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

1	#	Model_Name	Family	Equation	Variables	Purpose	Location	Implemented	Status	Cross_Refs	Domain_Type	Bind_Class
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	thermodynamic_bind
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	physical_bind
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	physical_bind
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	physical_bind
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	physical_bind
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	physical_bind
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	physical_bind
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	physical_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	unknown
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	geometric_bind
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	geometric_bind
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	control_bind
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	geometric_bind
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	control_bind
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	control_bind
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	control_bind
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	control_bind
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	control_bind
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	geometric_bind
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	geometric_bind
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	control_bind
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	control_bind
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	control_bind
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	control_bind
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	informational_bind
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	informational_bind
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	informational_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	physical_bind
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	physical_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	geometric_bind
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	control_bind
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	control_bind
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	geometric_bind
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	control_bind
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	control_bind
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	informational_bind
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	control_bind
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	control_bind
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	geometric_bind
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	geometric_bind
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	control_bind
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	control_bind
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	control_bind
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	control_bind
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	unknown
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	unknown
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	control_bind
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	unknown
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	thermodynamic_bind
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	thermodynamic_bind
137	141	PBACS_1bit_Transport	PBACS Signal	b_t = 1[v_t + e_{t-1} > θ_t]; e_t = v_t + e_{t-1} - b_t	v_t=input, e_t=error accumulator, θ_t=threshold	1-bit noise-shaped encoding with error feedback	docs/semantics/PBACS_CANONICAL_SIGNAL_ARCHITECTURE.md	Spec	✅	142,143,144,145	LAYER_K_SIGNAL	control_bind
138	142	PBACS_Phi_Traversal	PBACS Signal	Φ_{t+1} = Φ_t + 106070 (mod 2^32); idx = (Φ_t >> n) ⊕ MSB_flip	Φ=accumulator, 106070=φ·2^16, MSB=mirror bit	Deterministic φ-based scheduling for uniform coverage	docs/semantics/PBACS_CANONICAL_SIGNAL_ARCHITECTURE.md	Spec	✅	141,143	LAYER_F_CONTROL	control_bind
139	143	PBACS_Void_Mask_LUT	PBACS Signal	θ_t = LUT_void[idx]; attest = popcount(LUT[i] ∧ deviation)	LUT_void=8Kbit blue noise mask, idx=traversal index	Structured thresholding replaces arithmetic transforms	docs/semantics/PBACS_CANONICAL_SIGNAL_ARCHITECTURE.md	Spec	✅	141,142,145	LAYER_K_SIGNAL	control_bind
140	144	PBACS_SLUQ_Stress	PBACS Signal	a_{t+1} = a_t - (a_t >> 6) + α|e_t| + β|μ| + γ·attest	a=stress accumulator, e=residual, μ=density mismatch	Adaptive stress accumulation with decay	docs/semantics/PBACS_CANONICAL_SIGNAL_ARCHITECTURE.md	Spec	✅	141,146	LAYER_F_CONTROL	control_bind
141	145	PBACS_CMYK_Routing	PBACS Signal	s_t = a_t >> 14; π(s_t) ∈ {K,C,M,Y} for [0,1,2,3]	s=2-bit state, K=fast, C=monitor, M=verify, Y=prune	Policy-based adaptive routing with 4-state hysteresis	docs/semantics/PBACS_CANONICAL_SIGNAL_ARCHITECTURE.md	Spec	✅	144	LAYER_B_ROUTING	control_bind
142	146	PBACS_BracketedDIAT	PBACS Signal	ℬ = ⟨l,u,v,g_l,g_u⟩ with g_l + g_u = u - l	l,u=bounds, v=value, g=gap, scale	Constraint-preserving interval arithmetic with gap conservation	tools/lean/Semantics/Semantics/BracketedCalculus.lean	Lean	✅	141,147	LAYER_D_INVARIANTS	control_bind
143	147	PBACS_Unified_Update	PBACS Signal	X_{t+1} = F(X_t) where X = (Φ,e,a,s,b,ℬ)	Unified state vector with 8-step canonical loop	Complete PBACS signal transport with all 5 layers	docs/semantics/PBACS_CANONICAL_SIGNAL_ARCHITECTURE.md	Spec	✅	141,142,143,144,145,146	LAYER_F_CONTROL	control_bind
144	148	LUT_as_DSP	FPGA Signal	φ_corr = LUT_void[(Φ_acc >> n) ⊕ MSB_flip]	Φ_acc=32-bit accumulator, MSB_flip=mirror detection	LUT-based DSP replacing floating-point with table lookups	docs/semantics/LUT_AS_DSP_EQUATION.md	Spec	✅	142,149	LAYER_K_SIGNAL	control_bind
145	149	Mirror_LUT_Unified	FPGA Signal	ℳ*(q,s,t) = ⌊φ^{α·ℋ(q,s) + β·𝒯(t)}·2^n⌋ ⊕ ℱ(q)	q=query, s=state, t=time, ℋ=hash, ℱ=fold	Cross-domain mirror LUT unification	docs/semantics/MIRROR_LUT_EQUATIONS.md	Spec	✅	142,148	LAYER_K_SIGNAL	control_bind
146	150	Adaptive_1bit_CMYK	FPGA Signal	stress_t = α|e_t| + β|μ| + γ·popcount; s_t = a_t >> 14	1-bit encoder + CMYK stress routing merged	Adaptive 1-bit transport with stress-based state machine	docs/semantics/ADAPTIVE_1BIT_CMYK_MERGED.md	Spec	✅	141,145,147	LAYER_K_SIGNAL	control_bind
147	151	Extended_Cognitive_Load_v2	Cognitive Load	L_cog(x) = L_comp(x) + λ_D·E_dist(x); L_comp = λ_H·H(x) + λ_B·B(x) + λ_R·R(x); E_dist = μ_κ·Δκ(x) + μ_Θ·ΔΘ(x) + μ_Λ·ΔΛ(x) + μ_ρ·Δρ(x)	H=entropy, B=branching, R=recursion depth, Δκ=substrate mismatch, ΔΘ=temporal mismatch, ΔΛ=structural mismatch, Δρ=saturation imbalance	Pressure-adaptive cognitive load: complexity + distortion energy to maintain coherence	docs/semantics/PBACS_COGNITIVE_LOAD_REVISION.md	Spec	✅	6,7,8,152,153	LAYER_A_COMPRESSION	informational_bind
