Research Timeline
April 2026
Quantum Algebra Complete: [3, 6, 17, 117]
Quantum Moyal bracket algebra gains +1 dimension vs classical for all singular potentials. 117th generator: negative semi-definite, Legendre P₃ (octupole), 1/r¹⁴ divergence, NOT conserved. Quantum universality classification: singular → +1, polynomial → +0. Quantum commutant dim=40 (vs classical 41).
April 11, 2026
N=4 Level-3 Exact: 1,260 Dimensions
N=4 L3 rank = 1,260 (52 min, r6i.8xlarge). Full N=4 sequence now [6, 14, 62, 1260]. L2 formula corrected: N(4N²−9N+3)/2 for N≥4 (old cubic falsified at N=7,8). N=5 L3 OOM-blocked on 256 GB.
April 7–8, 2026
Extreme Mass Ratio Atlases Complete
Sun-Earth-Moon: 10,000/10,000 points, ranks 102–108, dynamic range 10²⁰–10²⁶ (6h28m, r6i.4xlarge). Sun-Jupiter-Asteroid: 10,000/10,000 points, ranks 91–100, dynamic range 10²⁵–10³² (9h33m). Most extreme mass ratio ever computed for this algebra.
April 2026
N=5–8 Scaling Probes Complete
First dimension sequences beyond N=4: N=5→[10,25,145], N=6→[15,39,279], N=7→[21,56,476]. Confirms d(0)=C(N,2) pattern. N=4 potential universality confirmed for 1/r², 1/r³, log(r).
March 27, 2026
Gap Workplan Phase 1 Complete (6/6)
All 6 free post-processing analyses done: SV landscape mining, spectral decay rate maps, spectral clustering, CG atlas comparison, Level-4 bar chart, SV #116 analytical prediction.
March 2026
15 Atlas Configurations Complete
Full atlas coverage for: equal-mass gravitational, helium, Li⁺, H⁻, positronium, muonic helium, H₂⁺, binary star, and 7 alternative potentials (1/r², 1/r³, log, composite, Coulomb variants).
March 2026
Paper 4: Calogero-Moser Integrability Test
Critical insight: [3, 6, 17, 116] is NOT a non-integrability certificate. 1D Calogero-Moser (exactly integrable) produces the same sequence. Singularity class (not integrability) drives the algebra's growth.
Feb–Mar 2026
S₃ Tier Decomposition Established
Level-3: 52 + 44 + 16 + 4 = 116 generators. Integer-quantized scaling exponents (α = 0,1,2,3). CG decomposition: 24A + 28A' + 52E (E-fraction = 2/3 constant). 32 syzygies + 8 true zeros.
February 2026
N=4 Sequence [6, 14, 62] Confirmed
Mass-invariant, d-independent. Gap ratio 3.4×10¹¹ at level 2. Three mass configurations tested.
February 2026
SymPy 1.13.3 Bug Fix: Dimension Correction
SymPy ≤1.10.1 produced incorrect [3, 5, 13, 69] for unequal masses. Version 1.13.3 corrected to universal [3, 6, 17, 116]. 63/156 level-3 expressions were wrong. All prior unequal-mass results re-validated.
Jan–Feb 2026
AWS Campaign: 19 Instances
Initial compute fleet: 19 r6i.4xlarge instances. Total cost ~$800–1,000 (single-threaded). Later reduced to ~$100 equivalent with multiprocessing (8× speedup).
January 2026
Core Dimension Sequence [3, 6, 17, 116] Established
First computation for equal-mass planar 3-body with 1/r potential. SVD gap ratio test confirms exact rank at each level. Level-4 lower bound d(4) ≥ 4,501.
Late 2025
Project Inception
Initial exploration of Poisson bracket structure for the N-body problem. exact_growth.py written as baseline engine. Auxiliary variable substitution u_ij = 1/r_ij developed to keep expressions polynomial.
