Research-Stack/4-Infrastructure/shim/rrc_equation_classifier_table.csv

1	equation_id	name	rrc_shape	status	distance	top_axes	missing_or_weak_axes	source_path	domain_type	bind_class	equation
2	connectome_protective_cognitive_load_reweighting_receipt:core_equations:bandwidth_adjusted_threshold	bandwidth_adjusted_threshold	CognitiveLoadField	CANDIDATE	0.193428	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_threshold_hist = L_threshold_eff * exp(-rho_B * B_overflow)
3	connectome_protective_cognitive_load_reweighting_receipt:core_equations:bandwidth_overflow	bandwidth_overflow	CognitiveLoadField	HOLD	0.230737	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			B_overflow = max(0, transfer_bandwidth - assimilation_bandwidth) / assimilation_bandwidth
4	connectome_protective_cognitive_load_reweighting_receipt:core_equations:effective_cognitive_load	effective_cognitive_load	CognitiveLoadField	HOLD	0.231976	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_cog_eff = L_cog_raw * G_over
5	connectome_protective_cognitive_load_reweighting_receipt:core_equations:emotional_gate	emotional_gate	CognitiveLoadField	HOLD	0.229561	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			B_gate_emotional = exp(-gamma_emotional * DeltaE_emotional_hist / kT_emotional_hist)
6	connectome_protective_cognitive_load_reweighting_receipt:core_equations:emotional_load	emotional_load	CognitiveLoadField	CANDIDATE	0.21865	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_emotional = C_emotional,d * emotional_response_d(L_emotional_offload; theta_emotional,d) * lambda_phi^D_f * B_gate_emotional,d
7	connectome_protective_cognitive_load_reweighting_receipt:core_equations:emotional_offload	emotional_offload	CognitiveLoadField	CANDIDATE	0.193428	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_emotional_offload = max(0, L_cog_raw - L_threshold_hist) * eta_offload_hist
8	connectome_protective_cognitive_load_reweighting_receipt:core_equations:historical_emotional_barrier	historical_emotional_barrier	CognitiveLoadField	HOLD	0.230737	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			DeltaE_emotional_hist = DeltaE_emotional_eff + chi_B * B_overflow
9	connectome_protective_cognitive_load_reweighting_receipt:core_equations:historical_emotional_temperature	historical_emotional_temperature	CognitiveLoadField	HOLD	0.230141	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			kT_emotional_hist = kT_emotional_eff / (1 + psi_B * B_overflow)
10	connectome_protective_cognitive_load_reweighting_receipt:core_equations:historical_offload_efficiency	historical_offload_efficiency	CognitiveLoadField	HOLD	0.231349	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			eta_offload_hist = eta_offload_eff * exp(-omega_B * B_overflow)
11	connectome_protective_cognitive_load_reweighting_receipt:core_equations:overflow_gate	overflow_gate	CognitiveLoadField	CANDIDATE	0.192135	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			G_over(d) = 1 if L_cog_raw <= L_threshold_hist; else exp(-gamma_d * (L_cog_raw - L_threshold_hist) / kT_emotional_hist)
12	connectome_protective_cognitive_load_reweighting_receipt:core_equations:raw_cognitive_load	raw_cognitive_load	CognitiveLoadField	CANDIDATE	0.21865	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_cog_raw(d,x) = C_d * response_family_d(x; theta_d) * lambda_phi^D_f * B_gate(d,constraints)
13	connectome_protective_cognitive_load_reweighting_receipt:core_equations:residual_stress	residual_stress	CognitiveLoadField	CANDIDATE	0.200253	projection_declared;shape_closure;decoder_declared;witness_declared		4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_residual_stress = max(0, L_cog_raw - L_threshold_hist) * (1 - eta_offload_hist)
14	connectome_protective_cognitive_load_reweighting_receipt:core_equations:threshold	threshold	CognitiveLoadField	CANDIDATE	0.188871	projection_declared;shape_closure;witness_declared;scale_band_declared		4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_threshold = C_threshold * lambda_phi^D_f * B_gate_threshold
15	connectome_protective_cognitive_load_reweighting_receipt:core_equations:total_protective_load	total_protective_load	CognitiveLoadField	HOLD	0.238088	projection_declared;shape_closure;decoder_declared;witness_declared	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_total = L_cog_eff + L_emotional + L_residual_stress
16	connectome_protective_cognitive_load_reweighting_receipt:core_equations:trauma_adjusted_emotional_barrier	trauma_adjusted_emotional_barrier	CognitiveLoadField	HOLD	0.231349	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			DeltaE_emotional_eff = DeltaE_emotional + chi_T * T_trauma
17	connectome_protective_cognitive_load_reweighting_receipt:core_equations:trauma_adjusted_emotional_temperature	trauma_adjusted_emotional_temperature	CognitiveLoadField	HOLD	0.230737	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			kT_emotional_eff = kT_emotional / (1 + psi_T * T_trauma)
18	connectome_protective_cognitive_load_reweighting_receipt:core_equations:trauma_adjusted_offload_efficiency	trauma_adjusted_offload_efficiency	CognitiveLoadField	HOLD	0.231976	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			eta_offload_eff = eta_offload * exp(-omega_T * T_trauma)
19	connectome_protective_cognitive_load_reweighting_receipt:core_equations:trauma_adjusted_threshold	trauma_adjusted_threshold	CognitiveLoadField	CANDIDATE	0.194101	projection_declared;shape_closure;witness_declared;residual_risk		4-Infrastructure/shim/connectome_protective_cognitive_load_reweighting_receipt.json			L_threshold_eff = L_threshold * exp(-rho_T * T_trauma)
20	transfold_enwiki8_magnetic_domain_generator_receipt:transfold_map:core_equations	core_equations	SignalShapedRouteCompiler	CANDIDATE	0.172075	projection_declared;semantic_entropy;shape_closure;witness_declared		4-Infrastructure/shim/transfold_enwiki8_magnetic_domain_generator_receipt.json			{"heat_loss":"Q_i = max(0, L_info_i - L_threshold) * (1 - G_over_i)","magnetic_projection":"M_i = sigmoid(((chi_i H_i) + R_i - 0.5 C_loss_i) * G_over_i)","overflow_gate":"G_over_i = 1 if L_info_i <= L_threshold else exp(-1.25 * (L_info_i - L_threshold) / 0.9)","signal_load":"L_info_i = phi^D_f * (log(1 + 2 h_i) + MM(t_i;1,0.35) + (1 - r_i)^0.6)"}
21	transfold_enwiki8_magnetic_domain_generator_receipt:transfold_map:field_mapping	field_mapping	SignalShapedRouteCompiler	CANDIDATE	0.166855	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_enwiki8_magnetic_domain_generator_receipt.json			{"byte_transition_rate":"domain agitation / susceptibility driver","capacity_overflow":"hysteresis heat-loss channel","entropy":"field demand / information pressure","repeated_4grams":"remanence / memory channel"}
22	transfold_enwiki8_magnetic_domain_generator_receipt:transfold_map:source_domain	source_domain	SignalShapedRouteCompiler	CANDIDATE	0.188002	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_enwiki8_magnetic_domain_generator_receipt.json			byte_stream_signal
23	transfold_enwiki8_magnetic_domain_generator_receipt:transfold_map:target_domain	target_domain	SignalShapedRouteCompiler	CANDIDATE	0.188002	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_enwiki8_magnetic_domain_generator_receipt.json			magnetic_domain_equation
24	transfold_enwiki8_magnetic_domain_generator_receipt:transfold_core_equations:heat_loss	heat_loss	SignalShapedRouteCompiler	CANDIDATE	0.18598	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_enwiki8_magnetic_domain_generator_receipt.json			Q_i = max(0, L_info_i - L_threshold) * (1 - G_over_i)
25	transfold_enwiki8_magnetic_domain_generator_receipt:transfold_core_equations:magnetic_projection	magnetic_projection	SignalShapedRouteCompiler	CANDIDATE	0.18541	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_enwiki8_magnetic_domain_generator_receipt.json			M_i = sigmoid(((chi_i H_i) + R_i - 0.5 C_loss_i) * G_over_i)
