuning	QCL Energy	λ(T) = λ₀ + α · (T - T₀); α=5e-6 /K (GaAs/AlGaAs)	dλ/dT ≈ 0.3 nm/K	Wavelength shift due to thermal expansion of quantum wells	core/gwl-vm/src/thermo/qcl_energy_model.rs	Rust+Python	✅	12,64,68	LAYER_G_ENERGY
68	68	Injection_Efficiency	QCL Energy	η = (0.5 + window_bonus) · spacing_eff · (1 - stress_penalty); clamped to [0,1]	window_bonus=0.3 if in atmospheric window	Dispatch efficiency at given stress level	core/gwl-vm/src/thermo/qcl_energy_model.rs	Rust+Python	✅	65,66,67,69	LAYER_G_ENERGY
69	69	Atmospheric_Windows	QCL Energy	Windows: (3,5), (8,12), (16,20) μm; transmission=1.0 inside, exp(-dist·0.5) outside	MWIR, LWIR, Far-IR bands	Lossless carrier propagation bands	core/gwl-vm/src/thermo/qcl_energy_model.rs	Rust+Python	✅	68,70	LAYER_G_ENERGY
70	70	Tuning_Range	QCL Energy	ν = 10⁴/λ [cm⁻¹]; DFB: ±7.5 cm⁻¹, EC: ±200 cm⁻¹; λ_min=10⁴/ν_max, λ_max=10⁴/ν_min	Center wavelength, tuning mode	Spectral tuning capability	core/gwl-vm/src/thermo/qcl_energy_model.rs	Rust+Python	✅	64,69	LAYER_G_ENERGY
71	71	Mutual_Information_Signal	MI Signal	MI(x) = baseline_bpb(x) - actual_bpb(x)	Bits-per-byte difference	Measures structural density in data	core/intrinsic/formalisms/ene_mi_signal.py	Python	✅	1,2,44,72,73	LAYER_A_COMPRESSION
72	72	kNN_MI_Prediction	MI Signal	MI_pred = Σ_i (w_i · MI_i · S_i) / Σ_i (w_i · S_i); w_i = 1/(d_i + ε)	k-nearest neighbors in feature space	Local MI estimation from similar inputs	core/intrinsic/formalisms/ene_mi_signal.py	Python	✅	71,73,74	LAYER_B_ROUTING
73	73	Surprise_Metric	MI Signal	surprise = log(1 + |MI_actual - MI_predicted|)	Log-scaled absolute difference	Learning trigger; prevents blowup	core/intrinsic/formalisms/ene_mi_signal.py	Python	✅	71,72,60	LAYER_B_ROUTING
74	74	Structure_Yield	MI Signal	ρ(x) = MI(x) / (cost(x) + ε)	Information per compute cost	ROI of computation; high MI + low cost = valuable	core/intrinsic/formalisms/ene_mi_signal.py	Python	✅	6,71,72	LAYER_A_COMPRESSION
75	75	Weighted_Feature_Distance	MI Signal	d(z₁,z₂) = √Σ_i w_i · ((z₁_i - z₂_i) / s_i)²	9-dim feature vector, learned weights, online scales	Scale-normalized weighted distance in MI feature space	core/intrinsic/formalisms/ene_mi_signal.py	Python	✅	4,72	LAYER_B_ROUTING
76	76	DAG_Force_Equilibrium	DAG Force	Σ F_in = Σ F_out at every node	Discrete analogue of ∇·σ = 0	Structural synthesis force balance	core/PTOS_FRAMEWORK/PAPER/paper.tex	TeX	✅	77,78	LAYER_C_BRAID
77	77	Constitutive_Law	DAG Force	σ = C : ε; ε = ½(∇u + ∇u^T)	C=stiffness tensor, u=displacement	Stress-strain relationship; linear elasticity	core/PTOS_FRAMEWORK/PAPER/paper.tex	TeX	✅	76	LAYER_C_BRAID
78	78	DAG_Global_Validity	DAG Force	V(G) = ∧_{v∈V} (ΣF_in = ΣF_out)	Universal quantification over all nodes	DAG constraint closure; proof by induction	core/PTOS_FRAMEWORK/PAPER/paper.tex	TeX	✅	37,76,77	LAYER_C_BRAID
