---
license: other
license_name: sovereign-source-license-v2
language:
- en
tags:
- lean4
- formal-verification
- formal-mathematics
- zero-sorry
- e7
- gates-normalization
- sovereign
- snapkitty
- mathlib4
- quantum-bridge
pretty_name: Snapkitty Research Papers
---

# Snapkitty Research Papers

Formal mathematics and sovereign AI research papers by Ahmad Ali Parr / SNAPKITTYWEST.  
All Lean 4 results are kernel-verified: zero sorry, compiled under Lean 4.19.0 + Mathlib 4.19.0.

## Papers

### Formal Mathematics (`formal-math/`)

| File | Description |
|------|-------------|
| `gkn_boole_e7_quartic.pdf` | GKN I₄ quartic invariant · Boole idempotency from Huntington postulates · E₇ generator symmetries on FTS56 · 45 pages · zero sorry |
| `attention_nand_decomposition_full.pdf` | Attention as NAND decomposition — full paper |
| `theorem_t1–t4.pdf` | Individual theorem certificates |

### Gates Normalization (`gates-normalization/`)

| File | Description |
|------|-------------|
| `gates_normalization_paper.tex` | ∑P=1 is the structural invariant of Δⁿ, not produced by softmax · log Z = Legendre dual of simplex · 12 theorems zero sorry |
| `GatesNormalization.lean` | Lean 4 source — all 14 theorems including `softmax_normalization`, `meta_inverted_decomposition`, `log_partition_enforces_normalization` |
| `gates_normalization_repro.py` | Python reproduction of all theorems |

### Sovereign OS (`sovereign-os/`)

| File | Description |
|------|-------------|
| `SNAPKITTYWEST_PAPER.pdf` | Full sovereign OS architecture paper |
| `SNAPKITTYWEST_ZENODO.pdf` | Zenodo canonical release |
| `SNAPKITTY_RED_BOOK.pdf` | Red book — system internals |
| `WAKING_THE_IMMUNE_SYSTEM.pdf` | Proof-gated execution is all you need |
| `RESONANCE_BLOCK_PAPER.pdf` | Resonance block architecture |

### Mathlib5 (`mathlib5/`)

| File | Description |
|------|-------------|
| `mathlib5_full.pdf` | Full 10-layer Lean 5 architecture — 36 chapters |
| `mathlib5_simple.pdf` | Simplified edition |
| `mathlib5_zenodo.pdf` | Zenodo canonical release |

## Key Theorems (zero sorry, Lean 4.19.0)

- `free_energy_legendre`: F_β = ⟨H⟩_ρ − (1/β)·S_vN(ρ) — quantum partition bridge
- `softmax_normalization`: ∑ softmax(v)ᵢ = 1 — structural, not produced
- `meta_inverted_decomposition`: log Z = meta-inverted sum
- `GKN I₄_homogeneous`: degree-4 homogeneity on FTS56
- `boole_idempotency_closed`: x·x = x ∧ x+x = x from Huntington postulates

## Trust

Bel Esprit D'Accord Irrevocable Trust · In loving memory of Eric Westerhoff  
All proceeds toward the Millennium Prize Problems.