KP Field Propagation ​

IMPORTANT

Spine Position: /04-mathematics/simulations/kp-field-propagation

Simulation Boundary ​

SIMULATION BOUNDARY

The computations displayed on this page represent a Simulation Candidate (M4-SIMULATION classification). This is an algorithmic execution stress-test of internal mathematical invariants.

DO NOT interpret this output as empirical confirmation or formal theorem proof. The environment is strictly a computational model.

Interpretation Boundary ​

INTERPRETATION BOUNDARY

Any metrics or timeseries data derived from this simulation are strictly confined to the defined parameter space and cannot be generalized to physical reality without corresponding formalization and review (S5 classification).

Model Purpose ​

Evaluates the propagation of a scalar amplitude wave across a 2D coupling lattice while tracing finite topological energy dampening constraints.

Contract Summary ​

  • Class: Field Model
  • Status: Prototype
  • Language: Python

Parameters ​

  • width: Lattice width
  • height: Lattice height
  • steps: Number of propagation steps
  • seed: Deterministic PRNG seed
  • initial_amplitude_probability: Probability of non-zero amplitude at start
  • coupling_strength: Strength of interaction between neighboring cells
  • phase_shift: Constant phase drift applied per step
  • damping_rate: Energy loss coefficient per step
  • boundary_density: Density of fixed structural boundary support nodes
  • resonance_threshold: Threshold for amplitude + boundary support to trigger resonance
  • instability_threshold: Threshold for amplitude drift to be marked unstable

State Variables ​

  • amplitude: Scalar magnitude
  • phase: Phase angle
  • coupling: Accumulated coupling
  • damping: Accumulated damping
  • boundary_support: Topological structural node presence

Observables ​

  • mean_amplitude
  • mean_phase
  • resonance_count
  • instability_count
  • coupling_energy
  • damping_loss
  • boundary_support_ratio

Invariants ​

  1. KP1: amplitude remains finite
  2. KP2: damping loss is non-negative
  3. KP3: coupling energy remains bounded
  4. KP4: boundary support ratio remains measurable
  5. KP5: resonance count is diagnostic only, not validation

Failure Conditions ​

  • non-finite amplitude
  • negative damping loss
  • coupling energy above threshold
  • boundary support collapse
  • instability spike

Output Schema ​

The Python engine maps data arrays inside simulations/outputs/kp_field_default.json directly into the Vue telemetry layer:

Stability Tracking ​

Reproducibility ​

Run the engine locally:

bash
python simulations/python/run_kp_field_propagation.py

SIMULATION BOUNDARY

The computations displayed on this page represent a Simulation Candidate (M4-SIMULATION classification). This is an algorithmic execution stress-test of internal mathematical invariants.

DO NOT interpret this output as empirical confirmation or formal theorem proof. The environment is strictly a computational model.

INTERPRETATION BOUNDARY

Any metrics or timeseries data derived from this simulation are strictly confined to the defined parameter space and cannot be generalized to physical reality without corresponding formalization and review (S5 classification).