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README.md
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---
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license: other
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license_name: sovereign-source-license-v2
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language:
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- en
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tags:
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- lean4
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- formal-verification
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- formal-mathematics
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- zero-sorry
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- e7
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- gates-normalization
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- sovereign
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- snapkitty
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- mathlib4
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- quantum-bridge
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pretty_name: Snapkitty Research Papers
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---
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# Snapkitty Research Papers
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Formal mathematics and sovereign AI research papers by Ahmad Ali Parr / SNAPKITTYWEST.
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All Lean 4 results are kernel-verified: zero sorry, compiled under Lean 4.19.0 + Mathlib 4.19.0.
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## Papers
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### Formal Mathematics (`formal-math/`)
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| File | Description |
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|------|-------------|
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| `gkn_boole_e7_quartic.pdf` | GKN I₄ quartic invariant · Boole idempotency from Huntington postulates · E₇ generator symmetries on FTS56 · 45 pages · zero sorry |
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| `attention_nand_decomposition_full.pdf` | Attention as NAND decomposition — full paper |
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| `theorem_t1–t4.pdf` | Individual theorem certificates |
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### Gates Normalization (`gates-normalization/`)
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| File | Description |
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|------|-------------|
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| `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 |
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| `GatesNormalization.lean` | Lean 4 source — all 14 theorems including `softmax_normalization`, `meta_inverted_decomposition`, `log_partition_enforces_normalization` |
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| `gates_normalization_repro.py` | Python reproduction of all theorems |
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### Sovereign OS (`sovereign-os/`)
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| File | Description |
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|------|-------------|
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| `SNAPKITTYWEST_PAPER.pdf` | Full sovereign OS architecture paper |
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| `SNAPKITTYWEST_ZENODO.pdf` | Zenodo canonical release |
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| `SNAPKITTY_RED_BOOK.pdf` | Red book — system internals |
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| `WAKING_THE_IMMUNE_SYSTEM.pdf` | Proof-gated execution is all you need |
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| `RESONANCE_BLOCK_PAPER.pdf` | Resonance block architecture |
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### Mathlib5 (`mathlib5/`)
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| File | Description |
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|------|-------------|
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| `mathlib5_full.pdf` | Full 10-layer Lean 5 architecture — 36 chapters |
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| `mathlib5_simple.pdf` | Simplified edition |
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| `mathlib5_zenodo.pdf` | Zenodo canonical release |
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## Key Theorems (zero sorry, Lean 4.19.0)
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- `free_energy_legendre`: F_β = ⟨H⟩_ρ − (1/β)·S_vN(ρ) — quantum partition bridge
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- `softmax_normalization`: ∑ softmax(v)ᵢ = 1 — structural, not produced
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- `meta_inverted_decomposition`: log Z = meta-inverted sum
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- `GKN I₄_homogeneous`: degree-4 homogeneity on FTS56
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- `boole_idempotency_closed`: x·x = x ∧ x+x = x from Huntington postulates
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## Trust
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Bel Esprit D'Accord Irrevocable Trust · In loving memory of Eric Westerhoff
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All proceeds toward the Millennium Prize Problems.
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