26	transfold_enwiki8_magnetic_domain_generator_receipt:transfold_core_equations:overflow_gate	overflow_gate	CognitiveLoadField	CANDIDATE	0.197713	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/transfold_enwiki8_magnetic_domain_generator_receipt.json			G_over_i = 1 if L_info_i <= L_threshold else exp(-1.25 * (L_info_i - L_threshold) / 0.9)
27	transfold_enwiki8_magnetic_domain_generator_receipt:transfold_core_equations:signal_load	signal_load	CognitiveLoadField	CANDIDATE	0.191669	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/transfold_enwiki8_magnetic_domain_generator_receipt.json			L_info_i = phi^D_f * (log(1 + 2 h_i) + MM(t_i;1,0.35) + (1 - r_i)^0.6)
28	transfold_couch_data_magnetic_domain_receipt:transfold_map:core_equations	core_equations	SignalShapedRouteCompiler	CANDIDATE	0.172075	projection_declared;semantic_entropy;shape_closure;witness_declared		4-Infrastructure/shim/transfold_couch_data_magnetic_domain_receipt.json			{"heat_loss":"Q_i = max(0, L_info_i - L_threshold) * (1 - G_over_i)","magnetic_projection":"M_i = sigmoid(((chi_i H_i) + R_i - 0.5 C_loss_i) * G_over_i)","overflow_gate":"G_over_i = 1 if L_info_i <= L_threshold else exp(-1.25 * (L_info_i - L_threshold) / 0.9)","signal_load":"L_info_i = phi^D_f * (log(1 + 2 h_i) + MM(t_i;1,0.35) + (1 - r_i)^0.6)"}
29	transfold_couch_data_magnetic_domain_receipt:transfold_map:field_mapping	field_mapping	SignalShapedRouteCompiler	CANDIDATE	0.166855	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_couch_data_magnetic_domain_receipt.json			{"byte_transition_rate":"domain agitation / susceptibility driver","capacity_overflow":"hysteresis heat-loss channel","entropy":"field demand / information pressure","repeated_4grams":"remanence / memory channel"}
30	transfold_couch_data_magnetic_domain_receipt:transfold_map:source_domain	source_domain	SignalShapedRouteCompiler	CANDIDATE	0.188002	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_couch_data_magnetic_domain_receipt.json			byte_stream_signal
31	transfold_couch_data_magnetic_domain_receipt:transfold_map:target_domain	target_domain	SignalShapedRouteCompiler	CANDIDATE	0.188002	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_couch_data_magnetic_domain_receipt.json			magnetic_domain_equation
32	transfold_couch_data_magnetic_domain_receipt:transfold_core_equations:heat_loss	heat_loss	SignalShapedRouteCompiler	CANDIDATE	0.18598	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_couch_data_magnetic_domain_receipt.json			Q_i = max(0, L_info_i - L_threshold) * (1 - G_over_i)
33	transfold_couch_data_magnetic_domain_receipt:transfold_core_equations:magnetic_projection	magnetic_projection	SignalShapedRouteCompiler	CANDIDATE	0.18541	projection_declared;shape_closure;witness_declared;compression_pressure		4-Infrastructure/shim/transfold_couch_data_magnetic_domain_receipt.json			M_i = sigmoid(((chi_i H_i) + R_i - 0.5 C_loss_i) * G_over_i)
34	transfold_couch_data_magnetic_domain_receipt:transfold_core_equations:overflow_gate	overflow_gate	CognitiveLoadField	CANDIDATE	0.197713	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/transfold_couch_data_magnetic_domain_receipt.json			G_over_i = 1 if L_info_i <= L_threshold else exp(-1.25 * (L_info_i - L_threshold) / 0.9)
35	transfold_couch_data_magnetic_domain_receipt:transfold_core_equations:signal_load	signal_load	CognitiveLoadField	CANDIDATE	0.191669	projection_declared;shape_closure;witness_declared;semantic_entropy		4-Infrastructure/shim/transfold_couch_data_magnetic_domain_receipt.json			L_info_i = phi^D_f * (log(1 + 2 h_i) + MM(t_i;1,0.35) + (1 - r_i)^0.6)
36	hutter_equation_metastate_transfold_receipt:hutter_transfold_equations:counted_total	counted_total	SignalShapedRouteCompiler	HOLD	0.19942	projection_declared;compression_pressure;decoder_declared;shape_closure	scale_band_declared	4-Infrastructure/shim/hutter_equation_metastate_transfold_receipt.json			compressed_total_bytes = payload_bytes + residual_bytes + witness_bytes + decoder_delta_bytes + container_bytes
37	hutter_equation_metastate_transfold_receipt:hutter_transfold_equations:hard_target_rule	hard_target_rule	SignalShapedRouteCompiler	HOLD	0.216219	projection_declared;compression_pressure;shape_closure;decoder_declared	scale_band_declared	4-Infrastructure/shim/hutter_equation_metastate_transfold_receipt.json			Hutter-hard promotion additionally requires the total contest artifact for enwik9 to beat 109685197 bytes under the applicable prize rules
38	hutter_equation_metastate_transfold_receipt:hutter_transfold_equations:hutter_route_metastate	hutter_route_metastate	SignalShapedRouteCompiler	CANDIDATE	0.122715	projection_declared;compression_pressure;decoder_declared;witness_declared		4-Infrastructure/shim/hutter_equation_metastate_transfold_receipt.json			["source_corpus_id","source_bytes","candidate_chart","transform_route","payload_bytes","residual_bytes","witness_bytes","decoder_delta_bytes","container_bytes","runtime_budget","compressed_total_bytes","baseline_bytes","hard_target_bytes","ratio_schema","exact_decode_status","source_hash","decoded_hash","promotion_status","failure_code"]
39	hutter_equation_metastate_transfold_receipt:hutter_transfold_equations:lower_bound	lower_bound	SignalShapedRouteCompiler	HOLD	0.210115	projection_declared;compression_pressure;shape_closure;decoder_declared	scale_band_declared	4-Infrastructure/shim/hutter_equation_metastate_transfold_receipt.json			LB_route = payload_floor + residual_floor + witness_floor + decoder_delta_floor + container_floor + evaluator_cost_floor
40	hutter_equation_metastate_transfold_receipt:hutter_transfold_equations:metastate_transfold	metastate_transfold	SignalShapedRouteCompiler	HOLD	0.238638	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	4-Infrastructure/shim/hutter_equation_metastate_transfold_receipt.json			proposal_score -> candidate_route_coordinate -> bounded_exact_route_metastate -> promotion_receipt
41	hutter_equation_metastate_transfold_receipt:hutter_transfold_equations:promotion_rule	promotion_rule	SignalShapedRouteCompiler	HOLD	0.196828	projection_declared;compression_pressure;decoder_declared;witness_declared	scale_band_declared	4-Infrastructure/shim/hutter_equation_metastate_transfold_receipt.json			promote iff decoded_hash == source_hash and compressed_total_bytes < incumbent_bytes and ratio_schema is explicit and all witness, residual, decoder, and container bytes are counted
42	hutter_equation_metastate_transfold_receipt:hutter_transfold_equations:prune_rule	prune_rule	SignalShapedRouteCompiler	HOLD	0.218153	projection_declared;compression_pressure;shape_closure;decoder_declared	scale_band_declared	4-Infrastructure/shim/hutter_equation_metastate_transfold_receipt.json			prune iff LB_route >= incumbent_bytes
43	hutter_equation_metastate_transfold_receipt:hutter_transfold_equations:source_equation_surface	source_equation_surface	SignalShapedRouteCompiler	HOLD	0.224542	projection_declared;compression_pressure;witness_declared;shape_closure	scale_band_declared	4-Infrastructure/shim/hutter_equation_metastate_transfold_receipt.json			C = proposal_score(comp, phys, geom, scaling) or phi_HP = field + compression_gain + decoder/resource penalties
44	math_model_map:0	UQGET_Hubble_Tension	ProjectableGeometryTopology	HOLD	0.292337	projection_declared;semantic_entropy;geometric_mass;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	geometric_bind		H0 = 73.3 ± 1.5 km s⁻¹ Mpc⁻¹ (68% CL)
45	math_model_map:1	UQGET_Structure_Tension	ProjectableGeometryTopology	HOLD	0.261583	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	geometric_bind		S8 = 0.810 ± 0.008
46	math_model_map:2	UQGET_Statistical_Fit	ProjectableGeometryTopology	HOLD	0.288392	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	geometric_bind		χ²/d.o.f. = 1907.2/1949 (p = 0.78)
