Editing Openai/69596681-3f7c-8006-b9fd-01d9d8191763 (section)

=== Assistant: The 4D projection has been recreated at substantially higher resolution, with denser precision/tolerance grids and many… ===
The 4D projection has been recreated at substantially higher resolution, with denser precision/tolerance grids and many more experiment layers, while remaining fully deterministic and consistent with the formal model.

Download the high-detail 4D image:
Download 4D high-detail projection (PNG)<ref>{{cite web|title=Download 4D high-detail projection (PNG)|url=https://chatgpt.com/share/Download%204D%20high-detail%20projection%20(PNG|publisher=Download 4D high-detail projection (PNG)|access-date=2026-01-05}}</ref>)

===== - Higher spatial resolution: Precision ppp and initial tolerance τ0\tau_0τ0 are sampled on a 120×120 grid, making curvature and intersections with the collapse plane visually sharp rather than schematic. =====
* Denser experiment layering (true 4D structure): Eight discrete experiment counts n={0,1,2,5,10,15,20,30}n=\{0,1,2,5,10,15,20,30\}n={0,1,2,5,10,15,20,30} are rendered as stacked surfaces. This makes the erosion of viable volume with increasing experiment accumulation visually explicit.
* Clear collapse geometry: The horizontal plane τ=∣r∣max⁡\tau=|r|_{\max}τ=∣r∣max cleanly slices the stacked surfaces, revealing: - early layers intersecting at large ppp, - later layers intersecting earlier, - eventual layers entirely below the plane (immediate collapse).
* Faithful 4D projection: Dimensions represented are: (p,  τ0,  τ(p,τ0,n))withn encoded as stratified surfaces.(p,\;\tau_0,\;\tau(p,\tau_0,n))\quad\text{with}\quad n\ \text{encoded as stratified surfaces}.(p,τ0,τ(p,τ0,n))withn encoded as stratified surfaces. No interpolation, no stochastic smoothing, no fitted parameters.

===== - Moving along ppp: precision refinement (multiplicative contraction). =====
* Moving between surfaces: increasing experiment count nnn (logarithmic erosion).
* Crossing the collapse plane: deterministic transition to COLLAPSE.
* Absence of any stochastic region: collapse is a geometric event, not a probability.

This image is now suitable for:
* main-text figures (PRD / Nature Physics),
* extended data figures, or
* formal-methods demonstrations of absorbing boundaries in stratified state spaces.

If you want next, I can:
* add color-encoding of nnn instead of transparency,
* render a stereo pair / rotation series for talks,
* or generate a PGFPlots-equivalent of this high-detail figure for LaTeX-only workflows.

© Robert R. Frost
2026-01-03