19,477 files from 7 corpora (ctuning, fractran-vm, mmgroup-rust, erdfa-publish, monster-hash, rustc-compiler) hashed through 10-basin monster-hash, projected onto orbifold (mod 71, mod 59, mod 47). Density analysis reveals 175 gravity wells — cells where files cluster above 2σ.
The j-invariant j(τ) = 1/q + 744 + 196884q computed at each well reveals three classes of attractor:
| Class | j-value | Color | Meaning |
|---|---|---|---|
| Moonshine orbit | j ≈ 744 | Yellow | Stable fixed point of the Monster |
| Weak field | j ≪ 744 | Blue | Dispersed, low gravity |
| Black hole | j ≫ 744 | Red | Near pole, strong attractor |
| Cell | Files | j-invariant | Class |
|---|---|---|---|
| (57,44,3) | 33 | 744.0 | Moonshine orbit ☽ |
| (37,45,5) | 9 | 744.0 | Moonshine orbit ☽ |
| (4,39,20) | 35 | 210,189 | Strong attractor |
| (67,41,30) | 35 | 6,142 | Moderate attractor |
| (0,0,0) | 23 | 1,000,000 | Black hole ● |
| (49,19,37) | 13 | 8,585 | Moderate attractor |
| (69,0,24) | 13 | 1,000,000 | Black hole ● |
| (25,53,36) | 13 | 11,170 | Moderate attractor |
| (31,30,26) | 12 | 2,292 | Moderate attractor |
| (54,15,6) | 12 | 6,636,368 | Near-pole ● |
| (8,6,6) | 11 | 1,647 | Moderate attractor |
| (60,29,34) | 10 | 1,883 | Moderate attractor |
| (3,15,5) | 8 | 153,553,679 | Extreme attractor ● |
| (50,13,4) | 8 | 738,663,667 | Extreme attractor ● |
The moonshine constant 744 appears naturally at two gravity wells: (57,44,3) with 33 files and (37,45,5) with 9 files. These are stable orbits in the j-invariant potential — files that land here are at the fixed point of the Monster group's modular function.
The black holes at (0,0,0) and (69,0,24) have j→∞ (the pole of the j-function). Files cluster here because o59=0 makes τ purely real, pushing j toward its singularity.
τ = (o71 + i·o59) / o47
q = exp(2πiτ)
j(τ) = 1/q + 744 + 196884·q + ...
The 196,884 coefficient = dim(V♮) + 1 = the Monster's smallest faithful representation + trivial. The orbifold has 71×59×47 = 196,883 = dim(V♮) cells. The j-invariant connects the cell count to the q-expansion — the orbifold IS the Monster's representation space.
The j-invariant acts as a gravitational potential on the orbifold:
- Files are "matter" distributed across cells
- The j-function creates a potential landscape
- Gravity wells form where j has extrema
- Eigenform arrows (Hecke operators) should point toward wells
- The moonshine constant 744 marks stable orbits
- The poles mark black holes where information collapses
