Theorems — Generative Collapse Dynamics
Every theorem derives from Axiom-0. Classical results emerge as degenerate limits.
20 theorems across 3 modules
Catalog
| ID | Name | Module |
|---|---|---|
T-SI-1 | The kernel is a stateless function; time enters only via the budget. | emergent_structural_insights |
T-SI-2 | The equator c = 1/2 is a saddle point of S + κ. | emergent_structural_insights |
T-SI-3 | Channel death cascades exponentially: IC ∝ exp(−β · n_dead / n). | emergent_structural_insights |
T-SI-4 | The Fisher-weighted entropy integral equals 2ζ(2) = π²/3. | emergent_structural_insights |
T-SI-5 | F + ω = 1 is the only exact symmetry; all others break by design. | emergent_structural_insights |
T-SI-6 | The Fisher metric is flat (g_F = 1); all complexity is extrinsic. | emergent_structural_insights |
T-KS-1 | Dimensionality Fragility Law. | kernel_structural_theorems |
T-KS-2 | Positional Democracy of Slaughter. | kernel_structural_theorems |
T-KS-3 | Weight-Induced Fragility Hierarchy. | kernel_structural_theorems |
T-KS-4 | Monitoring Paradox (Quantified). | kernel_structural_theorems |
T-KS-5 | Approximation Boundary. | kernel_structural_theorems |
T-KS-6 | U-Curve of Degradation. | kernel_structural_theorems |
T-KS-7 | p=3 Unification Web. | kernel_structural_theorems |
T-URC-1 | Tier-1 Kernel Identities. | universal_regime_calibration |
T-URC-2 | Universal Regime Concordance. | universal_regime_calibration |
T-URC-3 | Super-Exponential Repair. | universal_regime_calibration |
T-URC-4 | IC–Channel Vulnerability. | universal_regime_calibration |
T-URC-5 | Cross-Domain F Separation. | universal_regime_calibration |
T-URC-6 | Curvature–Regime Entailment. | universal_regime_calibration |
T-URC-7 | Entropy–Regime Correlation. | universal_regime_calibration |
Emergent Structural Insights
Source: closures/gcd/emergent_structural_insights.py
T-SI-1: The kernel is a stateless function; time enters only via the budget.
- Function:
theorem_TSI1_stateless_mirror() - Module:
emergent_structural_insights
T-SI-2: The equator c = 1/2 is a saddle point of S + κ.
- Function:
theorem_TSI2_equator_saddle() - Module:
emergent_structural_insights
T-SI-3: Channel death cascades exponentially: IC ∝ exp(−β · n_dead / n).
- Function:
theorem_TSI3_cascading_channel_death() - Module:
emergent_structural_insights
T-SI-4: The Fisher-weighted entropy integral equals 2ζ(2) = π²/3.
- Function:
theorem_TSI4_fisher_entropy_zeta_bridge() - Module:
emergent_structural_insights
T-SI-5: F + ω = 1 is the only exact symmetry; all others break by design.
- Function:
theorem_TSI5_symmetry_hierarchy() - Module:
emergent_structural_insights
T-SI-6: The Fisher metric is flat (g_F = 1); all complexity is extrinsic.
- Function:
theorem_TSI6_flat_base_extrinsic() - Module:
emergent_structural_insights
Kernel Structural Theorems
Source: closures/gcd/kernel_structural_theorems.py
T-KS-1: Dimensionality Fragility Law.
- Function:
theorem_TKS1_dimensionality_fragility() - Module:
kernel_structural_theorems
T-KS-2: Positional Democracy of Slaughter.
- Function:
theorem_TKS2_positional_democracy() - Module:
kernel_structural_theorems
T-KS-3: Weight-Induced Fragility Hierarchy.
- Function:
theorem_TKS3_weight_fragility() - Module:
kernel_structural_theorems
T-KS-4: Monitoring Paradox (Quantified).
- Function:
theorem_TKS4_monitoring_paradox() - Module:
kernel_structural_theorems
T-KS-5: Approximation Boundary.
- Function:
theorem_TKS5_approximation_boundary() - Module:
kernel_structural_theorems
T-KS-6: U-Curve of Degradation.
- Function:
theorem_TKS6_u_curve() - Module:
kernel_structural_theorems
T-KS-7: p=3 Unification Web.
- Function:
theorem_TKS7_p3_unification() - Module:
kernel_structural_theorems
Universal Regime Calibration
Source: closures/gcd/universal_regime_calibration.py
T-URC-1: Tier-1 Kernel Identities.
- Function:
theorem_T_URC_1_tier1() - Module:
universal_regime_calibration
T-URC-2: Universal Regime Concordance.
- Function:
theorem_T_URC_2_regime_concordance() - Module:
universal_regime_calibration
T-URC-3: Super-Exponential Repair.
- Function:
theorem_T_URC_3_super_exponential_repair() - Module:
universal_regime_calibration
T-URC-4: IC–Channel Vulnerability.
- Function:
theorem_T_URC_4_channel_vulnerability() - Module:
universal_regime_calibration
T-URC-5: Cross-Domain F Separation.
- Function:
theorem_T_URC_5_F_separation() - Module:
universal_regime_calibration
T-URC-6: Curvature–Regime Entailment.
- Function:
theorem_T_URC_6_curvature_entailment() - Module:
universal_regime_calibration
T-URC-7: Entropy–Regime Correlation.
- Function:
theorem_T_URC_7_entropy_correlation() - Module:
universal_regime_calibration
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