| --- |
| 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. |
|
|