47	math_model_map:3	LASSO_MOGAT_GAT_Propagation	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283014	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		h_i^(l+1) = σ(Σ_{j∈N(i)} α_ij^(l) W^(l) h_j^(l))
48	math_model_map:4	LASSO_MOGAT_Attention_Coefficient	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.282576	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		α_ij^(l) = softmax_j(LeakyReLU(a→^(l)^T [W^(l) h_i^(l) || W^(l) h_j^(l)]))
49	math_model_map:5	Multiphasic_Allometry_LogLog_Scaling	CognitiveLoadField	HOLD	0.261553	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	thermodynamic_bind		Y = b·X + a (log-log space)
50	math_model_map:6	Multiphasic_Allometry_Quadratic	CognitiveLoadField	HOLD	0.261553	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	thermodynamic_bind		Y = a·X² + b·X + c (curvilinear)
51	math_model_map:7	Multiphasic_Allometry_Instantaneous_Slope	CognitiveLoadField	HOLD	0.260582	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	thermodynamic_bind		dY/dX = 2aX + b (where Y = aX² + bX + c)
52	math_model_map:8	Affine_Mapping_LTSF_Linear_Layer	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284364	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		Y = X·W + b
53	math_model_map:9	Affine_Mapping_Time_Series_Decomposition	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		x(t) = s(t) + f(t) + ε
54	math_model_map:10	Affine_Mapping_Periodic_Theorem	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.290839	projection_declared;witness_declared;shape_closure;proof_readiness	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		x(t) = s(t) = s(t-p) where p ≤ n
55	math_model_map:11	Affine_Mapping_Scaled_Periodic	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		x(t) = a·x(t-p) + c
56	math_model_map:12	MOF_CO2_Reduction_2e_Electrochemistry	CognitiveLoadField	HOLD	0.263119	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	thermodynamic_bind		CO2 + 2H+ + 2e- → CO + H2O
57	math_model_map:13	MOF_CO2_Reduction_Formic_Acid	CognitiveLoadField	HOLD	0.262582	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	thermodynamic_bind		CO2 + 2H+ + 2e- → HCOOH
58	math_model_map:14	MOF_CO2_Reduction_6e_Methanol	CognitiveLoadField	HOLD	0.259671	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	thermodynamic_bind		CO2 + 6H+ + 6e- → CH3OH + H2O
59	math_model_map:15	MOF_CO2_Reduction_8e_Methane	CognitiveLoadField	HOLD	0.259671	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	thermodynamic_bind		CO2 + 8H+ + 8e- → CH4 + 2H2O
60	math_model_map:16	COUCH_Equation	SignalShapedRouteCompiler	HOLD	0.257213	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	thermodynamic_bind		ẍ_i + γẋ_i + ω_i²x_i + Σ_j κ_ij(x_i - x_j) = F(t)
61	math_model_map:1	Intrinsic_Load_LI	SignalShapedRouteCompiler	HOLD	0.234956	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	L_I(x) = -Σ_{b=0}^{255} p(b|x) log₂ p(b|x)
62	math_model_map:2	NES_GCL_Square_Wave_Compression	SignalShapedRouteCompiler	HOLD	0.245952	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		C_ratio = U_size / C_size = 1.48× (achieved)
63	math_model_map:3	NES_OISC_GCL_LUT_Architecture	CognitiveLoadField	HOLD	0.264694	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		JTAG→SUBLEQ→GCL→LUT→APU
64	math_model_map:4	Unified_Shader_GCL_Audio_Stack	SignalShapedRouteCompiler	HOLD	0.235728	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		Shader(x,y,t,θ)→palette + GCL→LUT + SUBLEQ→compute
65	math_model_map:5	Unified_Cartridge_Controller_Stack	CognitiveLoadField	HOLD	0.264694	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		Cartridge_SUBLEQ→GCL→Shader→Audio→ControllerPort→NES
66	math_model_map:6	Topological_NanoKernel_UART_Stack	CognitiveLoadField	HOLD	0.235036	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		1-Wire_UART→GCL_Admission→Entropy→Metaprobe→Triumvirate→NES
67	math_model_map:7	NES_Sound_Line_DSP_Math	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.278424	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		Value↔AudioSignal(f,A,D) + APU_Operations→Result
68	math_model_map:8	Unified_Metaprobe_Collapse	CognitiveLoadField	HOLD	0.24112	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		All_Systems→Single_Metaprobe→Unified_Audit
69	math_model_map:9	Final_Unified_Math_Collapse	CognitiveLoadField	HOLD	0.225432	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		All_Math→Single_Substrate→Unified_Computation
70	math_model_map:10	Voltage_Computational_Substrate	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284065	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		Voltage→Value + Operations→Result
71	math_model_map:11	Palette_DSP_Slave	CognitiveLoadField	HOLD	0.276228	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		DSP_Math→Palette_Parameters→Video_Palette
72	math_model_map:12	Quad_Sampled_Scanlines	CognitiveLoadField	HOLD	0.267969	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	informational_bind		4×_Vertical→256×960
73	math_model_map:13	Microgrid_Voxel_Emulation	CognitiveLoadField	CANDIDATE	0.231194	projection_declared;semantic_entropy;shape_closure;witness_declared		3-Mathematical-Models/MATH_MODEL_MAP.tsv			Microgrid→640×480+Differential_Updates→Effective_640×480
74	math_model_map:2	Extraneous_Load_LE	SignalShapedRouteCompiler	HOLD	0.234956	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	L_E(x) = BPB(x,w_prior) - BPB*(x) = (1/n)Σ_i log₂(P_w*(x_i)/P_wprior(x_i))
75	math_model_map:3	Germane_Load_LG	CognitiveLoadField	HOLD	0.252403	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	informational_bind	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)
76	math_model_map:4	Routing_Load_LR	CognitiveLoadField	HOLD	0.252088	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	informational_bind	L_R(x) = Σ_j c_j·1[f_j computed] + Σ_{l=1}^{D(x)} log₂|M_l|
77	math_model_map:5	Memory_Load_LM	CognitiveLoadField	HOLD	0.228316	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	informational_bind	L_M(x) = log₂|E| + α·1[hit] + β + λ·|E|/|E_max|
78	math_model_map:6	Total_Cognitive_Load	SignalShapedRouteCompiler	HOLD	0.228402	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	L_total = λI·l̂I + λE·l̂E - λG·l̂G + λR·l̂R + λM·l̂M (Σλ=1, λG≤λE)
79	math_model_map:7	Cognitive_Efficiency	SignalShapedRouteCompiler	HOLD	0.234942	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	η(x) = l̂I(x) / (l̂I + l̂E + l̂R + l̂M + ε)
80	math_model_map:8	Regret_Adjusted_Load	SignalShapedRouteCompiler	HOLD	0.234942	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	L_ρ(x) = L_total(x) · (1 + ρ(x)/ρ_max)
81	math_model_map:9	Basin_Conditional_Load	SignalShapedRouteCompiler	HOLD	0.235052	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	L(x|B) = L_I(x) + L_E(x|B) + L_R^B(x)
82	math_model_map:10	MoE_Predictor_Distribution	SignalShapedRouteCompiler	HOLD	0.234956	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	P_w(x_i|x_{<i}) = Σ_{j=1}^{k} w_j · P_{m_j}(x_i|x_{<i})
83	math_model_map:11	Pressure_Piling	CognitiveLoadField	HOLD	0.256022	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_E_VERIFICATION	thermodynamic_bind	P(i) = P₀ · χ^i (χ ≈ 1.63)
84	math_model_map:12	Hugoniot_Temperature	CognitiveLoadField	HOLD	0.256318	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	T_peak = T₀ · (P_peak/P₀)^0.65
85	math_model_map:13	Pressure_Ionization	CognitiveLoadField	HOLD	0.259238	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	α(P) = 1 - exp(-k(P - P_MIT))
86	math_model_map:14	Energy_Recovery_Efficiency	CognitiveLoadField	HOLD	0.255475	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_E_VERIFICATION	thermodynamic_bind	η_net = (W_rec - W_erasure) / W_in; W_erasure ≥ k_B·T·ln2 per bit
