Coherence-Gated Momentum Transfer — simulation code for
"Geometry-Limited Propulsion: An HLV–AILEE Formulation of Coherence-Gated Momentum Transfer"
Krüger & Feeney (2025)
Classical propulsion models absorb saturation losses into empirical efficiency terms. This repository implements the HLV–AILEE (Helix–Light–Vortex / Admissible-Interaction Lattice Energy–Exchange) formulation, which proposes a deeper explanation: momentum transfer is gated by the phase and geometric alignment between propulsion dynamics and an admissible host-lattice structure.
The central claim is that a coherence gate
controls realizable energy–momentum coupling. When alignment is good (Δφ ≈ 0), coupling proceeds normally. When alignment degrades, the gate collapses — and additional input power cannot compensate.
The model makes no reactionless or superluminal claims. All predictions are falsifiable. See §6 of the paper for the full falsification protocol.
A note on current status: The simulation code implements the HLV–AILEE mathematical framework faithfully and produces clean, falsifiable predictions. However, the bridge between the measurable Δφ proxies and the underlying lattice geometry remains theoretical — no empirical validation has been performed yet. What this repository provides is a numerically precise, testable formulation: the experiments needed to confirm or falsify it are the logical next step, and the measurement protocol in simulation_stub.ipynb and §7 of the paper is designed with exactly that in mind.
Geometry-Limited-Propulsion/
├── README.md
├── LICENSE
├── requirements.txt # Runtime dependencies
├── pyproject.toml # Build/system metadata
├── .gitignore # Common Python/Jupyter ignore rules
├── CITATION.cff # Citation metadata for GitHub/Zenodo
├── CONTRIBUTING.md # Contribution guidelines
├── CODE_OF_CONDUCT.md # Community standards
├── scripts/
│ └── run_verification.sh # Reproducible verification runner (install → test → snapshot)
├── src/
│ └── geometry_limited_propulsion/
│ ├── __init__.py # Package exports
│ ├── coherence_gate.py # Core gate function and velocity-gain law
│ ├── phase_alignment_metrics.py # Measurable Δφ proxies (Eqs. 7–9)
│ ├── lattice_reference.py # Derives f_lat, ψ_lat, and α from HLV geometry
│ └── simulation_stub.ipynb # End-to-end simulation notebook
├── tests/
│ └── test_coherence_gate.py # Unit tests for core gate behavior
├── figures/
│ ├── README.md # Caveat + per-figure descriptions
│ ├── generate_experimental_data.py # Generates all synthetic figures and CSV data
│ ├── fig1_thrust_vs_power.png # Gate-limited saturation: Δv vs. input power
│ ├── fig2_hysteresis_loop.png # Phase-window hysteresis: up/down timing sweep
│ ├── fig3_drifting_burn_timeseries.png # Drifting burn: Δφ, G(t), and cumulative Δv
│ ├── fig4_spectral_proxy_sweep.png # Spectral proxy Δφ_spec across frequency sweep
│ ├── fig5_gate_threshold_scan.png # Gate collapse scan with α calibration fit
│ └── fig6_proxy_summary_panel.png # All three proxies + composite G(t) summary
├── verification/
│ └── VERIFICATION_PLAN.md # Three-level plan for independent review
└── paper/
└── propulsion_hlv_ailee.md # Paper in Markdown (Unicode math)
A note on current status: The simulation code implements the HLV–AILEE mathematical framework faithfully and produces clean, falsifiable predictions. lattice_reference.py grounds the key free parameters (f_lat, ψ_lat, α) in the φ-harmonic structure of the quasicrystal geometry rather than leaving them as arbitrary user choices — making the full pipeline from theory to measurement deterministic for the first time. However, the bridge between these derived quantities and the physical host-lattice geometry remains theoretical: no empirical validation has been performed yet. What this repository provides is a numerically precise, testable formulation. The experiments needed to confirm or falsify it are the logical next step, and the measurement protocol in simulation_stub.ipynb and §7 of the paper is designed with exactly that in mind.