79	79	Cosine_Similarity	Bracket Braid	cos = x · x_ref / (‖x‖ · ‖x_ref‖)	Dot product of normalized vectors	Reference solution alignment	audit/benchmarks/benchmark_bracket_braid_sb.py	Python	✅	80	LAYER_K_SIGNAL
80	80	Gradient_Alignment	Bracket Braid	alignment = ∇g_i · ∇g_j / (‖∇g_i‖ · ‖∇g_j‖)	Cosine of gradient angle	Gradient coherence between brackets	audit/benchmarks/benchmark_bracket_braid_sb.py	Python	✅	79,81	LAYER_K_SIGNAL
81	81	Phase_Accumulation	Bracket Braid	phase += Σ y · dx	Work integral along trajectory	Cumulative phase along computational path	audit/benchmarks/benchmark_bracket_braid_sb.py	Python	✅	37,80	LAYER_K_SIGNAL
82	82	Metric_Tensor_From_Circumferences	GWL Riemannian Geometry	g_tt = M², g_tp = 0, g_pp = (N·cos(θ))²; a=C_eq/(2π), c=C_mer/(2π), f=(a-c)/a, e²=2f-f², N=a/√(1-e²sin²θ), M=a(1-e²)/(1-e²sin²θ)^(3/2)	C_eq=equatorial circumference, C_mer=meridional circumference, θ=latitude	Derive metric tensor from measured circumferences (oblate spheroid)	core/lean/geoweird/GWLKernel.lean	Lean	✅	83,84,87	LAYER_C_TOPOLOGY
83	83	Line_Element	GWL Riemannian Geometry	ds² = g_tt·dθ² + 2·g_tp·dθ·dφ + g_pp·dφ²	g_ij=metric tensor, dθ/dφ=differentials	Compute infinitesimal distance on 2D Riemannian surface	core/lean/geoweird/GWLKernel.lean	Lean	✅	82	LAYER_C_TOPOLOGY
84	84	Christoffel_Symbols_2D	GWL Connection	Gamma^k_ij = ½·g^kl·(∂_i g_jl + ∂_j g_il - ∂_l g_ij)	g=metric, gInv=inverse metric, dg=metric derivatives	Connection coefficients for geodesic integration	core/lean/geoweird/GWLKernel.lean	Lean	✅	82,85	LAYER_C_TOPOLOGY
85	85	Geodesic_Step_Symplectic_Euler	GWL Geodesic Integration	a^θ = -(Gamma^θ_tt·v_θ² + 2·Gamma^θ_tp·v_θ·v_φ + Gamma^θ_pp·v_φ²); v' = v + a·dt; x' = x + v'·dt	position=(θ,φ), velocity=(v_θ,v_φ), Gamma=Christoffel, dt=step	Single-step geodesic integration (symplectic Euler)	core/lean/geoweird/GWLKernel.lean	Lean	✅	83,84	LAYER_C_TOPOLOGY
86	86	Stereographic_Chart_Transition	GWL Coordinate Charts	u = 2·tan(θ/2)·cos(φ), v = 2·tan(θ/2)·sin(φ); θ = 2·atan(√(u²+v²)/2), φ = atan2(v,u); select when |cos(θ)| < 0.01	theta, phi, u, v	Avoid pole singularities via adaptive coordinate chart	core/lean/geoweird/GWL_Integrated.lean	Lean	✅	85	LAYER_C_TOPOLOGY
87	88	BLINK_GATE_Ternary_Clock	GWL Ternary State	φ = (τ mod T)/T, T=942/1000; ternary: φ<1/3→Q, φ<2/3→A, else L; φ' = (φ+1/4) mod 1 if surprise>threshold	τ=time, surprise, threshold, T=0.942s	Ternary clock action with phase modulation	core/lean/geoweird/GWLKernel.lean	Lean	✅	90	LAYER_C_TOPOLOGY
88	89	Geodesic_Step_Verlet	GWL Geodesic Integration (Integrated)	Same acceleration as M85 + Verlet velocity update + chart transition check	integratorMethod∈{SymplecticEuler,Verlet,AdaptiveVerlet}	Real geodesic integration with pole singularity handling	core/lean/geoweird/GWL_Integrated.lean	Lean	✅	84,85,86	LAYER_C_TOPOLOGY
