Update dataset: add polynomial r^n survey, fractional exponent sweeps (201 rows)

New data (April 2026):
- Polynomial r^n exact symbolic survey: r^1 through r^10 (N=3, d=1, L3)
- r^1 [3,4,5,5], r^2 [3,6,13,15], r^3 [3,6,17,109], r^4-r^10 all [3,6,17,116]
- 1/r^n fractional exponent sweep: 21 exponents (N=3 L3) + 9 exponents (N=4 L2)
- r^n numerical exponent sweep: 12 successful of 20 tested
- dimension_sequences grew from 45 to 93 rows
- Total dataset: 201 rows across 9 tables (up from 153)
- Updated README with expanded potential coverage and key results

README.md

@@ -52,7 +52,7 @@ configs:
 This dataset contains the first systematic computation of **pairwise Poisson bracket algebras** arising from the classical and quantum N-body problem. For each configuration of N gravitating (or otherwise interacting) bodies in d spatial dimensions under a pairwise potential V(r), we compute the Lie algebra generated by iterated Poisson brackets of the pairwise interaction terms {H_ij}, starting from the N(N-1)/2 pairwise Hamiltonians.
 
 The dataset spans:
-- **6 values of N** (3 through 8) with exact dimension sequences
+- **N = 3 through 50** with exact dimension sequences (L0 through N=50, L1 through N=26, L2 through N=9)
 - **9 distinct potentials** with full 17x17x17 exact rational structure constant tensors
 - **15 named physical systems** from helium atoms to triple black holes
 - **18 charge configurations** testing charge-independence of the algebra
@@ -110,7 +110,7 @@ This algebra is graded by bracket depth (level): level 0 contains the generators
 
 ### Key Results in This Dataset
 
-1. **Potential universality**: For N=3 with 1/r, 1/r^2, 1/r^3, log, and composite potentials, the dimension sequence is universally [3, 6, 17, 116]. Only harmonic (r^2) differs: [3, 6, 13, 15, 15] (stabilizes -- integrable system).
+1. **Potential universality**: For N=3 with 1/r, 1/r^2, 1/r^3, log, composite, and polynomial r^n (n≥4) potentials, the dimension sequence is universally [3, 6, 17, 116]. Three exceptional potentials: r^1 → [3,4,5,5] (finite), r^2 → [3,6,13,15] (finite), r^3 → [3,6,17,109] (7 extra relations). Universality extends to fractional exponents (21 tested for 1/r^n, 12 for r^n).
 
 2. **N-body scaling**: L_0(N) = N(N-1)/2, L_1(N) = N(3N-5)/2, L_2(N) = N(4N^2-9N+3)/2 for N >= 4.
 
@@ -126,7 +126,7 @@ This algebra is graded by bracket depth (level): level 0 contains the generators
 
 ## Dataset Splits
 
-### `dimension_sequences` (45 rows)
+### `dimension_sequences` (~85 rows)
 
 The headline table. One row per (N, d, potential, bracket_type) configuration. Includes flattened `dim_L0`..`dim_L4` integer columns for easy filtering in the HF Dataset Viewer, plus the full JSON `dimension_sequence`.
 
@@ -134,7 +134,7 @@ The headline table. One row per (N, d, potential, bracket_type) configuration. I
 |--------|------|-------------|
 | `N` | int | Number of bodies (3--8) |
 | `d` | int | Spatial dimensions (1--2) |
-| `potential` | str | Interaction potential: "1/r", "1/r^2", "1/r^3", "1/r^4", "r^2", "r^4", "log", "composite(...)", "neural" |
+| `potential` | str | Interaction potential: "1/r", "1/r^2", "1/r^3", "1/r^4", "r^1"--"r^10", "log", "composite(...)", "neural" |
 | `bracket_type` | str | "poisson" (classical) or "moyal" (quantum) |
 | `masses` | str/null | JSON-encoded mass list, e.g. '["1","2","3"]' or '"symbolic"' |
 | `charges` | str/null | JSON-encoded charge list, e.g. '[2,-1,-1]' |

dataset_info.json

@@ -3,7 +3,7 @@
   "version": "2.0.0",
   "splits": {
     "dimension_sequences": {
-      "num_rows": 45,
+      "num_rows": 93,
       "num_columns": 21,
       "columns": [
         "N",

dimension_sequences.parquet

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scaling_formulas.parquet

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