Argos Source Lapse

Public-scope note: This is a reproducible numerical toy model. It does not claim to derive gravity, reproduce general relativity, or establish B★(t) as physical theory.

A small, auditable numerical toy model for a bounded question:

Can a prescribed 2D source distribution (\rho(x,y)) generate a scalar field (\chi(x,y)) through a Poisson-like equation, and can (N = \exp(\chi)) serve as a visualized local clock-rate proxy?

Its purpose is to build a reproducible toy operator with explicit assumptions, controls, diagnostics, and failure modes.

Initial model

[ \nabla^2 \chi = \kappa \rho ]

[ N = \exp(\chi) ]

[ \frac{d\tau}{dt} = N ]

The initial baseline uses a centered Gaussian source on a 2D Cartesian grid with homogeneous Dirichlet boundary conditions:

[ \chi = 0 ]

at the outer edge of the numerical domain.

Baseline outputs

• source-density map
• scalar-field map (\chi)
• lapse proxy map (N)
• gradient-field visualization
• clock ratios between named sample points
• machine-readable diagnostics and run manifest

Setup

From this repository:

python3 -m venv .venv
source .venv/bin/activate
python3 -m pip install -e ".[dev]"

Run

Run the test suite:

python3 -m pytest

Generate the deterministic baseline artifacts:

python3 scripts/run_baseline.py

The baseline writes these files under artifacts/:

• source_density.png
• chi_field.png
• lapse_field.png
• gradient_field.png
• summary.json
• diagnostics.csv
• run_manifest.json

The same baseline can also be run through the installed console script:

argos-source-lapse --output-dir artifacts

Run one v0.2 source-geometry scenario explicitly:

python3 scripts/run_baseline.py --scenario centered_gaussian --output-dir artifacts/v0_2_centered_gaussian
python3 scripts/run_baseline.py --scenario two_gaussian --output-dir artifacts/v0_2_two_gaussian
python3 scripts/run_baseline.py --scenario elliptical_gaussian --output-dir artifacts/v0_2_elliptical_gaussian

Run all v0.2 scenarios and the combined comparison artifacts:

python3 scripts/run_baseline.py --scenario all --output-dir artifacts

The v0.2 all-mode writes:

• artifacts/v0_2_centered_gaussian/
• artifacts/v0_2_two_gaussian/
• artifacts/v0_2_elliptical_gaussian/
• artifacts/v0_2_comparison/

See docs/V0_2_SOURCE_GEOMETRY.md before interpreting the v0.2 outputs.

Numerical conventions

The implemented finite-difference equation is

[ \nabla_h^2 \chi = \kappa\rho ]

on a square Cartesian grid. The outer grid boundary is fixed to (\chi=0). With positive (\kappa) and positive source density, this sign convention gives a negative interior (\chi) field for the baseline Dirichlet problem. The lapse proxy is then computed pointwise as (N=\exp(\chi)).

The centered Gaussian is scaled so its discrete numerical integral, (\sum_{ij}\rho_{ij}\Delta x\Delta y), matches the requested source strength. No fitting to Schwarzschild, Newtonian trajectories, or external gravitational data is performed.

Initial acceptance criteria

The baseline is only accepted when all of these are reported:

1. flat control: (\rho=0 \Rightarrow \chi \approx 0,\ N \approx 1)
2. source normalization is correct
3. the interior Poisson residual is within the declared tolerance
4. a centered circular source produces an approximately radially symmetric field
5. selected observables are stable under grid refinement

Read docs/MODEL_SCOPE.md, docs/TEST_PLAN.md, and docs/RESULTS_INTERPRETATION.md before interpreting output.