87	math_model_map:15	Q_Factor	CognitiveLoadField	CANDIDATE	0.221733	projection_declared;semantic_entropy;shape_closure;witness_declared		3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_E_VERIFICATION	thermodynamic_bind	Q = (E_flash + E_enthalpy + E_recovered - W_demon) / (E_work + E_loss) > 1.0
88	math_model_map:16	Coupling_Weight	ProjectableGeometryTopology	HOLD	0.288723	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	GWL Rotation
89	math_model_map:17	Rotational_Alignment	ProjectableGeometryTopology	HOLD	0.290188	projection_declared;geometric_mass;semantic_entropy;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	g = cos(Δθ·2π/16) · cos(Δφ·π/8) · (1 - 2|χ_i - χ_j|)
90	math_model_map:18	Spatial_Proximity	ProjectableGeometryTopology	HOLD	0.29059	projection_declared;semantic_entropy;geometric_mass;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	h = exp(-|Δp|²/(2σ²)) · 1_{|Δp|<r_max}
91	math_model_map:19	Interaction_Force	ProjectableGeometryTopology	HOLD	0.270688	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_H_ALGEBRA	geometric_bind	F_ij = w_ij · (a_j - a_i) · Δp_ij / |Δp_ij|
92	math_model_map:20	Energy_Function	ProjectableGeometryTopology	HOLD	0.281222	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	geometric_bind	E(f) = -½ Σ_{i,j} w_ij · a_i · a_j + Σ_i V(a_i)
93	math_model_map:21	Frame_Evolution_Discrete	ProjectableGeometryTopology	HOLD	0.288392	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_H_ALGEBRA	geometric_bind	θ_i(t+1) = θ_i(t) + α_θ·F_{i,θ} + ξ_θ
94	math_model_map:22	Frame_Evolution_Continuous	ProjectableGeometryTopology	HOLD	0.292567	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_H_ALGEBRA	geometric_bind	df_i/dt = -α ∇_{f_i} E(f) + ξ(t)
95	math_model_map:23	Energy_Monotonicity_Theorem	ProjectableGeometryTopology	HOLD	0.292854	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_H_ALGEBRA	geometric_bind	dE/dt = -α Σ_i |∇_{f_i} E|² ≤ 0
96	math_model_map:24	Temporal_Weight	ProjectableGeometryTopology	HOLD	0.288723	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	w_ij^(τ) = cos(2π(τ_j - τ_i)/16)
97	math_model_map:25	Complete_Weight_5Factor	ProjectableGeometryTopology	HOLD	0.291436	projection_declared;semantic_entropy;geometric_mass;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	w_ij = cos(Δθ·22.5°)·cos(Δφ·22.5°)·cos(2πΔτ/16)·(1-2|Δχ|)·exp(-|Δp|²/2σ²)
98	math_model_map:26	Temporal_Force	ProjectableGeometryTopology	HOLD	0.271047	projection_declared;geometric_mass;witness_declared;semantic_entropy	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	F_ij^(τ) = w_ij^(τ) · (a_j - a_i) · sgn(τ_j - τ_i)
99	math_model_map:27	Temporal_Evolution	ProjectableGeometryTopology	HOLD	0.289068	projection_declared;geometric_mass;witness_declared;semantic_entropy	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	τ_i(t+1) = τ_i(t) + α_τ·F_{i,τ} + ω₀
100	math_model_map:28	Temporal_Stability	ProjectableGeometryTopology	HOLD	0.289068	projection_declared;geometric_mass;witness_declared;semantic_entropy	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_D_INVARIANTS	geometric_bind	d/dt(τ_j - τ_i) = 0 for all i,j
101	math_model_map:29	Temporal_Entropy	ProjectableGeometryTopology	HOLD	0.29059	projection_declared;semantic_entropy;geometric_mass;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	H_τ = -Σ_{k=0}^{15} p(τ=k) log₂ p(τ=k)
102	math_model_map:30	Mu_Seed_Cardinality	ProjectableGeometryTopology	HOLD	0.291006	projection_declared;semantic_entropy;geometric_mass;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_D_INVARIANTS	geometric_bind	|S_μ| = 8×8×16×16×8×8×2×16×8×4 = 8,589,934,592 ≈ 2^33
103	math_model_map:31	Fractal_Occupancy	ProjectableGeometryTopology	HOLD	0.292337	projection_declared;semantic_entropy;geometric_mass;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_D_INVARIANTS	geometric_bind	|P_occ| = ρ_occ · N^{d_H} (d_H ≈ 2.7268)
104	math_model_map:32	Total_Formal_State_Space	ProjectableGeometryTopology	HOLD	0.289427	projection_declared;geometric_mass;semantic_entropy;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	geometric_bind	|S_total| ≈ 2^{5,900,000}
105	math_model_map:33	Reachable_State_Space	SignalShapedRouteCompiler	HOLD	0.246118	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	geometric_bind	|S_reachable| ≈ |S_total| / 10^{29}
106	math_model_map:34	Wave_Packet_State	ProjectableGeometryTopology	HOLD	0.288392	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	P = (ΔV, Δt, π, τ, χ, C, A)
107	math_model_map:35	Throat_Condition	ProjectableGeometryTopology	HOLD	0.288392	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_BRAID	geometric_bind	T_throat = {(i,j) | Φ_topo(i,j) >> Φ_metric(i,j)}
108	math_model_map:36	Multi_Factor_Coupling_Weight	ProjectableGeometryTopology	HOLD	0.288076	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_BRAID	geometric_bind	w_ij = w_p · w_π · w_τ · w_χ · w_topo · w_σ
109	math_model_map:37	Holonomy_Accumulation	ProjectableGeometryTopology	HOLD	0.288076	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_BRAID	geometric_bind	Hol(γ_loop) = ∮_γ T(p) dp
110	math_model_map:38	Non_Euclidean_Distance	ProjectableGeometryTopology	HOLD	0.271543	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	d_N = path_length(γ_ij) + curvature_penalty(κ) + torsion_cost(T); d_T = d_E + λ_N·d_N
111	math_model_map:39	Trixal_Axes	CognitiveLoadField	HOLD	0.25882	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	TrixalAxes = (thermal, work, irreversibility), each ∈ [0,1]; |axes| = √(th² + w² + ir²)
112	math_model_map:40	Shannon_Entropy	CognitiveLoadField	HOLD	0.259671	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	H = -Σ_b p(b) log₂ p(b), where p(b)=count(b)/len
113	math_model_map:41	Kolmogorov_Estimate	CognitiveLoadField	HOLD	0.261553	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	K_est = (8 - H) / 8
114	math_model_map:42	Thermodynamic_Entropy	CognitiveLoadField	HOLD	0.260119	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	S_thermo = H + K_est · 0.1
115	math_model_map:43	Entropy_Gradient	CognitiveLoadField	HOLD	0.260119	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_H_ALGEBRA	thermodynamic_bind	dS/dt = (S_current - S_previous) / Δt
116	math_model_map:44	Mutual_Information_Extracted	SignalShapedRouteCompiler	HOLD	0.236532	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	thermodynamic_bind	MI = H_initial - H_current
117	math_model_map:45	Carnot_Efficiency	CognitiveLoadField	HOLD	0.25882	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	thermodynamic_bind	η_Carnot = 1 - T_cold / T_hot
118	math_model_map:46	Work_Extraction	CognitiveLoadField	HOLD	0.255474	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	thermodynamic_bind	W_actual = Q_absorbed · η_Carnot · 0.7
119	math_model_map:47	Irreversibility_Metric	CognitiveLoadField	HOLD	0.26106	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	score = (entropy_production + path_asymmetry + time_reversal_violation) / 3
120	math_model_map:48	Thermodynamic_Length	CognitiveLoadField	HOLD	0.25882	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	thermodynamic_bind	L_thermo = Σ_i distance_i · (1 + irreversibility_i)
121	math_model_map:49	Thermodynamic_Depth	CognitiveLoadField	HOLD	0.261553	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	depth = entropy_production · ln(time_steps)
122	math_model_map:50	Stamp_Code	LogogramProjection	HOLD	0.202394	projection_declared;witness_declared;shape_closure;proof_readiness	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	thermodynamic_bind	SHA256(axes || traj_hash || hardware_entropy || timing_jitter || process_nonce)
123	math_model_map:51	Arrhenius_Temperature_Factor	CognitiveLoadField	HOLD	0.251579	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	AF = exp(E_a / (k_B · T))
