// KERNEL-DAMPING EVIDENCE

Reproducible Structural Risk-Transition Analysis.

The Kernel-Damping Evidence Protocol documents a reproducible analysis-layer calculation for the SORT-AI Core-3 applications. It tests whether declared structural risk-transition scenarios admit a Gaussian kernel-damping reconstruction under the canonical SORT scale parameter σ0 = 0.00190643. The protocol is not a production benchmark, not a vendor telemetry study, and not a runtime optimization result. It is a reproducibility protocol for declared structural scenario fixtures.

Why an Evidence Protocol Is Required

The SORT-AI domain architecture defines structural problem forms, but a public research program also requires reproducible evidence artefacts. The evidence protocol specifies how declared scenario metrics are converted into risk variables, how risk transitions are mapped to damping quotients, how implied structure-mode magnitudes are computed, and how scenario-level dispersion and classification are reproduced. Its purpose is to make the Core-3 calculation inspectable, repeatable, and bounded.

INPUT

Declared Scenario Fixtures

Each scenario provides declared metric values and transformation rules. The release does not claim that these values are live vendor telemetry.

RECONSTRUCTION

Kernel-Damping Calculation

Risk transitions are converted into damping quotients κ and reconstructed through a fixed Gaussian kernel form to obtain implied structure-mode magnitudes ξ.

OUTPUT

Scenario Coherence

Scenario means, sample dispersions, and coefficients of variation are computed to classify structural coherence across Core, Boundary, and Overlap regimes.

Evidence Release Scope

  • Release IDsort_ai_core3_kernel_damping_v1
  • Version1.0.0-draft
  • Statusanalysis-layer evidence release
  • Canonical scale parameterσ0 = 0.00190643
  • MOCK dependencyMOCK v4 frozen structural reference architecture

The Core-3 set was selected because it spans three complementary coupling regimes in advanced AI systems. AI.01 represents physical and interconnect coupling. AI.04 represents logical and runtime-control coupling. AI.13 represents semantic and agentic coupling. The protocol applies the same reconstruction method across these distinct axes to test whether a common declared kernel-damping representation remains reproducible.

AI.01 · CLUSTER A

Interconnect Stability Control

Physical / interconnect coupling. 7 scenarios, 36 metrics.

AI.04 · CLUSTER C

Runtime Control Coherence

Logical / runtime-control coupling. 6 scenarios, 32 metrics.

AI.13 · CLUSTER D

Agentic System Stability

Semantic / agentic coupling. 7 scenarios, 36 metrics.

Kernel-Damping Reconstruction

κ_i = r_i(1) / r_i(0) κ_σ0(ξ_i) = exp[-(σ0 ξ_i)^2 / 2] ξ_i = sqrt(-2 ln κ_i) / σ0 σ0 = 0.00190643
  • κ is the damping quotient.
  • ξ is the implied structure-mode magnitude.
  • σ0 is fixed and is not re-fitted from AI telemetry.

Each metric is represented as a pair of declared risk values, r_i(0) and r_i(1). The quotient κ_i expresses the damping ratio between the comparison risk state and the baseline risk state. The Gaussian kernel form maps this quotient to an implied structure-mode magnitude ξ_i under the fixed canonical scale parameter σ0. No parameter is fitted from production telemetry in this procedure.

Risk Transformation and Classification

All variables are converted into risk variables, where lower is better. This allows heterogeneous scenario metrics to enter a common risk-transition representation. The coefficient of variation is then computed per scenario from the resulting ξ values. Lower CV values indicate a more internally coherent declared scenario class under the protocol; higher values indicate mixed or outlier-dominated behavior.

TransformationDefinition
identityr = x
riskr = x
healthr = 1 - x
multiplierr = x - 1

Coefficient-of-variation (CV) classification:

CV rangeRegime
CV ≤ 0.15coherent
0.15 < CV ≤ 0.25acceptable mixed / overlap
CV > 0.25unstable / outlier-dominated

Expected Outputs

The expected outputs define the reference reproduction state. A local run recomputes κ, ξ, scenario means, sample standard deviations, and coefficients of variation from the declared risk vectors and compares the generated results against the committed expected outputs.

  • applications3
  • scenarios20
  • metrics104
  • overall ξ mean969.35
  • overall ξ sample standard deviation137.0
  • overall CV0.141
  • overall classificationcoherent

Reproducibility Package

Repository structure:

evidence_releases/sort_ai_core3_kernel_damping_v1/
  data/
  docs/
  scripts/
  outputs_expected/
  outputs_generated/
  manifest.json
  CITATION.cff
  requirements.txt

Reproduction command:

cd evidence_releases/sort_ai_core3_kernel_damping_v1
python scripts/run_all.py

The script recomputes kappa, xi, scenario means, sample standard deviations, and coefficients of variation from the declared risk vectors.

Non-Claims

This evidence release does not claim production deployment, empirical benchmarking, vendor-specific measurement, runtime optimization, or execution by MOCK v4. It demonstrates reproducible structural calculation, not external system performance.