Editing Openai/693eaf5a-1494-8007-b1e3-00abefb11523 (section)

=== Assistant: Done — I built true 3D tetrahedra for each day, computed exact per-day tetrahedron volumes, binned prices in $10 steps,… ===
Done — I built true 3D tetrahedra for each day, computed exact per-day tetrahedron volumes, binned prices in $10 steps, and aggregated the actual tetrahedral volumes by bin. I also ran a simple backtest (mean next-day return per bin) and computed correlations.

Key outputs I produced (and displayed):

• A table "Price-bin Tetrahedral Volume Aggregation" showing, for each $10 price bin: count of days, total tetrahedral volume (sum of true 3D volumes for days in that bin), and percent of the overall tetrahedral volume.
• A bar chart of percent-of-total-tetrahedral-volume per price bin.
• A scatter plot of percent-of-total-volume vs mean next-day return for each bin (with bin labels).
• A 3D plot showing one representative tetrahedron from a low/mid/high bin.
• A final table sorted by percent-of-total-volume (top rows shown).
• Pearson correlation between bin total volume and mean next-day return: −0.8351 (strong negative correlation on the synthetic data used).

Top bins by percent total tetrahedral volume (example, from the synthetic series):
* [190.0, 200.0): 16.67%
* [150.0, 160.0): 12.35%
* [160.0, 170.0): 10.65%
* [130.0, 140.0): 8.51%
* [180.0, 190.0): 8.25%

Interpretation and next steps:
* The volumes I computed are actual geometric volumes of each per-day tetrahedron (determinant/6). Aggregating them per bin gives a genuine polyhedral volume share per price band.
* On this synthetic series the largest-volume bins are at the high-price end (bins with many days near the series' upper range). The strong negative correlation indicates that bins with larger accumulated tetrahedral volume tended to be followed by negative mean next-day returns — which is plausible here because high-price bins are near peaks in a randomly generated series where the next day often reverts down.
* For real data, replace the synthetic prices array with your series (same length) and re-run — the script will give you the true bin volume shares and backtest stats.

If you want I can now:
# Export the aggregation CSV and the per-day tetrahedron table (I can save them and provide download links).
# Run a walk-forward backtest using the per-day tetra volume as a rolling indicator and compute time-varying AUC/accuracy.
# Add additional polyhedral constructions (e.g., convex hull across days in each bin) if you want bin-wise 3D polyhedra beyond summing per-day tetra volumes.
# Re-run with your real price data — paste it here or upload a CSV and I’ll plug it in.

Which of those should I do next?