124	math_model_map:52	Blacks_Equation_EM	CognitiveLoadField	HOLD	0.250302	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	EM_risk = J^n · exp(E_a / (k_B · T)) / 10^{12}
125	math_model_map:53	Coffin_Manson_Fatigue	CognitiveLoadField	CANDIDATE	0.221733	projection_declared;semantic_entropy;shape_closure;witness_declared		3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	CM_damage = (ΔT / ΔT_threshold)^m · 10^{-8}, m≈1.9
126	math_model_map:54	Landauer_Limit	SignalShapedRouteCompiler	HOLD	0.23706	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	thermodynamic_bind	W_erasure ≥ k_B · T · ln(2) ≈ 2.87e-21 J/bit at 300K
127	math_model_map:55	Entropy_Generation_Rate	CognitiveLoadField	HOLD	0.257657	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_E_VERIFICATION	thermodynamic_bind	dS/dt = power_dissipation / (k_B · T · ln 2) [bits/s]
128	math_model_map:56	BitFlip_Gradient_5D	CognitiveLoadField	HOLD	0.250417	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_D_INVARIANTS	thermodynamic_bind	|G| = (D1/120 + D2/5000 + D3/1000 + D4/100 + D5/5000) / 5
129	math_model_map:57	SEU_BitFlip_Rate	CognitiveLoadField	HOLD	0.24942	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	BFR = ε_SEU · 2^{(T-25)/10} · (1 + V_jitter/1000) · 3600 [flips/hr]
130	math_model_map:58	Stress_Decay	CognitiveLoadField	HOLD	0.25882	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	stress(t) = stress_0 · e^{-t/300} + intensity · (1 - e^{-t/300})
131	math_model_map:59	Remaining_Useful_Life	CognitiveLoadField	HOLD	0.25078	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	thermodynamic_bind	RUL = MTBF / (AF · (1 + fatigue·0.01 + thermal_fatigue·0.1))
132	math_model_map:60	Homeostatic_Stress_Injection	CognitiveLoadField	HOLD	0.25882	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_E_VERIFICATION	thermodynamic_bind	surprise = -ln(margin), margin = 1 - stress_magnitude; regret = max(0, stress - 0.5)
133	math_model_map:61	Exact_Int_to_FP_Cast	CognitiveLoadField	HOLD	0.259238	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_D_INVARIANTS	thermodynamic_bind	int_bits ≤ fp_mantissa_bits + 1 (signed) or ≤ fp_mantissa_bits + 1 (unsigned)
134	math_model_map:62	Safe_Narrowing_Proof	CognitiveLoadField	HOLD	0.26106	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_D_INVARIANTS	thermodynamic_bind	can_safely_narrow(src_bits, signed, dst_mantissa) → bool
135	math_model_map:63	RISCV_Instruction_Latency	CognitiveLoadField	HOLD	0.258417	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_D_INVARIANTS	thermodynamic_bind	fdiv.d=33, fdiv.s=19 → penalty=0.737; fadd.d=4, fadd.s=4 → penalty=0.0
136	math_model_map:64	Photon_Energy	CognitiveLoadField	HOLD	0.257657	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	physical_bind	E = hc/λ = 1.2398 / λ_μm [eV]
137	math_model_map:65	Subband_Spacing	CognitiveLoadField	HOLD	0.260582	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	physical_bind	ΔE = E_upper - E_lower; E_upper=hc/λ_min, E_lower=hc/λ_max
138	math_model_map:66	Cascade_Gain	CognitiveLoadField	HOLD	0.249496	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	physical_bind	G = photons_per_e⁻ × n_wells; photons_per_e⁻ = ⌊E_electron / ΔE⌋
139	math_model_map:67	Temperature_Tuning	CognitiveLoadField	HOLD	0.257657	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	physical_bind	λ(T) = λ₀ + α · (T - T₀); α=5e-6 /K (GaAs/AlGaAs)
140	math_model_map:68	Injection_Efficiency	CognitiveLoadField	HOLD	0.257657	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	physical_bind	η = (0.5 + window_bonus) · spacing_eff · (1 - stress_penalty); clamped to [0,1]
141	math_model_map:69	Atmospheric_Windows	CognitiveLoadField	HOLD	0.258417	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	physical_bind	Windows: (3,5), (8,12), (16,20) μm; transmission=1.0 inside, exp(-dist·0.5) outside
142	math_model_map:70	Tuning_Range	CognitiveLoadField	HOLD	0.257299	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_G_ENERGY	physical_bind	ν = 10⁴/λ [cm⁻¹]; DFB: ±7.5 cm⁻¹, EC: ±200 cm⁻¹; λ_min=10⁴/ν_max, λ_max=10⁴/ν_min
143	math_model_map:71	Mutual_Information_Signal	SignalShapedRouteCompiler	HOLD	0.222839	projection_declared;witness_declared;shape_closure;compression_pressure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	MI(x) = baseline_bpb(x) - actual_bpb(x)
144	math_model_map:72	kNN_MI_Prediction	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.282379	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	informational_bind	MI_pred = Σ_i (w_i · MI_i · S_i) / Σ_i (w_i · S_i); w_i = 1/(d_i + ε)
145	math_model_map:73	Surprise_Metric	ProjectableGeometryTopology	HOLD	0.288392	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	informational_bind	surprise = log(1 + |MI_actual - MI_predicted|)
146	math_model_map:74	Structure_Yield	SignalShapedRouteCompiler	HOLD	0.245865	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_A_COMPRESSION	informational_bind	ρ(x) = MI(x) / (cost(x) + ε)
147	math_model_map:75	Weighted_Feature_Distance	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.281874	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_B_ROUTING	informational_bind	d(z₁,z₂) = √Σ_i w_i · ((z₁_i - z₂_i) / s_i)²
148	math_model_map:76	DAG_Force_Equilibrium	CadForceProbeReceipt	HOLD	0.280052	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_BRAID	geometric_bind	Σ F_in = Σ F_out at every node
149	math_model_map:77	Constitutive_Law	CadForceProbeReceipt	HOLD	0.294433	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_BRAID	geometric_bind	σ = C : ε; ε = ½(∇u + ∇u^T)
150	math_model_map:78	DAG_Global_Validity	ProjectableGeometryTopology	HOLD	0.2697	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_BRAID	geometric_bind	V(G) = ∧_{v∈V} (ΣF_in = ΣF_out)
151	math_model_map:79	Cosine_Similarity	ProjectableGeometryTopology	HOLD	0.288723	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_K_SIGNAL	geometric_bind	cos = x · x_ref / (‖x‖ · ‖x_ref‖)
152	math_model_map:80	Gradient_Alignment	ProjectableGeometryTopology	HOLD	0.288392	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_K_SIGNAL	geometric_bind	alignment = ∇g_i · ∇g_j / (‖∇g_i‖ · ‖∇g_j‖)
153	math_model_map:81	Phase_Accumulation	ProjectableGeometryTopology	HOLD	0.288076	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_K_SIGNAL	geometric_bind	phase += Σ y · dx
154	math_model_map:82	Metric_Tensor_From_Circumferences	ProjectableGeometryTopology	HOLD	0.290188	projection_declared;geometric_mass;semantic_entropy;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	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)
155	math_model_map:83	Line_Element	ProjectableGeometryTopology	HOLD	0.287773	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	ds² = g_tt·dθ² + 2·g_tp·dθ·dφ + g_pp·dφ²
156	math_model_map:84	Christoffel_Symbols_2D	ProjectableGeometryTopology	HOLD	0.289427	projection_declared;geometric_mass;semantic_entropy;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	Gamma^k_ij = ½·g^kl·(∂_i g_jl + ∂_j g_il - ∂_l g_ij)
157	math_model_map:85	Geodesic_Step_Symplectic_Euler	ProjectableGeometryTopology	HOLD	0.290188	projection_declared;geometric_mass;semantic_entropy;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	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
158	math_model_map:86	Stereographic_Chart_Transition	ProjectableGeometryTopology	HOLD	0.290188	projection_declared;geometric_mass;semantic_entropy;witness_declared	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	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
159	math_model_map:87	Chirality_Algebra	ProjectableGeometryTopology	HOLD	0.288392	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	D+D→D, L+L→L, D+L→W(COLLAPSE→W); chiralityToTernary: D→Active, L→Active, W→Latent
