UDEL · Threshold / Cascade Toy Simulator

Recoil Simulator

Five models of merger progress — linear drift, threshold activation, cascade snap, bounded cascade, and direct 4D gap-driven dynamics — with live parameter control and habitability collapse tracking.

Core Parameters

α — baseline drift 0.30

β — threshold amplitude 0.55

k — threshold sharpness 22.0

τ_c — threshold onset 0.45

γ — cascade steepness 6.0

μ — habitability sensitivity 3.0

4D Gap Parameters

Δ₀ — initial gap 1.00

Δ_c — critical gap 0.55

ε — gap smoothness 0.03

Warning Thresholds

R warning 1.20

R critical 1.50

H warning 0.50

H critical 0.10

Merger Progress τ 0.000

R_lin (final) — merger indicator

R_threshold (final) — merger indicator

R_cascade (bounded) — merger indicator

H_cascade (final) — habitability

τ_c from gap model — matches τ_c manual

Linear

Threshold

Cascade

Cascade (bounded)

R warning / critical

Merger Indicator R(τ) — Linear vs Threshold vs Cascade

Linear

Threshold

Cascade

Cascade (bounded)

Habitability H(τ) = exp(−μ·(R−1)) — Collapse under different regimes

4D inter-slice gap Δ(τ) — linear closure toward Δ_c

4D coupling activation C(Δ) — sigmoid triggered at critical gap

Gap-driven threshold

Gap-driven cascade

Direct 4D-gap-driven R(τ) models

Threshold Crossings — τ values

Model	R ≥ R_warn	R ≥ R_crit	H ≤ H_warn	H ≤ H_crit

This is a conceptual model only. Parameters are illustrative, not DESI-calibrated. A result matching default values defines what to look for — not confirmation of recoil. See the Claim Boundaries document.

How to Run the Python Simulation Locally

1. Install Python 3


                # Windows

                python.org → Download → ✔ Add to PATH


                # macOS

                brew install python3


                # Linux

                sudo apt install python3 python3-pip

2. Install packages & run


                pip install numpy matplotlib scipy


                # Place the .py file in a folder, then:

                cd C:\UDEL

                python Recoil.py

More simulations and the full physics suite: tales.zone/physics/simulations ↗