Dimension Sequences (Complete Record)
The Universal Singular Sequence (N=3)
[ 3, 6, 17, 116, ≥5604 ]
Level 0 through 4 · Level-4 lower bound from SVD at 200K samples
N=3: All Potentials
| Potential | d(0) | d(1) | d(2) | d(3) | Match? |
|---|---|---|---|---|---|
| 1/r (Newton/Coulomb) | 3 | 6 | 17 | 116 | ✓ |
| 1/r² (Calogero-Moser) | 3 | 6 | 17 | 116 | ✓ |
| 1/r³ (cubic) | 3 | 6 | 17 | 116 | ✓ |
| 1/r⁴ (quartic singular) | 3 | 6 | 17 | 116 | ✓ |
| log(r) (2D vortices) | 3 | 6 | 17 | 116 | ✓ |
| 1/r + 1/r² (composite) | 3 | 6 | 17 | 116 | ✓ |
| 1/r + harmonic (Penning trap) | 3 | 6 | 17 | 116 | ✓ |
| r⁴ (quartic regular) | 3 | 6 | 17 | 116 | ✓ |
| r² (harmonic) | 3 | 6 | 13 | 15 | FINITE |
N=4: Potential Universality
| Potential | d(0) | d(1) | d(2) | d(3) | Match ref? |
|---|---|---|---|---|---|
| 1/r (reference) | 6 | 14 | 62 | 1260 | - |
| 1/r² | 6 | 14 | 62 | - | ✓ |
| 1/r³ | 6 | 14 | 62 | - | ✓ |
| log(r) | 6 | 14 | 62 | - | ✓ |
N=5 through N=8 (d=1, 1/r)
| N | d(0) | d(1) | d(2) | Time |
|---|---|---|---|---|
| 5 | 10 | 25 | 145 | 8s |
| 6 | 15 | 39 | 279 | 16s |
| 7 | 21 | 56 | 476 | 65s |
| 8 | 28 | 76 | 301? | partial |
d(0) = C(N,2) confirmed · d(1) sequence: 6, 14, 25, 39, 56, 76 · N=8 d(2) may be truncated by memory
N-Body Scaling Formulas
| N | d(0) | d(1) | d(2) | d(3) | Status |
|---|---|---|---|---|---|
| 3 | 3 | 6 | 17 | 116 | ✓ Full sequence |
| 4 | 6 | 14 | 62 | 1260 | ✓ L3 exact (Apr 11) |
| 5 | 10 | 25 | 145 | OOM | d=1 only |
| 6 | 15 | 39 | 279 | - | d=1 |
| 7 | 21 | 56 | 476 | - | d=1 |
| 8 | 28 | 76 | 748 | - | d=1 |
d(0) = C(N,2) · d(1) = N(3N−5)/2 · d(2) = N(4N²−9N+3)/2 for N≥4 (corrected Apr 11; old cubic falsified at N=7,8)
L3: two data points, N=3→116 and N=4→1260; predicts new_L3(5)=5990 if pattern continues
L3: two data points, N=3→116 and N=4→1260; predicts new_L3(5)=5990 if pattern continues
Internal Structure (Level 3, N=3)
| Tier | Count | Scaling Exponent | S₃ Decomposition |
|---|---|---|---|
| Tier 0 (core) | 52 | ε⁰ | Dominant generators |
| Tier 1 | 44 | ε¹ | First-order scaling |
| Tier 2 | 16 | ε² | Second-order |
| Tier 3 | 4 | ε³ | Weakest generators |
| Total | 116 | 24A + 28A′ + 52E |
E-type irrep fraction = 2/3 at every bracket level · 40 null generators: 32 syzygies + 8 momentum zeros
Quantum Commutator Algebra
| Potential | Classical d(3) | Quantum d(3) | Δ | Class |
|---|---|---|---|---|
| 1/r (Newton/Coulomb) | 116 | 117 | +1 | Singular |
| 1/r² (Calogero-Moser) | 116 | 117 | +1 | Singular |
| 1/r³ | 116 | 117 | +1 | Singular |
| 1/r⁴ | 116 | 117 | +1 | Singular |
| r² (harmonic) | 15 | 15 | +0 | Regular |
| r⁴ (quartic regular) | 116 | 116 | +0 | Regular |
117th generator: sum-of-squares proof g = −(9/4)[(A−B)² + A²], negative semi-definite · Legendre P₃ (octupole) · 1/r¹⁴ collision divergence · NOT conserved ([G,H]≠0, 919 terms)
Gap Work Plan: 28 Items across 5 Phases
▶
Phase 1: Free Post-Processing
COMPLETE
1.1Done
Spectral Depth Mining: Interior SV Landscapes
SV #50, #80, #100, #110 as shape-sphere heatmaps. Done.
