Curated Paper III results

The release contains one complete stationary-continuation study and two selected time-integration figure families. These are the only reader-facing numerical objects. The larger historical archive is preserved for provenance, but folder names and legacy galleries do not define evidence status.

Stationary continuation across four regimes

Validated current · v1 4 cases · 3 meshes · 8 amplitudes · 96 states

The local coefficient, measured independently

Instead of integrating in time, this experiment prescribes the signed first-cosine amplitude and solves the stationary finite-difference equations. For each mesh it fits

\[ \chi_h(A)-\chi_h^*=c_{2,h}A^2+c_{4,h}A^4, \]

then compares \(c_{2,h}\) with the analytical value \(\beta_{n_0}/\alpha_{n_0}\).

Case	Direction	Theory \(c_2\)	\(c_{2,160}\)	Finest relative error
Non-minimal a=10, beta=0	Supercritical	0.0084254463	0.0084220572	4.02e-4
Non-minimal beta=3	Subcritical	-19.66671032	-19.64492609	1.11e-3
Minimal m=gamma=1	Supercritical	1.922989917	1.922366447	3.24e-4
Minimal m=gamma=2	Subcritical	-1.148587331	-1.150522206	1.68e-3

The coefficient errors refine at observed order 1.998--2.009. All 780 of 780 acceptance gates pass. The largest full stationary u residual is 8.51e-11, the largest independently reconstructed elliptic residual is 1.14e-10, and the largest fixed-mass error is 3.33e-16.

Immutable v1 bundle Fit summary Checksums Vector figure

Near-threshold time integration

These two three-panel composites are the time-dependent figures retained in the manuscript. They use fixed perturbations and report semidiscrete behavior on the named archives.

Quasi-linear supercritical benchmark

Validated current Logistic equilibrium · mode n = 1

Parameters: a=10, b=alpha=m=gamma=mu=nu=L=1, beta=0

The full center-graph calculation gives

\[ \chi^*=2.188281623751274, \qquad \beta_{1}=0.076503080515203>0. \]

The below-threshold trajectory returns toward the constant state; the two above-threshold trajectories approach symmetry-related patterns. For the 1%-above run, the final cosine amplitude is 1.62372574646, compared with the leading-order prediction 1.61159217017.

Raw validated family Corrected constants Vector figure

Nonlinear-mobility supercritical benchmark

Validated current Logistic equilibrium · mode n = 1

Parameters: a=b=alpha=1, m=2, beta=1, gamma=2, mu=nu=L=1

The corrected analytical values are

\[ \chi^*=11.970925584731697, \qquad \beta_{1}=9.508880363384589>0. \]

Fixed positive and negative seeds above threshold produce opposite patterned trajectories, while the selected below-threshold run decays. This family tests nonlinear chemotactic mobility and nonlinear signal production.

Raw validated family Corrected constants Vector figure

Provenance boundary

Four earlier families remain versioned but are excluded from the current contract: two time-dependent minimal-model archives with conservation or classification problems, the obsolete beta=3 coefficient-seeded runs, and the reclassified all-ones coefficient-seeded runs. Their exact Git paths and reasons are recorded under provenance_only in the manifest; this page intentionally provides no galleries or preview links for them.

Scientific scope

The figures and fitted coefficients are evidence about the spatially semidiscrete computations. The continuous-PDE conclusions come from the manuscript's analysis.

Machine-readable record

The Paper III evidence manifest freezes the two evidence layers, all source revisions, figure hashes, v1 checksums, case IDs, branch slopes, acceptance metrics, and provenance exclusions. CI resolves every declared object from Git and rejects a reader-facing link to any provenance-only raw family.