1. Clone and install dependencies
git clone https://github.com/dfeen87/Geometry-Limited-Propulsion.git
cd Geometry-Limited-Propulsion
pip install -r requirements.txt
# Optional (needed only for delta_phi_spectral):
pip install scipySciPy is optional — it is only required for the spectral proxy (delta_phi_spectral). All other functionality runs on NumPy alone.
2. Run the notebook
cd src
jupyter notebook simulation_stub.ipynb3. Use the library directly
import numpy as np
from coherence_gate import coherence_gate, hlv_ailee_delta_v
# Gate value at a given phase deviation
G = coherence_gate(delta_phi=0.5, alpha=2.0)
print(f"G = {G:.4f}") # → 0.7788
# Gated velocity gain over a burn
N = 500
t = np.linspace(0, 100, N)
p_in = np.full(N, 5e5) # 500 kW constant
mass = np.linspace(1000, 600, N) # propellant burn [kg]
velocity = np.linspace(100, 400, N) # reference trajectory [m/s]
delta_phi = 0.05 + 0.8 * (t / t[-1])**2 # slowly drifting misalignment
dv = hlv_ailee_delta_v(
t, mass, delta_phi,
isp=350.0, eta=0.85, alpha=2.0,
mode='power',
p_in=p_in,
velocity=velocity,
)
print(f"Δv = {dv:.2f} m/s")scripts/run_verification.sh provides a single-command reproducibility check:
bash scripts/run_verification.shIt performs three steps in sequence:
| Step | Action |
|---|---|
| 1 | Install the package in editable mode (pip install -e .) |
| 2 | Run the full unit-test suite (pytest -q) |
| 3 | Record the current commit hash and write a sorted dependency snapshot to verification/requirements-lock.txt |
The script requires only a standard Python environment with pip and pytest available.
verification/VERIFICATION_PLAN.md defines a three-level plan for independent review:
| Level | Scope | Key pass criteria |
|---|---|---|
| 1 — Code Reliability (immediate) | Isolated install + unit tests | All tests pass; results repeat on two consecutive runs |
| 2 — Numerical Consistency (short-term) | Deterministic sweeps; notebook figure reproduction | Curves stable under fixed seed/config; no sign or unit errors |
| 3 — Experimental Readiness (medium-term) | Pre-registered perturbation protocol; data schema | Independent reviewer can reproduce headline plots from raw data |
Recommended next artifacts (per the plan): verification/baseline_results.json, verification/reproduce_notebook.py, and verification/data_schema.md.
| Function | Description |
|---|---|
coherence_gate(delta_phi, alpha) |
Gate function G(t) = exp(−α·Δφ²); returns values in (0, 1] |
classical_delta_v(isp, m0, mf) |
Tsiolkovsky baseline Δv = Isp·g₀·ln(M₀/Mf) |
hlv_ailee_delta_v(t, mass, delta_phi, isp, eta, alpha, *, mode='power', p_in, velocity) |
mode='power' (electric/ion): gated velocity gain via power integral — requires p_in and velocity arrays |
hlv_ailee_delta_v(t, mass, delta_phi, isp, eta, alpha, *, mode='rocket', m_dot) |
mode='rocket' (chemical): gated Tsiolkovsky integration — requires m_dot array; eta is unused |
gate_vs_phase_sweep(delta_phi_values, alpha) |
Sweep G over a range of Δφ — useful for plotting acceptance-window shape |
hysteresis_sweep(phi_up, phi_down, alpha_up, alpha_down) |
Asymmetric up/down sweep for hysteresis loop visualization (Figure 2) |
| Function | Proxy | Paper equation |
|---|---|---|
delta_phi_temporal(f_sys, f_lat) |
Fractional frequency mismatch | Eq. 7 |
delta_phi_spatial(vflow, dx, dy) |
Vorticity-to-speed ratio via 2-D curl | Eq. 8 |
delta_phi_spectral(thrust, lat, sr) |
L¹ distance between normalised PSDs | Eq. 9 |
composite_delta_phi(*proxies, weights) |
Weighted RMS combination of any proxies | — |
The table below summarises how HLV–AILEE predictions differ from classical expectations, and how each can be tested.