1.2Done
Spectral Decay Rate Map
Log-slope between SV #80–#115 at each grid point. Done.
1.3Done
Spectral Clustering on Shape Sphere
k-means/hierarchical clustering on 156-dim SV vectors. Done.
1.4Done
Clebsch-Gordan Predictions vs Full Atlas
CG doublet count comparison on full shape sphere. Done.
1.5Done
Level-4 Comparison Chart
Bar chart + convergence curves of d(4) across configs. Done.
1.6Done
Analytical Prediction of SV #116
Predict weakest generator landscape from symbolic structure. R²=0.630 correlation. Done (Apr 1, 2026).
▶
Phase 2: Light Compute (hours, local/small AWS)
4/7
2.1Done
N=5 Level 1–2
Third data point for d_N(k) vs N. Result: N=5 gives [10, 25, 145]. Formula L2(N)=N(4N²−9N+3)/2 (N≥4) confirmed. N=5 L3 OOM-blocked on 256 GB.
2.2Done
N=4 with 1/r², 1/r³, log(r)
Result: all three potentials confirmed [6, 14, 62] (Apr 1, 2026, 500 samples each). Paper 3 prediction #2 confirmed: potential invariance holds at N=4.
2.3Done
r⁴ Potential (Regular)
Result: classical [3, 6, 17, 116]; quantum [3, 6, 17, 116] (no growth). Quantum corrections exist but are linearly dependent. Confirms regular/singular dichotomy extends to quantum case.
2.4Done
Charge Sweep Phase 3 (+1/+q/−1)
Result: q = 1, 2, 3, 4, 5, 6, 8, 10, 15, 20 all give [3, 6, 17, 116] (Mar 24, 2026). Charge-sign invariance confirmed for arbitrary nucleus charge.
2.5Not Started
S₄ Tier Decomposition (N=4)
Does S₃ tier structure generalize to S₄? Integer-quantized scaling?
2.6Not Started
Harmonic Dimension 15: Rep Theory Derivation
Derive dim=15 from isotropic oscillator Lie algebra (sp(4,ℝ) or similar).
2.7Not Started
H₃⁺ and Ozone Molecular Systems
Molecular triatomic reconfirmation. High outreach value.
▶
Phase 3: Medium Compute ($10–$200 AWS)
2/5
3.1Not Started
Parametric Exponent Sweep (1,015 values of n)
Gap ratio vs n continuous curve. Script ready. Est. $13–50. VERY HIGH impact.
3.2Blocked
Yukawa Potential (3 Scenarios)
Lambdification/OOM issues. Recursion fix deployed but not confirmed.
3.3Done
Re-run 7 Retracted Gravitational Configs
Result: 4 of 7 directly confirmed [3, 6, 17, 116]; 3 (Sun-Earth-Moon, Sun-Jupiter-Asteroid, LISA) show rank deficit at extreme mass ratios, consistent with mass invariance theorem (SVD conditioning, not algebraic). Completed Mar 24, 2026.
3.4Done
Complete Interrupted Atlases
Sun-Earth-Moon: done April 7, 2026 (6h28m, 10,000 points, ranks 102–108). Sun-Jupiter-Asteroid: done April 8, 2026 (9h33m, 10,000 points, ranks 91–100). Most extreme mass ratios computed.
3.5Not Started
Lagrange Hires 1000×1000 Scan
Resolve concentric ring features and isosceles beads. Est. $3–12.
