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Reproduce

A one-command determinism receipt for a tested module: the sheaf (connection) Laplacian. The output below was produced by an actual seeded run (numpy default_rng(0) / default_rng(2)), is bit-for-bit identical across repeated runs, and matches the invariants asserted in tests/test_sheaf_laplacian.py (the general, non-orthogonal case).

Environment

  • Python 3.10, 3.11, or 3.12 (not 3.13+; the numpy<2.0 / scipy<1.14 pins required by geomstats have no wheels there -- see LIMITATIONS.md).
  • Pins used to produce the receipt below: numpy 1.26.4, scipy 1.13.1, geomstats 2.8.0 (resolved by the constraints in pyproject.toml).

Install

git clone https://github.com/smaniches/GROUPOID.git
cd GROUPOID
pip install -e ".[dev]"

Run

pip install -e ".[dev]"          # one-time, if not already installed
python scripts/reproduce_sheaf_laplacian.py

groupoid logs at DEBUG by default. To see only the receipt, set the log level (the receipt itself prints on stdout regardless):

# Linux / macOS
LOGURU_LEVEL=WARNING python scripts/reproduce_sheaf_laplacian.py
# Windows PowerShell
$env:LOGURU_LEVEL="WARNING"; python scripts/reproduce_sheaf_laplacian.py

Expected output (deterministic, exact)

seed                     : 0
graph                    : nodes=['A', 'B', 'C', 'D'] edges=[('A', 'B'), ('A', 'C'), ('B', 'D'), ('C', 'D')]
stalk_dim                : 3
L shape                  : (12, 12)
max|L - deltaT_delta|    : 4.441e-16   (expect < 1e-12)
max|L - L^T| (symmetry)  : 0.000e+00   (expect < 1e-12)
min eigenvalue (PSD)     : 2.813e-02   (expect >= -1e-9)
||L @ consistent_section|| : 6.189e-16   (expect < 1e-9, in kernel)
||L @ constant_section||   : 3.368e+00   (expect > 1e-3, NOT in kernel)
dim ker(L)                 : 3   (expect == stalk_dim = 3)
RESULT: sheaf-Laplacian invariants hold (deltaT-delta, PSD, kernel).

The floating-point residuals (4.441e-16, 6.189e-16) are at machine epsilon and may differ in the last digit on a different BLAS/CPU; the bracketed tolerances (< 1e-12, < 1e-9, > 1e-3, == 3) are the contract and hold across platforms. The integer dim ker(L) = 3 and min eigenvalue sign are exact invariants, not approximations.

What this proves

  • L == delta^T delta against an independently constructed coboundary delta (not reusing the builder's block formula).
  • L is symmetric and positive-semidefinite (min eigenvalue >= 0).
  • For orthogonal transport R_uv = g_v g_u^{-1}, transport-consistent global sections lie in ker(L), constant sections do not, and dim ker(L) equals the stalk dimension (no spurious kernel).

To run the full property-based test suite (Hypothesis, 500 examples per property) instead of this single receipt:

pytest tests/ -v