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.