89	90	Waveprobe_Risk_Function	Waveprobe Control	risk(s) = (1 + γ·(1-cos(θ)))/d² + η·h; γ=3, η=0.8	d=distance, θ=torsion angle, h=heat	Combined risk metric for hysteretic control	core/lean/geoweird/WaveprobeKernel.lean	Lean	✅	91,92	LAYER_F_CONTROL
90	91	Waveprobe_Heat_Evolution	Waveprobe Control	h' = α·h + β·a; α=0.95, β=0.2	h=heat, a=excitation value (E1=1,E2=2,E3=3,E4=4)	Heat accumulation with exponential decay	core/lean/geoweird/WaveprobeKernel.lean	Lean	✅	90	LAYER_F_CONTROL
91	92	Waveprobe_Mode_Hysteresis	Waveprobe Control	locked→caution if risk<B_recover=2; caution→locked if risk≥B_lock=5; normal→caution if risk≥B_warn=3	B_recover=2, B_warn=3, B_lock=5	Hysteretic mode transitions with risk barriers	core/lean/geoweird/WaveprobeKernel.lean	Lean	✅	90	LAYER_F_CONTROL
92	94	Universe_Collision_Consensus	Emergence System	canCollide: dim_a==dim_b AND type_a!=type_b; strength=min(vol_a,vol_b)/vol_intersection; invariant: κ_a·κ_b>0→SphereLike, <0→HyperbolicLike	two universes with manifolds, types, axioms	Compute intersection of computational universes for witness generation	core/lean/geoweird/EmergenceSystem.lean	Lean	✅	93	LAYER_E_VERIFICATION
93	95	Shannon_Type_Entropy_Swarm	Swarm Coordination	H = -Σ(p_i·log₂(p_i)) where p_i=w_i/Σw; confidence update: reinforced=min(conf+0.1,1.0), decayed=conf·0.95	learned types, weights, confidence threshold=0.8	Measure uncertainty in agent's universe type assignment	core/lean/geoweird/SwarmCoordination.lean	Lean	✅	94	LAYER_B_ROUTING
94	96	Mean_Curvature_From_Constraints	Constraint Geometry	kappa = (cyclicRatio - treeRatio)·2.0; range [-2,2]	cyclicRatio=count(Cyclic)/total, treeRatio=count(Hierarchical)/total	Estimate curvature from constraint topology	core/lean/geoweird/ConstraintGeometry.lean	Lean	✅	97	LAYER_C_TOPOLOGY
95	97	Universe_Type_Scoring	Constraint Geometry	scoreEuclidean=flatness+translation+noTime+linearGrowth; scoreHyperbolic=negativeCurve+exponential+treeLike; scoreSpherical=positiveCurve+compact+rotation; scoreLorentzian=time+causal+mixedMetric; each capped at 1.0	constraint features (curvature, symmetry, causality, etc.)	Score how well each universe type fits domain constraints	core/lean/geoweird/ConstraintGeometry.lean	Lean	✅	96	LAYER_C_TOPOLOGY
96	98	Homeostatic_Pressure_Dynamics	Homeostatic Control	s_t = α·surprise_t + β·regret_t; p_{t+1} = γ·p_t + s_t; surprise=-log(P_actual); regret=max(0,log(P_optimal)-log(P_actual))	p=pressure, λ=canal width, s=stress, γ=decay∈(0,1), α,β weights	Pressure-driven exploration-exploitation control	docs/HOMEOSTATIC_CONTROL_SPEC.tex	LaTeX	✅	99,100	LAYER_B_ROUTING
97	99	Canal_Deformation	Homeostatic Control	λ_t = λ₀·(σ + (1-σ)·e^{-ξ·p_t}); λ_t ∈ [λ₀·σ, λ₀]	λ₀=base canal width, σ∈(0,1)=min fraction, ξ=sensitivity	Adaptive selectivity controlled by pressure	docs/HOMEOSTATIC_CONTROL_SPEC.tex	LaTeX	✅	98	LAYER_B_ROUTING