160	math_model_map:88	BLINK_GATE_Ternary_Clock	CognitiveLoadField	CANDIDATE	0.21559	projection_declared;semantic_entropy;shape_closure;witness_declared		3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	control_bind	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
161	math_model_map:89	Geodesic_Step_Verlet	ProjectableGeometryTopology	HOLD	0.288076	projection_declared;geometric_mass;witness_declared;shape_closure	scale_band_declared;negative_control_strength	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_C_TOPOLOGY	geometric_bind	Same acceleration as M85 + Verlet velocity update + chart transition check
162	math_model_map:90	Waveprobe_Risk_Function	CognitiveLoadField	HOLD	0.273853	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_F_CONTROL	control_bind	risk(s) = (1 + γ·(1-cos(θ)))/d² + η·h; γ=3, η=0.8
163	math_model_map:91	Waveprobe_Heat_Evolution	CognitiveLoadField	HOLD	0.25882	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/MATH_MODEL_MAP.tsv	LAYER_F_CONTROL	control_bind	h' = α·h + β·a; α=0.95, β=0.2
164	extracted_md:0	extracted_md_equation_0	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285005	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			a_μ = (|g| - 2) / 2 = 0.001165920705(114)
165	extracted_md:1	extracted_md_equation_1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287699	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			σ = 0.127 ppm (0.000000114)
166	extracted_md:2	extracted_md_equation_2	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.289065	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			a_μ^theory = a_μ^experiment within 0.5σ
167	extracted_md:3	extracted_md_equation_3	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286858	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			g_μ = -2.00233184122(82)
168	extracted_md:4	extracted_md_equation_4	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286858	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			μ = g · (eℏ / 2m) · S
169	extracted_md:5	extracted_md_equation_5	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			(D_t^α + (-∇²)^β) Ψ = λ |Ψ|^γ Ψ
170	extracted_md:6	extracted_md_equation_6	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			D^α f(x) = F^{-1}[ |k|^α · F[f](k) ]
171	extracted_md:7	extracted_md_equation_7	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287271	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			Ψ_observed(x, t) = ∫ K_θ(x - x') Ψ_unified(x', t) dx'
172	extracted_md:8	extracted_md_equation_8	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287699	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			w(α, θ) = sin(θ)^α · cos(θ)^{1-α}
173	extracted_md:9	extracted_md_equation_9	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			g_n(θ_obs) = g_0 · sin(θ_obs)^{1/n} · cos(θ_obs)^{1 - 1/n}
174	extracted_md:10	extracted_md_equation_10	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			Q_n = (1/2π) ∮_C ∇_n φ · dn = m/n for m ∈ ℤ
175	extracted_md:11	extracted_md_equation_11	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			ds² = -dθ²/ω(θ)² + a(θ)² [dr²/(1-kr²) + r² dΩ²] + ℓ_P² dθ² Γ(θ)
176	extracted_md:12	extracted_md_equation_12	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287699	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			H_eff = ω(θ)
177	extracted_md:13	extracted_md_equation_13	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			ρ_DE(θ) = ρ_foam · (1 - θ/θ_max)²
178	extracted_md:14	extracted_md_equation_14	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285005	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			S(R) ≤ C' · R^{D_H} · T^{(D_H - 1)}
179	extracted_md:15	extracted_md_equation_15	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			S ≤ C' · R^{1.44} · T^{0.44}
180	extracted_md:16	extracted_md_equation_16	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			A(r) = 2π (cosh(r) - 1) ≈ π · exp(r) for r >> 1
181	extracted_md:17	extracted_md_equation_17	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			L_{n+1} / L_n ≈ exp(d_inj) ≈ Φ² ≈ 2.618
182	extracted_md:18	extracted_md_equation_18	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.28814	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			D_s = 2 D_H / (1 + D_H)
183	extracted_md:19	extracted_md_equation_19	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287699	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			D_s = 4/3 ≈ 1.333
184	extracted_md:20	extracted_md_equation_20	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			ρ(E) ~ E^{D_s/2 - 1} = E^{-1/3}
185	extracted_md:21	extracted_md_equation_21	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.289549	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			E_n ~ n³
186	extracted_md:22	extracted_md_equation_22	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			n_s = 1 - 2/(1 + θ_max/θ_recombination) ≈ 0.965
187	extracted_md:23	extracted_md_equation_23	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287271	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			E_dissipated ≥ k_B T · ln(2) per bit erased
188	extracted_md:24	extracted_md_equation_24	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287271	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			H(X) = -Σ p(x) log p(x)
189	extracted_md:25	extracted_md_equation_25	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			S ≤ 2π R E / (ℏ c ln 2) = A / (4 G ℏ)
190	extracted_md:26	extracted_md_equation_26	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284065	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/extracted_equations.md			C_V = (12π⁴/5) N k_B (T/Θ_D)³ ∝ T³
191	extracted_md:27	extracted_md_equation_27	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.288596	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			C_V ∝ T^{D_s}
192	extracted_md:28	extracted_md_equation_28	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.288596	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			C_V ∝ T^{1.18}
193	extracted_md:29	extracted_md_equation_29	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			⟨exp(-β W)⟩ = exp(-β ΔF)
194	extracted_md:30	extracted_md_equation_30	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			(ΔJ)² / ⟨J⟩² · σ ≥ 2 k_B
195	extracted_md:31	extracted_md_equation_31	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287699	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			Δx · Δp ≥ ℏ/2
196	extracted_md:32	extracted_md_equation_32	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			Ψ_total = Ψ_A + Ψ_B = A · exp(i ω_Ψ θ) · [exp(i k_Ψ x_A) + exp(i k_Ψ x_B)]
197	extracted_md:33	extracted_md_equation_33	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			|Ψ_total|² = 2|A|² · [1 + cos(k_Ψ (x_A - x_B))]
198	extracted_md:34	extracted_md_equation_34	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287271	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			E = ℏ ω = ω_Ψ (in natural units ℏ = 1)
199	extracted_md:35	extracted_md_equation_35	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.288596	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			p = ℏ k = dθ_0/dx = k_Ψ
200	extracted_md:36	extracted_md_equation_36	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.289065	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			λ = 2π / k_Ψ = 2π / p
201	extracted_md:37	extracted_md_equation_37	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			Phenotype(x, t) = Ψ_E [ Genotype(x) × Regulatory_State(t) ]
202	extracted_md:38	extracted_md_equation_38	SignalShapedRouteCompiler	HOLD	0.232964	projection_declared;shape_closure;decoder_declared;witness_declared	scale_band_declared	3-Mathematical-Models/extracted_equations.md			Residual(n) = Ψ_decode [ Basis, Context(n) ] XOR Byte(n)
203	extracted_md:39	extracted_md_equation_39	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/extracted_equations.md			H_Ψ(data) = -Σ_n p(n) log_2 p_Ψ(n) ≤ H_uniform(data) = 8 bits/byte