▶
Phase 4: Verification & Theory
Theory
4.1Done
Independent CAS Verification (Mathematica)
Wolfram Language 14.3 reproduces [3, 6, 17, 116] for both 1/r (40s) and 1/r² (50s), and the harmonic closure [3, 6, 13, 15, 15] through L=4 (Apr 21, 2026). Independent rank algorithm:
MatrixRank over Rationals on a SparseArray. The headline numbers now stand on two unrelated CAS implementations and two unrelated rank algorithms.4.2In Review
OEIS Submission of [3, 6, 17, 116]: A395423
Submitted to OEIS Apr 21, 2026; A-number A395423 assigned, awaiting editorial review. Source-format draft and human-readable companion staged in
OEIS/candidates/A395423.md. Four further candidate sequences drafted (N=4 singular, N=3 harmonic, L2 closed-form, A095794 cross-reference) for follow-on submission once the headline entry is approved.4.3Not Started
Level-4 Bound Improvement
Current: d(4) ≥ 5,604 at 200K samples. mpmath at 4.4% when reclaimed.
▶
Phase 5: Quantum Algebra (New, Apr 2026)
Quantum
5.1Done
Quantum Commutator Rank (N=3, d=2)
Result: [3, 6, 17, 117], one extra dimension vs classical 116. Confirmed in both d=1 and d=2. Engine: QuantumNBodyAlgebra with Moyal bracket.
5.2Done
117th Generator Identification & Characterization
Sum-of-squares proof: g = −(9/4)[(A−B)² + A²], negative semi-definite. Legendre P₃ (octupole) structure. Scaling degree −8. 1/r¹⁴ collision divergence. Not conserved ([G,H]≠0).
5.3Done
Quantum Universality Classification
Tested 1/r, 1/r², 1/r³, 1/r⁴ (all singular → +1), r², r⁴ (polynomial → no growth). Classification: singularity at r=0 is load-bearing for quantum correction.
5.4Done
Energy Bound Search (Quantum Commutant)
Quantum commutant dim=40 (156−116); classical commutant dim=41 (156−115). SMALLER: quantization removes one conservation law. 117th generator not conserved. Energy bound via this approach ruled out.
5.5Not Started
Quantum Rank for N=4 / Quantum N-body Scaling
Does N=4 quantum algebra also gain +1 at L2 or L3? Predict [6, 14, 63] if singularity universality extends to higher N.
5.6Not Started
Post-Newtonian 2PN Quantum Rank
1PN: −1/r − 1/r² gives [3,6,17,116] (no change). 2PN: −1/r − 1/r² − 1/r³ level 3 in progress locally.
5.7Blocked
N=5 d=1 Level-3 Exact Rank
OOM-killed on r6i.8xlarge (256 GB, 8 workers). 1.1M L3 brackets checkpointed on S3. Matrix 1.1M×760K over ℚ exceeds 256 GB. Options: modular rank over GF(p), r6i.16xlarge (512 GB), or out-of-core streaming.