98	100	Decision_Reweighting_Homeostatic	Homeostatic Control	score_t = log(P_expected) - λ_t·s_t	λ_t from canal deformation, s_t=stress	Reduce penalty on high-stress paths when pressure rises	docs/HOMEOSTATIC_CONTROL_SPEC.tex	LaTeX	✅	98,99	LAYER_B_ROUTING
99	101	Homeostatic_Equilibrium	Homeostatic Control	(1-γ)·p* = s(p*); stability: |γ + s'(p*)| < 1	p*=fixed point, γ=decay, s'=stress derivative	Stability condition for homeostatic fixed point	docs/HOMEOSTATIC_CONTROL_SPEC.tex	LaTeX	✅	98	LAYER_B_ROUTING
100	102	Hutter_Shape_Equation	Information Theory	H(W) = H₀ - I_local - I_structural - I_semantic - I_syntactic - I_cross; H₀=8.0, H(W)≈0.92 bpb (115 MB); I(W)=ΣI_k≈7.08 bpb	H₀=uniform baseline (8 bpb), I_k=mutual information wedges per layer	Hierarchical entropy decomposition for compression	docs/geometry/HUTTER_SHAPE_EQUATION.md	Documented	✅	103	LAYER_A_COMPRESSION
101	103	Hutter_Manifold_Deformation	Information Theory	Δ_t = M_{t+1} - M_t; v(x,t) = Φ_{t+1}(x) - Φ_t(x); H(x,t)=‖v(x,t)‖²; ε=½(∇v+(∇v)^T)	M_t=manifold state at release t, Φ_t=embedding, v=velocity, ε=strain	Model Hutter corpus evolution as tensor field deformation	docs/roadmap/HUTTER_MANIFOLD_DYNAMICS.md	Documented	✅	102,104	LAYER_J_DYNAMICS
102	104	SHA256_Field_Equations	Information Theory	Δ_manifold = μ_{t+1} - μ_t; ΔΣ = Σ_{t+1} - Σ_t; SHA256(μ_t‖Σ_t) → chain_hash; chunk_residual = f - μ_t	μ_t=manifold mean, Σ_t=covariance, f=chunk feature	Track Wikipedia knowledge evolution as hash-chained manifold deltas	docs/roadmap/SHA256_FIELD_EQUATIONS.md	Documented	✅	102,103	LAYER_J_DYNAMICS
103	105	Dyson_Swarm_Geodesic_Equation	Dyson Swarm Geodesics	d²x^μ/dτ² + Gamma^μ_νλ(dx^ν/dτ)(dx^λ/dτ) = η^μ(τ); <η^μ(τ)η^ν(τ')> = 2D·δ^μν·δ(τ-τ')	x^μ=position in data space, Q=QUBO matrix, Gamma=Christoffel, η=thermal noise	Model carrier state waves as geodesics on QUBO-derived data manifold	docs/geometry/DYSON_SWARM_GEODESIC_EQUATIONS_2026-04-09.md	Documented	✅	84,85,106	LAYER_C_TOPOLOGY
104	106	Metric_From_QUBO_Hessian	Dyson Swarm Geodesics	g_μν(x) = δ_μν + α·∂²E/∂x^μ∂x^ν = δ_μν + α·Q_μν	Q=QUBO matrix, α=scaling, δ=Kronecker delta	Define Riemannian metric from QUBO energy landscape	docs/geometry/DYSON_SWARM_GEODESIC_EQUATIONS_2026-04-09.md	Documented	✅	105	LAYER_C_TOPOLOGY
105	107	Langevin_Geodesic_Damping	Dyson Swarm Geodesics	d²x^μ/dτ² + Gamma^μ_νλ(dx^ν/dτ)(dx^λ/dτ) = -γ(dx^μ/dτ) + √(2D)·ξ^μ(τ)	γ=damping coefficient, D=diffusion, ξ=Gaussian white noise	Damped stochastic geodesic with thermal friction	docs/geometry/DYSON_SWARM_GEODESIC_EQUATIONS_2026-04-09.md	Documented	✅	105	LAYER_C_TOPOLOGY
106	108	Alcubierre_Information_Metric	Virtual Alcubierre	dI² = -dτ² + (dH - β·dτ)²; β = v_eff·f·Ω; v_eff = v_local/(1-φ)	τ=proper time, H=entropy, β=shift vector, φ=foam score, Ω=opcode coupling	Information-theoretic model for search acceleration via negative curvature	docs/geometry/Virtual_Alcubierre_Information_Metric_Proof.md	Documented	✅	83,98	LAYER_G_ENERGY