148	153	Release_Index_R	Manifold Dynamics	R(x) = E_dist(x) / (ρ_avail(x) + ε)	E_dist=distortion energy, ρ_avail=effective available resource flow, ε=small constant	Critical threshold: R<1 gradual adaptation, R≥1 discontinuous reconfiguration/throat/reset	docs/semantics/PBACS_COGNITIVE_LOAD_REVISION.md	Spec	✅	151,152	LAYER_F_CONTROL	control_bind
149	154	PBACS_Stress_v2	PBACS Signal	stress_t = α|e_t| + β|μ̂_t - μ*_t| + γ·attest_t + δ·Ê_dist(x_t)	e=residual, μ=density mismatch, attest=attestation, Ê_dist=stored manifold mismatch energy	Upgraded stress: reacts to signal AND stored manifold mismatch energy	docs/semantics/PBACS_COGNITIVE_LOAD_REVISION.md	Spec	✅	144,151,145	LAYER_F_CONTROL	control_bind
150	155	Cognitive_Load_Revised_Admissibility	Cognitive Load	L_cog(x) ≤ L_max ∧ R(x) < 1; violation modes: L>L_max→NoSurface, R≥1→Forced Transition/Throat/Reset	L_max=maximum load, R=release index, NoSurface/Throat=failure modes	Two-constraint admissibility: load AND release index must both be satisfied	docs/semantics/PBACS_COGNITIVE_LOAD_REVISION.md	Spec	✅	151,153	LAYER_E_VERIFICATION	control_bind
151	156	Normalized_Cognitive_Load_v2	Cognitive Load	L̂_cog(x) = λ_H·Ĥ(x) + λ_B·B̂(x) + λ_R·R̂(x) + λ_D·Ê_dist(x); Ê_dist = μ_κ·Δ̂κ + μ_Θ·Δ̂Θ + μ_Λ·Δ̂Λ + μ_ρ·Δ̂ρ	All components normalized [0,1], λ weights sum to 1	Operational normalized form for simulation and thresholding	docs/semantics/PBACS_COGNITIVE_LOAD_REVISION.md	Spec	✅	151	LAYER_A_COMPRESSION	informational_bind
152	157	Phonon_Graph_Force	Phonon Graph	F(i, j) = e^(-d/127) * cos(2πd/127); d = |i - j|	d=distance between positions, 127=φ⁷≈29.03→period, e^(-d/127)=damping	Damped oscillating force law holding engrams together; self-contained, 32 chars	docs/semantics/PHONON_GRAPH_EQUATION.md	Spec	✅	6,152	LAYER_K_SIGNAL	physical_bind
153	158	Phonon_Damage_Trace	Phonon Graph	DamagePattern(i) = F(i, i₀) ⊕ F(i, i₁) ⊕ ... ⊕ F(i, iₙ)	i₀...iₙ=reference positions, ⊕=XOR of force signatures	Junk DNA pattern: repeating phonon force signature attached to code sections	docs/semantics/PHONON_DAMAGE_TRACE.md	Spec	✅	157	LAYER_E_VERIFICATION	informational_bind
154	159	Phonon_Rederivation_Mechanism	Phonon Graph	HowDamaged = argmin_D ||ObservedPattern - ExpectedPattern(D)||; D ∈ {bit_flip, shift, truncation, swap}	D=damage type, ExpectedPattern(D)=phonon signature under damage model D	Post-hoc damage reconstruction: compare observed to expected under each damage model	docs/semantics/PHONON_REDERIVATION.md	Spec	✅	157,158	LAYER_E_VERIFICATION	control_bind
155	160	Emoji_Machine_Core	Emoji Machine	LUT[s] → (emit, next); next = emit; s,emit,next ∈ Unicode	LUT=lookup table, s=current state/codepoint, emit=output codepoint	Quine-like self-referential machine: output IS next state address	docs/semantics/EMOJI_MACHINE.md	Spec	⚠️	-	LAYER_K_SIGNAL	control_bind
156	161	Emoji_Machine_Bounded	Emoji Machine	LUT[s] → (emit, next); next = emit; s,emit,next ∈ Fin 65536 (BMP only)	LUT=64K entries, s=16-bit state index, emit=output codepoint	Finite version: restricted to Basic Multilingual Plane (16-bit)	docs/semantics/EMOJI_MACHINE.md	Spec	✅	160	LAYER_K_SIGNAL	control_bind