Physical Systems Catalog
Universality Evidence Matrix
| Parameter | Tested Values | N=3 | N=4 | N≥5 |
|---|---|---|---|---|
| Mass ratios | 0.001 to 10⁶ (25+ configs) | ✓ Invariant | ✓ (3 configs) | - |
| Spatial dimension d | d = 1, 2, 3 | ✓ Invariant | ✓ Invariant | d=1 only |
| Potential type | 1/r, 1/r², 1/r³, 1/r⁴, log(r), composite | ✓ Invariant | ✓ Confirmed | 1/r only |
| Charge sign | All-attract, all-repulse, mixed | ✓ Invariant | Not tested | - |
| Charge magnitude | |q| = 1–20 (10 values) | ✓ Invariant | Not tested | - |
Gravitational
| System | Masses | Sequence | Atlas |
|---|---|---|---|
| Equal-mass 3-body | 1:1:1 | [3, 6, 17, 116] | ✓ Complete |
| Sun-Earth-Moon | 1 : 3×10⁻⁶ : 3.7×10⁻⁸ | [3, 6, 17, 102–108]‡‡ | ✓ Complete |
| Sun-Jupiter-Asteroid | 1 : 9.5×10⁻⁴ : 10⁻¹⁰ | [3, 6, 17, 91–100]‡‡ | ✓ Complete |
| Binary Star + Planet | 1:1:0.001 | [3, 6, 17, 116]‡ | ✓ Complete |
| Triple BH (LISA) | 1:0.01:10⁻⁵ | [3, 6, 17, 116]† | ✓ Complete |
Atomic / Coulomb
| System | Charges | Masses | Sequence | Atlas |
|---|---|---|---|---|
| Helium atom | (+2,−1,−1) | 7294:1:1 | [3, 6, 17, 116] | ✓ |
| Li⁺ ion | (+3,−1,−1) | 12789:1:1 | [3, 6, 17, 111] | ✓ |
| H⁻ ion | (+1,−1,−1) | 1836:1:1 | [3, 6, 17, 116] | ✓ |
| Positronium Ps⁻ | (+1,−1,−1) | 1:1:1 | [3, 6, 17, 116] | ✓ |
| Muonic Helium | (+2,−1,−1) | 7294:1:207 | [3, 6, 17, 116] | ✓ |
| H₂⁺ molecular ion | (+1,+1,−1) | 1836:1836:1 | [3, 6, 17, 115] | ✓ |
Alternative Potentials
| System | Potential | Sequence | Notes |
|---|---|---|---|
| Calogero-Moser | 1/r² | [3, 6, 17, 116] | Integrable in 1D, same sequence |
| Cubic potential | 1/r³ | [3, 6, 17, 116] | Jahn-Teller ring observed |
| Quartic singular | 1/r⁴ | [3, 6, 17, 116] | Quantum: [3,6,17,117], singular class confirmed |
| 2D Vortices | log(r) | [3, 6, 17, 116] | Transcendental singularity |
| Composite | 1/r + 1/r² | [3, 6, 17, 116] | Multi-pole universal; PN 1PN: [3,6,17,116] |
| Harmonic oscillator | r² | [3, 6, 13, 15] | FINITE: saturates at dim 15 |
| Quartic regular | r⁴ | [3, 6, 17, 116] | Polynomial but infinite; quantum: no growth (+0) |
| Penning trap | 1/r + harmonic | [3, 6, 17, 116] | All-repulsive + external trap |
Nuclear / Plasma (In Progress)
| System | Potential | Status | Notes |
|---|---|---|---|
| Tritium / He-3 | Yukawa | In progress | Recursion fix deployed |
| p-n-n Scattering | Yukawa | In progress | |
| Dusty Plasma | Yukawa | Failed (OOM) | Lambdification issue |
† Inferred from mass ratio sweep + diagnostic (SymPy 1.10.1 artifact corrected).
‡ Directly re-run on AWS with SymPy 1.13.3 and confirmed.
‡‡ Ranks 102–108 / 91–100 reflect extreme dynamic range (10²⁰–10³²); SVD conditioning limits detection. Algebraic dimension confirmed as 116 by mass invariance theorem. Atlas completed April 2026.
‡ Directly re-run on AWS with SymPy 1.13.3 and confirmed.
‡‡ Ranks 102–108 / 91–100 reflect extreme dynamic range (10²⁰–10³²); SVD conditioning limits detection. Algebraic dimension confirmed as 116 by mass invariance theorem. Atlas completed April 2026.
Papers (4 Drafted + 1 Outline)
1
Super-exponential growth of the Poisson algebra generated by pairwise Hamiltonians of the planar three-body problem
preprint.tex
Dimension sequence [3, 6, 17, 116], mass invariance theorem, potential comparison (harmonic/Newton/CM), level-4 lower bound d(4) ≥ 4,501. Reframed from "non-integrability certificate" to "structural algebraic invariant" after CM reckoning.
2
S₃-equivariant jet filtration of the three-body Poisson algebra: tier decomposition, integer scaling exponents, and syzygy structure
paper2_s3_filtration.tex
52+44+16+4 = 116 tier decomposition. CG verification: 24A + 28A' + 52E. E-fraction = 2/3 at every bracket level. 32 syzygies + 8 true zeros. Integer-quantized scaling exponents α = 0, 1, 2, 3.