107	110	Ray_Casting_Braid_Step	Braid Topology	R(s) = G_new + s·d⃗; collision: ‖R(s) - P_j‖ < T; D_topo = ∫_L σ(s)·P(s) ds	G_new=new point, d⃗=direction, P_j=existing peak, T=threshold, σ=coherence, P=purity	Geometric parent selection for Merkle braiding via raycasting	docs/formal_spec/RAYCAST_MMR_BRAID_TOPOLOGY.md	Documented	✅	111,112	LAYER_C_BRAID
108	111	Fast_Inverse_Square_Root	Braid Topology	0x5f3759df bit-hack for 1/d calculation; DIAT constraint: y_inv·y_sqrt ≈ C² where C=2^{16}	k=index, y_inv=1/√k, y_sqrt=√k, 16.16 fixed-point	Near-constant-time intersection calculation	docs/formal_spec/THETA_TAN_RAYCAST_AMMR.md	Documented	✅	110	LAYER_C_BRAID
109	112	UVMAP_Projection	Braid Topology	32-bit packed texel: (v<<16)|u; U-axis: distance-based albedo (t×1000); V-axis: spectral frequency index (k from DIAT)	t=distance, k=frequency index	Encode raycast intersections for stochastic UV map rendering	docs/formal_spec/THETA_TAN_RAYCAST_AMMR.md	Documented	✅	110	LAYER_C_BRAID
110	113	Boltzmann_Transport_Equation_ThetaTaN	Theta-TaN Phonon Physics	κ_ph^{αβ} = (1/V)·Σ_{pq} C_V(pq)·v_{pq}^α·F_{pq}^β; C_V(pq)=ℏω·∂n₀/∂T; v_{pq}^α=∂ω/∂q_α	C_V=mode heat capacity, v=phonon group velocity, F=mean free displacement	Model lattice thermal conductivity in θ-phase TaN via phonon BTE	docs/formal_spec/THETA_TAN_RAYCAST_AMMR.md	Documented	✅	114	LAYER_G_ENERGY
111	114	Phonon_Scattering_Matrix	Theta-TaN Phonon Physics	τ_{pq}^{-1} = τ_{3ph}^{-1} + τ_{4ph}^{-1} + τ_{ph-iso}^{-1} + τ_{ph-el}^{-1}	3-phonon, 4-phonon, isotope, electron-phonon scattering channels	Total phonon scattering rate as sum of independent channels	docs/formal_spec/THETA_TAN_RAYCAST_AMMR.md	Documented	✅	113	LAYER_G_ENERGY
112	115	Tensor_Field_QUBO	Non-Euclidean UV QUBO	F_u = -stress_xx·du - stress_xy·dv, F_v = -stress_yx·du - stress_yy·dv; wave = amplitude·e^{-dist·0.1}·cos(phase+dist); spin_i = 1 if wave>0 else 0	tensor=[stress_xx,stress_xy,stress_yx,stress_yy] per grid point	Map QUBO to tensor field with wave-like carrier propagation	audit/benchmarks/benchmark_tensor_carrier.rs	Rust	✅	116,117	LAYER_C_TOPOLOGY
113	116	Non_Euclidean_UV_Distance	Non-Euclidean UV QUBO	Hyperbolic (Poincare): d = acosh(1 + 2·|p1-p2|²/((1-|p1|²)(1-|p2|²))); Spherical: d = acos(dot(p1,p2)); energy uses non-Euclidean distance	UV points, geometry type∈{Euclidean,Hyperbolic,Spherical}	Map QUBO to non-Euclidean surface where frustration=curvature	audit/benchmarks/benchmark_non_euclidean_uv.rs	Rust	✅	15,115	LAYER_C_TOPOLOGY
114	117	PGA_Cl301_NFold_Mechanics	Geometric Algebra	16D algebra: scalar(1)+vector(4)+bivector(6)+trivector(4)+pseudoscalar(1); B_i=I·e_i; SE(3) motor: M=R+ε(½·t·R); CFA: h_i^{l+1}=h_i^l+Σ_j M_{ij}^l·h_j^l·M_{ji}^l	PGA multivectors, motors, curvature κ, torsion τ	Unified framework for protein structures using projective geometric algebra	docs/geometry/GEOMETRIC_FIRST_LANGUAGE_Protein_NFold_Mechanics.md	Documented	✅	84,96,105	LAYER_H_ALGEBRA