157	162	Emoji_Machine_Recovery_Claim	Emoji Machine	∀ positions p in trajectory T: LUT[p] must equal the unique successor in T	T=trajectory/cycle, p=position in state space, LUT[p]=required transition	Structural constraint: valid trajectories enforce their own consistency	docs/semantics/EMOJI_MACHINE.md	Spec	⚠️	160,161	LAYER_E_VERIFICATION	control_bind
158	163	Prime_Hash_Watermark	Combined System	Every P bits: embed prime π where π = HashToPrime(H(chunk)); H=SHA256, chunk=preceding P bits	P=period (≈127=φ⁷), π=prime encoding hash, chunk=bit segment	Periodic prime watermarks for integrity verification; primes encode hash of preceding stream	docs/semantics/PRIME_HASH_WATERMARK.md	Spec	⚠️	157,6	LAYER_E_VERIFICATION	control_bind
159	164	Cartesian_Map_Encoding	Encoding System	Symbol(s) → (x, y) ∈ Fin W × Fin H; W×H = 2^16 = 65536	s=symbol index, (x,y)=Cartesian coordinates, W=width, H=height	Fixed 2D grid replaces UTF-8: 16-bit address space, direct indexing, no parsing	docs/semantics/CARTESIAN_MAP_ENCODING.md	Spec	✅	160,161	LAYER_K_SIGNAL	control_bind
160	165	Unified_Cartesian_State_Machine	Cartesian System	(xₜ₊₁, yₜ₊₁) = LUT[xₜ, yₜ]; x,y ∈ Fin 256	LUT=64K entry table, (x,y)=current state, emit=next state	Self-contained state machine: output coordinate IS next address	docs/semantics/CARTESIAN_PHONON_PRIME_INTEGRATION.md	Spec	✅	164,152	LAYER_K_SIGNAL	control_bind
161	166	Cartesian_Manhattan_Distance	Cartesian System	d_M(cᵢ, cⱼ) = |xᵢ - xⱼ| + |yᵢ - yⱼ|	cᵢ,cⱼ=coordinates, d_M=Manhattan distance	Hardware-efficient distance: no multiply, no sqrt	docs/semantics/CARTESIAN_PHONON_PRIME_INTEGRATION.md	Spec	✅	157,165	LAYER_C_TOPOLOGY	geometric_bind
162	167	Cartesian_Phonon_Force_Law	Cartesian System	F(cᵢ,cⱼ) = e^(-d_M/127) * cos(2πd_M/127); d_M=|xᵢ-xⱼ|+|yᵢ-yⱼ|	d_M=Manhattan distance, 127=phonon period	Phonon correlation on 2D grid using Manhattan metric	docs/semantics/CARTESIAN_PHONON_PRIME_INTEGRATION.md	Spec	✅	157,166	LAYER_K_SIGNAL	physical_bind
163	168	Neighbor_Consensus_Recovery	Cartesian System	LUT_repaired[x,y] = mode{LUT[x±1,y], LUT[x,y±1]}	mode=majority vote, neighbors=4-connected (N,S,E,W)	Self-healing: repair damaged cell via neighbor consensus	docs/semantics/CARTESIAN_PHONON_PRIME_INTEGRATION.md	Spec	✅	165,167	LAYER_E_VERIFICATION	control_bind
164	169	Error_Dimension_Correction	Cartesian System	e = ErrorType × Magnitude; CorrectionSpace = (x, y, e) ∈ Fin 256 × Fin 256 × Fin N	e=error coordinate, N=error type space	Errors induce new dimensional axis; damage becomes navigable coordinate	docs/semantics/ERROR_DIMENSION_CORRECTION.md	Spec	⚠️	165,168	LAYER_E_VERIFICATION	control_bind
165	170	Original_Coordinate_Neighborhood_Recovery	Cartesian System	N(x,y) = {(x±1,y), (x,y±1), (x±1,y±1)}; Recovery: ∀n∈N(x,y), Verify(n) → Consensus(x,y)	(x,y)=original coordinate, N=8-connected neighborhood, Verify=attestation check	Use original coordinate to locate neighborhood; verify neighbors to recover damaged cell	docs/semantics/NEIGHBORHOOD_RECOVERY.md	Spec	✅	165,168	LAYER_E_VERIFICATION	control_bind
166	171	Waveprobe_Overlap_Energy_QUBO	Waveprobe QUBO	E(s) = ⟨ψ_past|P̂|ψ_past⟩ = |⟨ψ_curr|ψ_past⟩|²; P̂ = |ψ_curr⟩⟨ψ_curr|	|ψ⟩∈ℂⁿ state vector, P̂=projector, s=candidate state	Overlap energy between active engram state and past witness trace (QUBO objective)	docs/specs/waveprobe_qubo_spec.tex	Spec	✅	172,173,90	LAYER_F_CONTROL	control_bind