3
Universal dimension sequences of pairwise Poisson algebras: independence from spatial dimension, potential exponent, and charge sign
paper3_universality.tex
N=4 sequence [6, 14, 62, 1260] (L3 exact, Apr 11, 2026). N=5 sequence [10, 25, 145] (L2; L3 OOM-blocked). N=7 [21, 56, 476], N=8 [28, 76, 748]. N-body scaling: L0=C(N,2), L1=N(3N−5)/2, L2=N(4N²−9N+3)/2 (N≥4). d-independence for N=3 and N=4. Pole-order invariance. Charge-sign invariance. Mass invariance proved over ℚ(m₁,m₂,m₃). Formal universality conjecture + three falsifiable predictions (P1 confirmed through L2).
4
The Poisson Algebra of Pairwise Interactions: A Calogero-Moser Integrability Test
paper4_calogero_integrability.tex
1D CM (exactly integrable) gives [3, 6, 17, 116]. Singularity class invariance. Galperin superintegrable mass ratios all universal. Revtex4-2, 4 pages.
5
Quantum deformation of the three-body Poisson algebra: Moyal bracket correction, universality across singular potentials, and the 117th generator
quantum_algebra.py · (paper5 draft not yet started)
Quantum rank [3, 6, 17, 117] (+1 vs classical). 117th generator: negative semi-definite, Legendre P₃ angular structure, 1/r¹⁴ collision divergence, NOT conserved ([G,H]≠0, 919 terms). Quantum universality: all singular 1/rⁿ → [3,6,17,117]; polynomial rⁿ → no growth. Energy bound ruled out: quantum commutant dim=40 < classical 41.
Publication Blockers
arXiv endorsement needed
math-ph / dynamical systems (no endorser yet)
Current preprint host
Zenodo (DOI: 10.5281/zenodo.18899804)
Existing arXiv publication
cs.RO/math.GN (topological robotics, doesn't carry over)
SageMath verification (4.1)
Essential for credibility (not started)
Conjectures & Open Questions
Universality Conjecture (Revised, March 2026)
For N ≥ 3 particles in d ≥ 1 spatial dimensions, interacting via a singular central potential: (1) the pairwise Poisson algebra has infinite GK dimension; (2) the cumulative dimension sequence d_N(n) depends only on N; (3) the sequence is independent of spatial dimension, potential type (within singular class), mass ratios, and charge configurations. For regular potentials (V polynomial in r), the algebra is finite-dimensional.
✓ N=3 sequence proved
✓ N=4 sequence [6,14,62,1260]
✓ Mass invariance proved over ℚ(m₁,m₂,m₃)
✓ d-independence (d=1,2,3)
✓ Potential-type invariance (5+ types)
✓ Charge-sign invariance
✓ N=5 sequence [10,25,145]
✓ N=4 with 1/r², 1/r³, log(r) → [6,14,62]
Quantum Universality Conjecture (April 2026)
For all singular potentials (1/rⁿ, n ≥ 1), the quantum Moyal bracket algebra is exactly one dimension larger than the classical Poisson bracket algebra at level 3: dquantum(3) = dclassical(3) + 1. The extra generator is negative semi-definite (Legendre P₃ angular structure, 1/r¹⁴ divergence at collision), and is NOT conserved. For polynomial potentials (rⁿ), there is no quantum correction at any level.
✓ 1/r: [3,6,17,117] vs classical 116
✓ 1/r²: [3,6,17,117] confirmed
✓ 1/r³: [3,6,17,117] confirmed
✓ 1/r⁴: [3,6,17,117] confirmed
✓ r²: no quantum growth
✓ r⁴: no quantum growth
○ N=4 quantum not yet tested
○ log(r) not tractable (non-algebraic)
Critical Locus Conjecture
The local rank of the Poisson algebra, viewed on the reduced configuration space (shape sphere for N=3), has its critical locus at exactly the fixed-point set of the S_N action. Rank drops occur only at symmetric configurations: Lagrange (S₃), Euler (Z₂), isosceles (Z₂).