115	118	Sine_Gordon_Equation	Geometric Algebra	d²θ/dt² - c²·d²θ/ds² + (m²c⁴/ℏ²)·sin(θ) = 0	θ=phase, c=wave speed, m=mass, ℏ=reduced Planck constant	Soliton dynamics in protein backbone	docs/geometry/GEOMETRIC_FIRST_LANGUAGE_Protein_NFold_Mechanics.md	Documented	✅	117	LAYER_H_ALGEBRA
116	119	Curvature_Torsion_Coupling_NFold	Geometric Algebra	κ_n = f(κ_{n-1}, τ_{n-1}, S_n), τ_n = g(κ_n, τ_{n-1}, S_n); Γ^λ_{μν} = {Levi-Civita}^λ_{μν} + K^λ_{μν} (contortion)	κ=curvature, τ=torsion, S_n=substrate properties, K=contortion tensor	Curvature-torsion coupling in N-fold mechanics	docs/geometry/GEOMETRIC_FIRST_LANGUAGE_Protein_NFold_Mechanics.md	Documented	✅	117	LAYER_H_ALGEBRA
117	120	Hormone_Half_Life_to_Decay_Rate	Hormone Derivation	remaining = 2^{-t_sec/(T_half_min·60)}; decay_rate = 1 - remaining; Ebbinghaus: R(t) = e^{-t/S} where S = T_half/ln(2)	T_half=biological half-life (min), pulse_interval_sec=10.0	Convert biological half-life to computational decay rate	lab/hormone_derivation.py	Python	✅	98,59	LAYER_B_ROUTING
118	121	Logit_Z_Normalization	Hormone Derivation	logit(x) = log(x/(1-x)); z = (logit(x) - mean_logit) / std_logit	x∈[0,1], mean_logit, std_logit from calibration	Transform bounded concentration to z-score	lab/hormone_derivation.py	Python	✅	120	LAYER_B_ROUTING
119	123	Voxel_Key_Encoding	Heerich Voxel	key = ((x+512)&0x3FF)<<20 | ((y+512)&0x3FF)<<10 | ((z+512)&0x3FF); inverse: decode bit fields; range [-512,511] per axis, 30-bit	x,y,z integers	Fast 30-bit integer address for n-space positions	tools/heerich_model.py	Python	✅	124	LAYER_I_ENCODING
120	124	Microvoxel_Seed_4Byte_Encoding	Microvoxel Seed	32-bit: delta_p[9:0]|region[13:10]|gamma[18:14]|activation[22:19]|polarity[26:23]|confidence[30:27]|flag[31]; switch: eff<0.8→EXCLUDE, <1.2→EXPLORE, ≥1.2→PROMOTE	delta_p, region, gamma, activation, polarity, confidence	Compressed self-evolving program via ternary switch encoding	lab/microvoxel_seed_self_evolving_encoder.py	Python	✅	1,123	LAYER_I_ENCODING
121	125	DCVN_Verification_Invariant_Survival	DCVN Verification	4 invariants: completeness(c), consistency(s), freshness(f), provenance(p); survival mask: bit set if value≥threshold; participation: 4→FULL(1.0), ≥2→PARTIAL(0.5), ≥1→OBSERVER(0.1), 0→ABSENT(0.0); variance=var([c,s,f,p])/4	c,s,f,p∈[0,1], thresholds	Graduated participation based on invariant health in verification swarm	lab/consensus_net/verification_core.py	Python	✅	10,11	LAYER_E_VERIFICATION