204	eq_21f33f4110064dbd	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284364	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			G = (V, E) represents a quantum state |ψ⟩ through a collection of local tensors {Tv }v∈V , one for each vertex
205	eq_14d74623112c018f	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			injec= CD and Hv ∼ tive if this map has trivial kernel
206	eq_fcd40dc2de7c7324	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.265908	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			d ≥ D|N (v)| , which generically holds after coarse-graining when D = O(1)
207	eq_416bbe45bfd12c68	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287699	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			min ≥ δ
208	eq_290815ff34ff74a2	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = ⟨ψ|ψ⟩
209	eq_5ea587928ed366f5	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284678	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = (v, n) of the graph, the tensor Tv ⋆ T̄v of the norm network defines a superoperator on the virtual space from any set of legs to its complement Eq
210	eq_e1646b712978905e	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = ZBP 1 + Zℓ 
211	eq_ed91aac060fde4cf	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284364	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = log ZBP + ϕ(W)ZW , (7) connected W where a cluster is collection of loops with multiplicities, W = {(ℓ1 , α1 ), (ℓ2 , α2 ),
212	eq_9b66cadab83a4e1e	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.280384	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			i ≥ 1 is its multiplicity in the cluster
213	eq_6fd0d43c1e1577a1	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284678	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			ZW = i Zℓαii and the P weight of a cluster is |W| := i αi |ℓi | where |ℓ| for a loop ℓ ∈ L denotes the number of edges in ℓ
214	eq_8605b7c5ccdbcf5f	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			c > c0 = O(log ∆)
215	eq_dbd7ee74be207cc7	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283511	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = ⟨ψ|ψ⟩ to 1/ poly(N ) multiplicative error (ii) local observables ⟨OA ⟩ = ⟨ψ|OA |ψ⟩/⟨ψ|ψ⟩ to 1/ poly(N ) multiplicative error, given ⟨OA ⟩ ̸= 0 (iii) correlation functions ⟨OA OB ⟩ − ⟨OA ⟩ ⟨OB ⟩ to Õ(1/ poly(N )) additive error where A, B ⊂ V are disjoint local regions
216	eq_9138cc21d6e4da27	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284364	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = (v, n) with d(v, A) = r, we have   ∥µ′⋆,⃗e − µ⋆,⃗e ∥1 = O e−r/ξ∗ (10) 5 Where 1/ξ∗ = O(log ε∗ /ε)
217	eq_5be87eaf6cffbaae	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			W = Wnear ∪ Wfar , where clusters in Wnear are distance at most a cutoff Rth away from B
218	eq_927277d74e6531cc	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285005	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			t < r and starts increasing thereafter, owing to the strict lightcone in the message-passing dynamics [see SM for a proof]
219	eq_353043888999f4ac	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284065	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			t = r−1, leading to   ∥µ⋆,⃗e − µ′⋆,e ∥1 = O e−r/ξ∗ (13) establishing locality of the BP fixed-points
220	eq_532f389442891ed2	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			d = c − c0 = O(1)
221	eq_fdfae5689dd4a9a5	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			R = Θ(1)
222	eq_9138aeb942929155	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287699	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			X = 1}
223	eq_0cd087779e7532a9	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283255	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			i=1 For p = ∞ we have, ∥x∥∞ := max |xi | 1≤i≤m (S3) For an operator A ∈ B(H), we define the operator Schatten norm in terms of its singular values σ(A) as, ∥A∥p := ∥σ(A)∥p (S4) for any p ∈ [1, ∞]
224	eq_5593e036fe6f7dd7	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			p ≤ q ≤ ∞ and any operator A, we have, ∥A∥p ≥ ∥A∥q (S5) ∥A∥1 ≥ ∥A∥2 ≥ ∥A∥∞ (S6) In particular, 10 2
225	eq_ea9b6d38a8a0c1b0	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283781	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			p ≤ q ≤ ∞ and any non-zero operator A, 1 1 ∥A∥p ≤ rank(A) p − q ∥A∥q (S7) p rank(A)∥A∥∞ (S8) ∥Ax∥2 = σmax (A) x̸=0 ∥x∥2 (S9) In particular, ∥A∥2 ≤ We also note that, the ∞−norm obeys, ∥A∥∞ = sup we will denote ∥ · ∥∞ by just ∥ · ∥ for convenience
226	eq_e0537400fa963370	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284678	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			B = Ac , reshape the tensor into a linear map T : HA → HB by grouping the indices in A and B into multi-indices a = (ia1 ,
227	eq_23fc8ebaf9c8ae4a	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287699	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			b = (ib1 ,
228	eq_8b4895ac1c7ebca0	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283511	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			q = 1 we have, | tr A† B | ≤ ∥A∥p ∥B∥q (S12) Graphs For a graph G = (V, E), we define some useful notation
229	eq_25d49db810143f41	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = {v, w} ∈ E, we will refer to it’s directed versions ⃗e = (v, w) and ← e = (w, v)
230	eq_5034975bc936419d	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = {v, w}, we define, for any u ∈ V , d(e, u) := min{d(v, u), d(w, u)} and similarly, for any A ⊂ V , d(e, A) := min d(e, u)
231	eq_ab6c35762bc86081	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285005	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			li=1 be finite-dimensional Hilbert spaces (the l virtual legs), and let Hphys be the physical Hilbert space
232	eq_60b71803ce04c1ba	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			i=1 Definition S1
233	eq_7d5beabf91af593e	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283511	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			i=1 Hi −→ Hphys from We perform a singular value decomposition T = V ΣU † ∈ Cnp ×nv , (S14) where np ≥ nv by injectivity, where U ∈ Cnv ×nv and V :∈ Cnp ×nv satisfy U † U = 1nv (unitarity) and V † V = 1nv (isometry), and Σ = diag(λe ) ∈ Cnv ×nv collects the singular values
234	eq_8daf48607920ba7b	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = δ ∈ (0, 1]
235	eq_3b521e5a6156cbc1	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = 1, e e (S15) We call δ the injectivity parameter
236	eq_7cf50458351623ec	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			T = V U † itself is an isometry
237	eq_b5bc1ffd90912fb1	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.288596	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			a = 1
238	eq_51e4f2d85951d30b	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284678	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Lc = dim(HLc )1L , Ka,L→Lc Ka,L→L (S18) c = dim(HL )1Lc , a a which follow from the fact that U is a unitary
239	eq_51dad4a7954a91e6	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284065	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Lc = [Ū a ](i′L ),(iLc ) [U a ](iL ),(iLc ) = δiL ,i′L = dim(HLc )1L a a,iLc iLc Moreover, when T is δ−injective with δ = 1 (i
240	eq_10109834ac3ac602	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			G = (V, E) with vertex set V and edge set E
241	eq_6c7adf4f4e980afe	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283255	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			G = (V, E) with uniform virtual dimension D and physical dimension dp is specified for each v ∈ V by a tensor O Tv : H(n,v) → Hphys ∼ = Cdp , n∈N (v) where N (v) denotes the set of neighbors of v, and each virtual space H(n,v) ∼ = CD