✓ 99,000 grid points, 11 configs
✓ No non-symmetric anomalies found
✓ Cross-potential consistency
○ S₄ extension untested (N=4)
Cosmological Perspective (Speculative)
If the universality conjecture holds for general N, the S_N symmetric fixed point of the cosmic N-body problem corresponds to the homogeneous, isotropic universe. The critical locus conjecture predicts a rank drop at this point: an algebraic explanation for the dimensional reduction from ~3×10⁸⁰ degrees of freedom to the Friedmann equation's single scale factor a(t).
✓ d=3 explicitly computed
✓ Charge-sign invariant (EM too)
○ Only N=3,4 tested
○ GR not modeled
Falsifiable Predictions (Paper 3)
Three predictions that would falsify or strengthen the universality conjecture:
✓ P1: N=5, d=1 → [10, 25, 145] confirmed through L2; L3 in progress (AWS r6i.8xlarge)
✓ P2: N=4 with 1/r², 1/r³, log(r) → all confirmed [6, 14, 62] (Apr 1, 2026)
○ P3: d(4) for 1/r² → predict matches d(4) for 1/r (level-4 universality)
Infrastructure & Compute
Core Engines
exact_growth.py: N=3 symbolic Poisson bracket engine (levels 0-3)
exact_growth_nbody.py: Generalized engine (N, d, potential, charges)
quantum_algebra.py: QuantumNBodyAlgebra with Moyal bracket (ℏ-deformation)
symbolic_rank_nbody.py: Exact rank over ℚ and ℚ(m₁,m₂,…) for mass invariance proofs
stability_atlas.py: Shape-sphere atlas scanner (exact engine)
multi_epsilon_atlas.py: Adaptive + multi-epsilon scanning
targeted_adaptive_scan.py: Regional high-resolution scans
Lambdify Pipeline (4-layer fallback)
Layer 1: Standard sp.lambdify (fast numpy)
Layer 2: Flat-file no-CSE (pycode → temp .py)
Layer 3: Flat-file with CSE (slower, smaller code)
Layer 4: Point-by-point xreplace (last resort, ~1000× slower)
1/r² result: 92 via L1, 63 via L2, 0 xreplace
AWS Campaign
S3 bucket: s3://3body-compute-290318/
Atlas instances: r6i.4xlarge (16 vCPU, 128 GB)
Level-4 mpmath: r6i.8xlarge → r6a.8xlarge (spot)
Multiprocessing: --workers N (fork-based, 8× speedup)
Total data: 9.04 GB synced locally
S3 sync caveat: Use cp --recursive for numpy arrays (size-identical trap)
Completed Compute (Apr 2026)
Sun-Earth-Moon atlas: Complete, April 7, 2026 (6h28m, r6i.4xlarge on-demand)
10,000 / 10,000 valid points · ranks 102–108 · dynamic range 10²⁰–10²⁶
Sun-Jupiter-Asteroid atlas: Complete, April 8, 2026 (9h33m, r6i.4xlarge on-demand)
10,000 / 10,000 valid points · ranks 91–100 · dynamic range 10²⁵–10³² (most extreme)
Level-4 mpmath rank: 667/15,000 rows (4.4%)
Cost History
Original campaign: ~$800–1,000 (19 instances, single-threaded, 48h)
With multiprocessing: ~$100–125 equivalent
1/r² atlas (w/ fixes): $2.50 (was projected $28)
Parametric sweep estimate: $13–50 (Tier 3 hybrid)
Atlas fleet peak: $435/day (16 atlas + 1 mpmath)
Known Issues
Yukawa lambdification: OOM/recursion on deeply nested exp(-μ/u)
SymPy version sensitivity: 1.10.1 fails 63/156 L3 expressions
Level-4 mpmath derivatives cache: 243 MB, must sync to S3
Li⁺ dim=111, H₂⁺ dim=115: SVD artifact or real physics? Under investigation