167	172	Waveprobe_QUBO_Matrix	Waveprobe QUBO	Q_ij = c̄_i · c_j; objective: maximize x†Qx over candidate states in search window W	c_i=complex coefficients of |ψ_curr⟩, x=candidate selection vector, W=search window	QUBO matrix form of local Waveprobe selection problem	docs/specs/waveprobe_qubo_spec.tex	Spec	✅	171	LAYER_F_CONTROL	control_bind
168	173	Waveprobe_Phase_Lock_Coherence	Waveprobe QUBO	φ(s,x) = w_e·φ_e + w_r·φ_r + w_d·φ_d; w_e=0.4, w_r=0.3, w_d=0.3	φ_e=normalized Shannon entropy, φ_r=byte repetition rate, φ_d=4-gram dictionary potential	Fused phase-lock coherence scalar governing Waveprobe overlap magnitude	docs/specs/waveprobe_qubo_spec.tex	Spec	✅	171,131	LAYER_F_CONTROL	informational_bind
169	174	Waveprobe_Bell_Bound	Waveprobe QUBO	|⟨O_AB⟩| ≤ 2; violations (>2) confirm non-classical selection advantage	O_AB=causal order observable between candidate arms A,B	Bell-like bound distinguishing classical matching from quantum-inspired Waveprobe selection	docs/specs/waveprobe_qubo_spec.tex	Spec	✅	171	LAYER_E_VERIFICATION	control_bind
170	175	Waveprobe_BPB_Conservation	Waveprobe QUBO	BPB(x, s_probe) ≤ BPB(x, s_local); injection admitted iff local bits-per-byte does not increase	BPB=bits-per-byte, s_probe=injected state, s_local=current local state	Information-conservative injection rule preventing spoiler termination of compression trace	docs/specs/waveprobe_qubo_spec.tex	Spec	✅	171,2	LAYER_D_INVARIANTS	informational_bind
171	554	Boltzmann_State_Weighting	State Weighting	P_i = e^{-\Delta G_i / RT} / \sum e^{-\Delta G_j / RT}	ΔG_i=relative energy, R=gas constant, T=temperature	Weighted average of multiple candidate states based on local stability/energy	tools/lean/Semantics/Semantics/Extensions/ManifoldBlit.lean	Documented	✅	141,412	LAYER_M_LEAN_SEMANTICS	state_bind
172	555	Rubric_as_Reward_RaR	Agent Logic	R(τ) = Σ w_j · f_judge(τ, r_j)	τ=agent trajectory, r_j=rubric criteria, w_j=weights	Training autonomous agents via semantic judge models and group relative policy optimization	infra/access_control/orchestrator.py	Documented	✅	6,10,412	LAYER_M_LEAN_SEMANTICS	agent_bind
173	556	Global_Metric_Learning_GML	Metric Learning	d_M^2(x_i,x_j) = (x_i-x_j)^T M (x_i-x_j)	M=PSD matrix, L=decomposition (M=L^TL), S=similar, R=triplets	Optimizing the distance metric directly on the PSD manifold to improve manifold-to-manifold mapping	core/field_solver_emulator.py	Documented	✅	38,75,412	LAYER_C_TOPOLOGY	metric_bind
174	557	Equation_Chain_YEC	Identity Logic	0 -> 1 -> X -> 1 -> 0	0=Balance, 1=Identity, X=Transformation	Structural lifecycle for mathematical reasoning and invariant verification	tools/lean/Semantics/Semantics/Quantization.lean	Documented	✅	532,412	LAYER_M_LEAN_SEMANTICS	logic_bind
175	558	Differential_Spectral_Correction_DSC	Signal Correction	xL' = xL + s · (xL - yL)	xL=current low-freq, yL=predicted clean low-freq, s=scaler	Correcting spectral bias and SNR-t drift in iterative reconstruction and signal transport	core/src/dsp_neuromorphic_translation.rs	Documented	✅	141,142,425	LAYER_K_SIGNAL	signal_bind
176	559	Autogenetic_Update_Rule	Agent Evolution	A_{t+1} = A_t + η ∇_A [M_t + Φ]	η=meta-learning rate, M_t=meta-objective, Φ=homeostasis	Mathematical framework for autonomous self-modification of agent protocols and logic	infra/access_control/orchestrator.py	Documented	✅	555,412,101	LAYER_F_CONTROL	agent_bind