| Observable | Classical expectation | HLV–AILEE prediction | Test |
|---|---|---|---|
| Thrust vs. power | Smooth saturation | Threshold-like collapse beyond Δφ window | Sweep power at fixed geometry; look for non-linearity |
| Timing offsets | Small, continuous degradation | Sharp non-linear drop sensitive to phase drift | Introduce controlled timing offsets |
| Ignition / shutdown history | Mostly irrelevant | Hysteresis / path dependence | Up/down sweeps of timing and geometry controls |
| Reduced-power regime | Lower Δv | Potential "sweet spot" under improved alignment | Reduce power while improving phase alignment |
The model is falsified if:
- No measurable correlation exists between Δφ proxies and coupling efficiency,
- Increased power fully compensates induced misalignment (no gate-collapse regime), or
- Controlled phase drift produces no threshold-like degradation or hysteresis.
simulation_stub.ipynb covers six sections:
- Gate shape — G(Δφ) plotted for α ∈ {0.5, 1.0, 2.0, 5.0}; shows narrowing acceptance window with increasing sharpness.
- Hysteresis loop — Asymmetric α values on up/down sweep branches reproduce Figure 2 of the paper, with shaded hysteresis window.
- Δv vs. power — Three-way comparison (Δφ = 0, 0.3, 1.2) demonstrates gate-limited saturation vs. classical linear scaling.
- Temporal proxy — Simulated frequency drift mapped through Eq. 7; plots f_sys(t) alongside Δφ_temp(t).
- Spectral proxy — Welch PSD comparison of a 50 Hz thrust tone against aligned and misaligned lattice references; Δφ_spec printed for each case.
- Full integration — Three-panel plot: (i) time-varying Δφ and composite, (ii) gate G(t) over the burn, (iii) cumulative Δv gated vs. ungated with final suppression factor.
For physical experiments, Section 7 of the paper outlines a four-phase protocol:
Phase 1 — Baseline
Measure thrust, Isp, input power, spectra.
Log geometry and environment.
Phase 2 — Perturbations
Introduce timing offsets.
Modulate geometry.
Induce controlled phase drift.
Record ignition/shutdown sequences.
Phase 3 — Analysis
Fit α from observed threshold data.
Plot hysteresis loops (up vs. down sweeps).
Compare against null/surrogate baselines.
Phase 4 — Replication
Pre-register all metrics and thresholds.
Release raw data and configuration.
Independent lab replication.
If you use this code in your work, please cite the paper:
@misc{kruger_feeney_2025_hlv_ailee,
author = {Krüger, Marcel and Feeney, Don},
title = {Geometry-Limited Propulsion: An {HLV–AILEE} Formulation
of Coherence-Gated Momentum Transfer},
year = {2025},
note = {Manuscript draft},
}The HLV mathematical framework this builds on:
@misc{kruger_2025_hlv,
author = {Krüger, Marcel},
title = {A Mathematical Unification of the Helix–Light–Vortex ({HLV})
Framework: Discrete Geometry, Spiral Time, Unified
Lagrangians, and {TOE}-Level Structure},
year = {2025},
publisher = {Zenodo},
}Marcel Krüger · Independent Researcher, HLV–RFP (Meiningen, Germany)
✉ marcelkrueger092@gmail.com · ORCID 0009-0002-5709-9729
Don Feeney · Independent Researcher (Pennsylvania, USA)
✉ dfeen87@gmail.com · ORCID 0009-0003-1350-4160
This project is released under the MIT License.
We acknowledge Claude (Anthropic) for assistance with simulation code development and contributions to PAPER.md. We also thank Codex (OpenAI) and Copilot (Microsoft) for final code‑review support prior to versioned releases. All scientific content, theoretical constructs, and experimental claims originate solely from the authors.