Reproducibility supplement
Long-wavelength stability and finite-wavelength instability of a coherent neutrino equilibrium
6 November 2026

Requirements: Python 3.9 or later, standard library only. No network access,
package installation or external files are needed. Unzip into any directory.
Do not run Python with -O: assertions perform certificate checks.

Run from any working directory:
  python3 verify_state.py
  python3 verify_longwave.py
  python3 verify_continuum.py

The first two commands normally complete in less than a second. The last
regenerates both continuous-angle certificates and may take several minutes.
It prints panel progress, tail bounds, winding number 1 and a nonzero minor.
Scripts read data/ and print results; they do not overwrite saved certificates.

verify_state.py reconstructs the rational equilibrium from the article's
formulas, verifies its eight residuals and strict positivity, reconstructs
sector characteristic polynomials and Routh signs, and compares 192 Jacobian
entries with direct differentiation of the 2x2 matrix laws.

verify_longwave.py checks exact rational phase vectors and projections,
Lyapunov positivity/dissipation and inverse norms, two phase-diffusion
coefficient calculations, local dissipation, contour resolvent estimates,
Cauchy remainder, moving-complement estimates and the final K=8370547 bound.
The finite inequalities are checked; the functional-analytic proof is in
the accompanying article.

verify_continuum.py recomputes the rational operator and continuous-angle
resolvent integral, with directed Decimal intervals, 128 angular panels,
and Taylor orders 16 and 32. It regenerates whole-edge determinant hulls,
checks their winding +1 and a whole-box nonzero rank-five minor. The higher
order run constructs the Jacobian from the density-matrix commutator and
anticommutator. Both runs share the interval arithmetic engine; they are
not two unrelated validation implementations. Saved interval coefficients
and root certificates are included for inspection, but the verifier does
not accept their success flags as proof. Reality of the unique root and
nonzero continuum eigenfunction reconstruction are analytical consequences
explained in the article.

Expected real eigenvalue enclosure at q=3/64:
  16548364370979/144115188075855872 < sigma
  sigma < 51741326394403/144115188075855872
Longwave interval: |q| <= 2^-62. Physical norm bound: K=8370547.
The radius and K are conservative sufficient bounds, not measurements.

Files:
  data/state.json: exact rational state (the positive sqrt(U) is implicit)
  data/operator.json: rational A,B,C,M0,M1 matrices
  data/*certificate.json: rational/interval finite witnesses
  data/*integral-coefficients.json: saved polynomial interval coefficients
  exact.py, algebra.py: exact rational operations and sector matrices
  matrix_audit.py: direct 2x2 density-matrix differentiation
  intervals.py: directed rectangular interval arithmetic
  SHA256SUMS: file integrity values, not scientific validation

Scope: vacuum-free, single-energy, two-flavor, axial perturbations and fixed
isotropic diagonal reservoirs. No source trajectory, physical wavelength,
rounding robustness, full instability band or nonlinear outcome is claimed.
No astrophysical simulation or observational dataset is included.