122	126	Watanabe_Total_Correlation	Tensor Field Analysis	TC = ΣH(X_i) - H(X_1,...,X_n); KSG estimator for MI; Kolmogorov: len(compressed)/len(original); formula complexity: 0.4·kolmogorov + 0.4·entropy/8 + 0.2·CV	feature vectors, variant formulas, Hutter submission data	Rigorous tensor field analysis of Hutter variants	lab/hutter/tensor_field_analysis_rigorous.py	Python	✅	102,103	LAYER_A_COMPRESSION
123	127	Relation_Sieve_5_Symbol	Cache Sieve	pack 5 2-bit symbols into 10-bit: sig=(T<<8)|(D<<6)|(C<<4)|(A<<2)|R; torsion: value<t0→00,<t1→01,<t2→10,else 11; coherence inverted: ≥c2→00,≥c1→01,≥c0→10,else 11; classify: REJECT if T=11,A=11,C=11,(T≥10&C≥10),(D=11&A≥10),(R=11&C≥10); HOLD if any=10 or C∈{01,10}; else PASS	T=torsion, D=drift, C=coherence, A=angular momentum, R=radius	Structural classification of cache manifolds into PASS/HOLD/REJECT	tools/cache_sieve_exploration.py	Python	✅	115,128	LAYER_D_INVARIANTS
124	128	Proxy_Extraction_From_Manifold	Cache Sieve	torsion = Σ|τ_i|(i<32)·100; drift = |φ_corr|·255; coherence = 255-torsion; angmom from geometry plugin; radius = |radius-1.0|·255	τ=torsion gradient samples, φ_corr=correlation	Manifold features to discrete scalars	tools/cache_sieve_exploration.py	Python	✅	127	LAYER_D_INVARIANTS
125	129	SEISMIC_Shell_Detection	Topological Encoder	0.35 ≤ φ_corr < 0.47; PHI-offset retry: φ_offset = φ_corr·PHI mod 1.0; SHA256 pattern hash: phi_weighted_profile[i]=τ_i·PHI^{-i/100}; hash=SHA256(φ_corr:path_length:Σphi_weighted_profile); orientation=(φ_corr·PHI) mod 2π	φ_corr, τ=torsion, PHI=golden ratio	Detect SEISMIC torsion shells for "The Wall" construction	tools/topological_encoder.py	Python	✅	19,37	LAYER_I_ENCODING
126	130	Half_Mobius_Closure_Integral	Topological Encoder	∮τ·ds = π; solve: accumulated = Σ(τ_i·step_size); return path_length s when accumulated ≥ π	τ=torsion gradient samples, step_size, φ_corr=correlation	Half-twist closure condition for topologically stable wall	tools/topological_encoder.py	Python	✅	41,129	LAYER_C_BRAID
127	131	Regret_Field_Blink_Cycle	KDA Control	R_magnitude = surprise·(predicted_bpb - actual_bpb)/actual_bpb; blink_duration = baseline_ms + (regret_ms - baseline_ms)·R_magnitude ∈ [500ms,700ms]; decay: R *= e^{-λ·dt}, λ=2.0	surprise, predicted/actual bpb, blink baseline/regret, decay lambda	Adaptive blink cycle control via regret field magnitude	lab/CONCEPT_STAGE/2_KDA_Control_Kernel_Source.py	Python	✅	88,90,25	LAYER_F_CONTROL
128	132	Hugoniot_Shock_Physics	KDA Control	Rankine-Hugoniot relations: T-P relationship for shock compression; transient vs equilibrium temperature; E_kinetic = ½·I·ω² (plasma flywheel); E_harvested = E_stored·efficiency	Pressure(GPa), temperature(K), moment of inertia, RPM	Thermodynamic state computation for plasma substrate	lab/CONCEPT_STAGE/2_KDA_Control_Kernel_Source.py	Python	✅	25,98	LAYER_F_CONTROL
