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| # Monster Moonshine OEIS Sequences | |
| # Exponent of each SSP prime in Monster irreducible representations | |
| # n: irrep index (0-193), value: exponent of prime in irrep n | |
| exp_2: 0, 0, 2, 1, 2, 0, 1, 1, 0, 0, 0, 0, 0, 1, 12, 0, 0, 3, 0, 1, 2, 0, 1, 3, 0, 0, 0, 0, 7, 0, 0, 0, 0, 4, 0, 3, 1, 1, 2, 2, 18, 18, 18, 1, 1, 18, 1, 1, 5, 19, 2, 2, 0, 0, 0, 0, 5, 0, 17, 17, 12, 0, 3, 16, 6, 3, 2, 1, 3, 2, 0, 0, 0, 0, 0, 3, 0, 6, 4, 2, 31, 31, 1, 1, 2, 2, 0, 3, 1, 1, 1, 0, 1, 3, 6, 10, 18, 11, 0, 0, 0, 46, 46, 0, 1, 1, 0, 0, 3, 0, 2, 18, 4, 0, 3, 7, 2, 3, 18, 3, 13, 0, 43, 43, 43, 20, 0, 1, 1, 9, 1, 2, 42, 3, 18, 18, 21, 0, 1, 42, 1, 16, 0, 2, 28, 18, 2, 32, 2, 2, 3, 1, 0, 10, 4, 2, 18, 20, 32, 0, 0, 12, 1, 2, 1, 0, 3, 0, 18, 6, 0, 42, 12, 0, 42, 0, 0, 0, 0, 0, 44, 0, 2, 2, 0, 0, 2, 7, 0, 1, 1, 1, 46, 0 | |
| exp_3: 0, 0, 0, 0, 0, 0, 1, 1, 6, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 19, 19, 6, 0, 3, 1, 0, 2, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 12, 12, 1, 0, 0, 0, 1, 2, 2, 1, 1, 0, 0, 7, 0, 0, 0, 1, 6, 0, 3, 3, 17, 3, 12, 0, 0, 18 |
| To: submit@oeis.org | |
| Subject: New OEIS Sequences: Monster Moonshine Exponents (15 sequences from A001379) | |
| Dear OEIS Editors, | |
| I would like to submit 15 new integer sequences derived from the Monster group irreducible representations, related to Monstrous Moonshine. | |
| BACKGROUND: | |
| The Monster group is the largest sporadic simple group (order |M| ≈ 8.08×10^53). It has 194 irreducible representations with dimensions given in OEIS A001379. The j-invariant modular form coefficients decompose as weighted sums of these dimensions - this is the McKay-Thompson observation that inspired Monstrous Moonshine (Conway & Norton 1979, proven by Borcherds 1992). |
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| <title>Monster Moonshine LLM Brief Generator</title> | |
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| <title>Monster Moonshine Matrix - SSP × 194 Irreps</title> | |
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| {"2": [0, 0, 2, 1, 2, 0, 1, 1, 0, 0, 0, 0, 0, 1, 12, 0, 0, 3, 0, 1, 2, 0, 1, 3, 0, 0, 0, 0, 7, 0, 0, 0, 0, 4, 0, 3, 1, 1, 2, 2, 18, 18, 18, 1, 1, 18, 1, 1, 5, 19, 2, 2, 0, 0, 0, 0, 5, 0, 17, 17, 12, 0, 3, 16, 6, 3, 2, 1, 3, 2, 0, 0, 0, 0, 0, 3, 0, 6, 4, 2, 31, 31, 1, 1, 2, 2, 0, 3, 1, 1, 1, 0, 1, 3, 6, 10, 18, 11, 0, 0, 0, 46, 46, 0, 1, 1, 0, 0, 3, 0, 2, 18, 4, 0, 3, 7, 2, 3, 18, 3, 13, 0, 43, 43, 43, 20, 0, 1, 1, 9, 1, 2, 42, 3, 18, 18, 21, 0, 1, 42, 1, 16, 0, 2, 28, 18, 2, 32, 2, 2, 3, 1, 0, 10, 4, 2, 18, 20, 32, 0, 0, 12, 1, 2, 1, 0, 3, 0, 18, 6, 0, 42, 12, 0, 42, 0, 0, 0, 0, 0, 44, 0, 2, 2, 0, 0, 2, 7, 0, 1, 1, 1, 46, 0], "3": [0, 0, 0, 0, 0, 0, 1, 1, 6, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 19, 19, 6, 0, 3, 1, 0, 2, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 12, 12, 1, 0, 0, 0, 1, 2, 2, 1, 1, 0, 0, 7, 0, 0, 0, 1, 6, 0, 3, 3, 17, 3, 12, 0, 0, 18, 18, 3, 0, 0, 0, 17, 17, 3, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0, 0, 3, 9, 1, 1, 1, 1, 3, 2, 13, 13, 19, 0, 0, 3, 19, 19, 19, 19, 0, 6, 0, 0, 12, 3, 2, 9, 1, 6, 0, 6, 0, 19, |
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 |
|---|