DynamisLab/src/steady_pinball_theory/RESULTS.md

Reset campaign results and claim matrix

All values below were generated from scratch after deletion of the previous project. Runtime arrays remain outside this source tree under /tmp/steady-*; these are diagnostic/production candidates, not a clean tagged archival release.

Sign oracle

Celeris source defines Cartesian lattice coordinates and (Uw,Vw)=(-omega*ry,omega*rx). With body order front, rear_y_plus, rear_y_minus, paired D20 runs at s=5, tU/D=250 give:

• [0,+Omega,-Omega]: direct q_ctl-q_in E_inf_vector(x/D=10)=0.13764; compact steady wake.
• [0,-Omega,+Omega]: E_inf_vector=0.64593; broad deficit/wake.

The accepted numerical cloak branch is therefore [0,+Omega,-Omega]. Its outer cardinal surfaces move upstream and its gap-facing cardinal surfaces downstream under the solver law; “outer-surface downstream boat-tail” is not an accurate description of this branch.

Rotation search

At D20, Re_D=50, H/D=15, uniform inlet and free-slip horizontal walls, the accepted branch was scanned from s=0 to 7 for tU/D=250. The direct profile objective falls from 1.046 at passive s=0 to 0.0232 near s=3.45-3.55, then rises to 0.0604 at s=4, 0.1376 at s=5, and 0.2972 at s=7. The current candidate interval is s=3.45-3.55; resolution of the flat pointwise maximum does not justify a unique optimum more precise than this interval.

Numerical sensitivity

At s=3.55, matched q-in references give E_inf={0.04549,0.02317,0.02348} for D={10,20,30}. D20 and D30 agree within 3.1e-4; D10 is not converged. Lateral half-height sensitivity at D20 gives E_inf=0.02382 for H/D=12, 0.02317 for 15, and 0.02478 for 18. Fine-grid D30 local values are 0.02353,0.02348,0.02921 at s=3.45,3.55,3.65.

Late-window changes in the scanned steady candidates are O(1e-5-1e-4) in the profile diagnostic. Neighboring cold-start cases at D30 (s=3.4,3.5,3.6,3.7) likewise settle over tU/D=250. This is empirical cold-start steadiness only; no checkpoint perturbation decay or global eigenanalysis has been completed.

Analytical representation and finite-Re interface

The MFS solver enforces cylinder no penetration and zero source per body for unbounded and image-strip formulations. Tests cover collocation order, source radius and image-layer sensitivity. A strip circulation scan predicts near cancellation at |Gamma|/(U D) about 4.25 (sign depends on body/circulation convention), with boundary residual below 1e-14 in that solve. Outer-mask fits to D30 CFD at s=3.45,3.55,3.65 yield signed Gamma_eff/(UD)=-4.293,-4.339,-4.384, close in magnitude to the inviscid cancellation value; residual component RMS is about 1.9-2.1% U. This supports a circulation-dominated outer mechanism but does not close boundary layers, pressure, force or separation.

Claim matrix

Supported now:

• exact numeric action/body mapping and action-reversal ordering;
• direct q-in profile metric at the historical x/D=10 plane;
• a D20/D30-converged low-error candidate interval near s=3.45-3.55 in the tested Celeris setup;
• numerical MFS no-penetration/image-strip representation and effective-circulation magnitude agreement.

Bounded/descriptive:

• empirical cold-start steadiness through tU/D=250;
• circulation-dominated outer-flow interpretation;
• lateral-domain sensitivity over H/D=12-18.

Not supported:

• global stability, unique attractor, perturbation decay, or exact optimum;
• independent Navier-Stokes reproduction (no independent NS package is installed);
• pressure/drag/base-bleed/separation closure;
• JFM-ready exact Schottky-Klein derivation or clean immutable production release;
• three-dimensional, experimental, energetic or other-Re generality.