129	133	Waveprobe_Binning_Functions	Waveprobe Control	binDistance: d<0.5→near(0), d<1→mid(1), else far(2); binTorsion: |sin(θ)|<1/3→aligned(0), <2/3→skewed(1), else twisted(2); binHeat: h<2→cool(0), h<5→warm(1), else hot(2)	d=distance, θ=torsion angle, h=heat	3-category binning for LUT policy indexing	core/lean/geoweird/WaveprobeKernel.lean	Lean	✅	90	LAYER_F_CONTROL
130	134	Waveprobe_LUT_Policy	Waveprobe Control	baseLUT: 3×3×3 lookup mapping (distBin,torsionBin,heatBin)→Excitation; applyMode: normal=pass, caution=cap E2, locked=force E1; nextMode: hysteretic transitions by risk vs B_recover/B_warn/B_lock	3 bins × 3 bins × 3 bins = 27 entries	Base control policy with mode override	core/lean/geoweird/WaveprobeKernel.lean	Lean	✅	90,133	LAYER_F_CONTROL
131	135	Parallel_Transport_Writhe	Non-Euclidean Geometry	project to oblique 2D: (x+z·cos(π/4)·0.5, y+z·cos(π/4)·0.5); deltas=consecutive differences; wr = Σ(ax·by - ay·bx)/(n-1)	history of nd_points, window W=16, dox=doy=cos(π/4)·0.5	Parallel-transport writhe in curved PCA manifold	tools/geometry_noneuclidean.py	Python	✅	35,51	LAYER_C_TOPOLOGY
132	136	NE_Path_Validation	Geometry Verifier	PHI-weighted distance: d = √(Σ w_i·(a_i-b_i)²) where w_i=PHI^{-i}; metric continuity: max_jump>5.0→fail; writhe bound: |writhe|>2.0→fail; parallel transport: |sim-prev_sim|>1.5→instability	14D concept vectors, PHI weights, path points	Validate paths through non-Euclidean concept space	tools/geometry_verifier.py	Python	✅	37,51,135	LAYER_C_TOPOLOGY
133	137	Hormone_Concentration_Normalization	Hormone Derivation	normalized = (value - species_min)/(species_max - species_min); modulation = effect_size·(1 - CV_species); CV = std/mean across species	concentration values, species min/max, effect sizes, cross-species variance	Normalize biological concentrations to computational 0-1 range	lab/hormone_derivation.py	Python	✅	120	LAYER_B_ROUTING
134	138	Thermal_Finality_BEA	BEA Thermo Bridge	confidence = min(bea_confidence + avg_irreversibility/n, 1.0); time_to_reverse = exp(total_irreversibility·100); weight = work_done/(1+entropy)·(1-0.5·irreversibility)	bea_confidence, irreversibility array, work_done, entropy	Integrate thermodynamic process tracking with BEA consensus	core/gwl-vm/src/thermo/bea_thermo_bridge.rs	Rust	✅	21,11,27	LAYER_E_VERIFICATION
135	139	Entropy_Generation_Rate_Informatic	Informatic Stress	dS/dt = power_dissipation/(k_B·T·ln(2)) [bits/s]; k_B=8.617e-5 eV/K; LANDAUER_LIMIT_300K=2.87e-21 J/bit	power_dissipation, temperature, Boltzmann constant	Rate of entropy generation from computational dissipation	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	55,14,54	LAYER_G_ENERGY
136	140	Remaining_Useful_Life_Prediction	Informatic Stress	RUL = MTBF/(AF·(1+fatigue·0.01+thermal_fatigue·0.1)); MTBF=10^9/FIT_rate; AF=Arrhenius acceleration factor	MTBF, acceleration factor, fatigue, thermal fatigue	Hardware lifetime prediction under current stress	core/gwl-vm/src/thermo/informatic_stress.rs	Rust	✅	51,52,53,56,57,58	LAYER_G_ENERGY