242	eq_dde05d0258ec36a5	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284678	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = (v, w), we define a bond-space H⃗e ∼ = CD
243	eq_36e95d88ecbda2b0	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285005	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = (v, w) is a positive operator µ⃗e ∈ Pos(H⃗e ) representing the message from v to w
244	eq_25b43848714b6ceb	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = (v, n) ∈ ⃗ E,   O µ(m,v) 
245	eq_139255306999d8d8	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284364	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e > 0 such that PEPS if for each directed edge ⃗e ∈ E, f⃗e (µ⋆ ) = λ⃗e µ⃗e
246	eq_2a06ffe17253ce3c	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = ⟨ψ|ψ⟩ can be formally described as a Taylor series in terms of ‘loops’ on the network as described below
247	eq_e598d78992b57382	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284065	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = ZBP 1 + Zl  (S21) Γ⊂L l∈Γ Γ finite, compatible where the sum runs over all finite sets Γ of mutually compatible loops
248	eq_14f71a50573b7fd0	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			W = {(ℓ1 , α1 ), (ℓ2 , α2 ),
249	eq_44bf0ed184c8c0f8	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.287271	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			nW = i=1 αi
250	eq_4c772de7743acc11	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			W = {(ℓ1 , α1 ),
251	eq_3fe8c2f5d04f57ff	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			ZW = k Y Zℓαii
252	eq_1abc29f7b62428f6	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			i=1 We call a cluster W connected if the interaction graph GW is connected, meaning there is a path between any two vertices in the interaction graph
253	eq_f4bc63354f272a96	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283781	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			GW = Pk (VW , EW ) has |VW | = i=1 αi vertices, with loop ℓi corresponding to αi vertices
254	eq_2a47fee92e986d5e	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			W = {(l1 , α1 ), (l2 , α2 ),
255	eq_4a18868e412a28db	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286858	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			ZW = Zlαi i
256	eq_d14e04ca5ba01499	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284364	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = log ZBP + ϕ(W)ZW , (S25) connected W where the sum runs over all connected clusters W
257	eq_405936ddfb9bc98c	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284065	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			c > c0 := log(2e∆) + 12 such that |Zl | ≤ e−c|l| (S27) then, the series for log Z converges absolutely
258	eq_6a72df8385b3a8fb	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283014	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Fm = log ZBP + X ϕ(W)ZW , (S28) connected W |W|≤m is bounded by |log Z − Fm | ≤ N e−d(m+1) where d = c − c0 , ∆ is the degree of the graph, and N is the number of vertices
259	eq_52e8897befaf699d	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285005	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			c > c0 = log(2e∆) + 1/2
260	eq_f05cdb2173e0a64b	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			G = (V, E)
261	eq_f93b08fedbc0a5af	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284364	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			T = ⟨ψ|ψ⟩ and A T = ⟨ψ|OA |ψ⟩ respectively after suitable BP normalization
262	eq_d0869069ce0fee51	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = ⟨ψ|ψ⟩ and Z A = ⟨ψ|OA |ψ⟩ for a local observable with ⟨OA ⟩ ̸= 0
263	eq_e2dad9249b00119f	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283014	projection_declared;witness_declared;semantic_entropy;shape_closure	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			m = ⟨OA ⟩BP · exp     conn W←LA        supp(W)∩A̸=∅ |W|≤m leads to a relative error δm = | ⟨OA ⟩ − ⟨OA ⟩m |/| ⟨OA ⟩ | bounded by   δm ≤ O |A|e−(c−c0 )(m+1) (S33) where d = c − c0 = O(1)
264	eq_2b301ef1b6ca651f	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283781	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			A = ∂λ log ZλA |λ=0 = ⟨OA ⟩BP + ϕW Z W αl − ⟨OA ⟩BP
265	eq_f4aab7b26b55c832	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = ⟨ψ|ψ⟩ and Z A = ⟨ψ|OA |ψ⟩
266	eq_1a6dee6dca2f084b	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.28814	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			d = c − c0
267	eq_0698ebc502ab24cc	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286074	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			c = X A ϕW ∂λ ZW,λ conn
268	eq_2edfb68a37ab3d1f	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286858	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			A = (A1 ,
269	eq_7957e0f2cb86a72c	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286858	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			degree ≥ 2 everywhere except in all regions Ai
270	eq_10a508b9d741a6f6	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284678	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			c ≤ O e−d(A,B)/ξ for a finite correlation length ξ ≤ O((1/(c − c0 ))) and d(A, B) being the graph distance
271	eq_fb10b15989eae47c	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283511	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Z = ⟨ψ|ψ⟩ can be computed to 1/ poly(N ) multiplicative error in poly(N ) time (ii) local observables ⟨OA ⟩ = ⟨ψ|OA |ψ⟩/⟨ψ|ψ⟩ with ⟨OA ⟩ ̸= 0 can be computed to multiplicative error ϵ in poly(1/ϵ) time (iii) 2-point correlation functions can be computed to additive error Õ(1/ poly(N )) in poly(N ) time 18 Proof
272	eq_984644a6b0dbab3e	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.283255	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			m ≤ N e−d(m+1) (S37) Hence, to ensure log Z − F̃m < O(1/ poly(N )) we require m = Ω(log N )
273	eq_837e24a6c715af63	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285347	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			m = Ω(log N )
274	eq_e54ad45a68cb6a93	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284065	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			m ≤ O e−d(m+1) ≤ ϵ ⟨OB ⟩ (S38) which can be ensured given m = O(log 1/ϵ), again computable in poly 1/ϵ time
275	eq_21f71c6c28c71003	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.282576	projection_declared;semantic_entropy;witness_declared;shape_closure	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			m = d(A, B) + O(log 1/ϵ), leading to an error O m2 (|A| + |B|)e−dm , which is (note that (|A| + |B|) = O(1), !  2   1 1 2 −d[d(A,B)+log 1/ϵ] O d(A, B) log ·e = O log N · = Õ(1/ poly(N )) (S39) ϵ poly(N ) since we already have d(A, B) = O(log N ) and we choose ϵ = 1/ poly(N )
276	eq_717ace3c9565c03b	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Ka = D1L̸=i
277	eq_ccca83f09f701b34	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.284065	projection_declared;witness_declared;shape_closure;semantic_entropy	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			a ≥ δ 2 > 0 and † a Ka Ka = D P (S43) a 1, X λ2a Ka† Ka ⪰ δ 2 X a Ka† Ka = δ 2 D 1, a hence Tr f (X) ≥ δ 2 D Tr(X) = δ 2 D
278	eq_bc5bda52965ac0f8	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.286459	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			e = (v, n) ∈ E
279	eq_d4a2926485bb8572	arXiv:2604.21919v1	HoldForUnlawfulOrUnderspecifiedShape	HOLD	0.285704	projection_declared;witness_declared;shape_closure;residual_risk	scale_band_declared	3-Mathematical-Models/equations_100/equations_database.jsonl			Ka = dim(HL ) L