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<h1>Formal Verification</h1>
<p class="lede">Machine-checked proofs in Lean 4 and Agda, verified compilers and cross-language verification.</p>
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<article class="card" data-kind="model" data-new="true" data-search="ai-free universalword: forth, bcpl and wolfram front ends into one machine-word ir, with a lean proof for every stage. lean4 forth bcpl model parr source">
<div class="card-top"><span class="badge new">New</span><span class="badge kind">model</span><span class="badge lic">Parr Source</span></div>
<h3><a href="https://huggingface.co/Snapkitty/ai-free">ai-free</a></h3>
<p>UniversalWord: Forth, BCPL and Wolfram front ends into one machine-word IR, with a Lean proof for every stage.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">forth</span><span class="tag">bcpl</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/ai-free">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYAGENT9NOVA/ai-free">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="true" data-search="assertica deterministic proof-language compiler in haskell with 768+ tests. haskell model bsl-1.0">
<div class="card-top"><span class="badge new">New</span><span class="badge kind">model</span><span class="badge lic">BSL-1.0</span></div>
<h3><a href="https://huggingface.co/Snapkitty/assertica">assertica</a></h3>
<p>Deterministic proof-language compiler in Haskell with 768+ tests.</p>
<div class="card-foot"><div class="tags"><span class="tag">haskell</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/assertica">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYAGENT9NOVA/assertica">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="true" data-search="icp-dag-crystallizer icp-dag v1.0 governance protocol formalized across prolog, datalog and other logic languages, with a relational lattice kernel. prolog datalog model sl-agpl3-001 covenant">
<div class="card-top"><span class="badge new">New</span><span class="badge kind">model</span><span class="badge lic">SL-AGPL3-001</span></div>
<h3><a href="https://huggingface.co/Snapkitty/icp-dag-crystallizer">icp-dag-crystallizer</a></h3>
<p>ICP-DAG v1.0 governance protocol formalized across Prolog, Datalog and other logic languages, with a relational lattice kernel.</p>
<div class="card-foot"><div class="tags"><span class="tag">prolog</span><span class="tag">datalog</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/icp-dag-crystallizer">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/icp-dag-crystallizer">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="true" data-search="PIRTM alloy counter-paper on the hcalc verification logs: shows each check restates its own fact, and that the same method &quot;proves&quot; a false claim. alloy model agpl-3.0">
<div class="card-top"><span class="badge new">New</span><span class="badge kind">model</span><span class="badge lic">AGPL-3.0</span></div>
<h3><a href="https://huggingface.co/Snapkitty/PIRTM">PIRTM</a></h3>
<p>Alloy counter-paper on the HCALC verification logs: shows each check restates its own fact, and that the same method &quot;proves&quot; a false claim.</p>
<div class="card-foot"><div class="tags"><span class="tag">alloy</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/PIRTM">Hugging Face</a><a class="link" href="https://github.com/AHMADALIPARR/PIRTM">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="true" data-search="riemann-gas riemann (primon) gas over the first primes, with kernel-verified zeta-truncation theorems in lean 4. does not claim rh. lean4 python model agpl-3.0">
<div class="card-top"><span class="badge new">New</span><span class="badge kind">model</span><span class="badge lic">AGPL-3.0</span></div>
<h3><a href="https://huggingface.co/Snapkitty/riemann-gas">riemann-gas</a></h3>
<p>Riemann (primon) gas over the first primes, with kernel-verified zeta-truncation theorems in Lean 4. Does not claim RH.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">python</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/riemann-gas">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/riemann-gas">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="true" data-search="sparse-router-formal formally verified locality-aware work-stealing scheduler: rust with kani proofs, lean 4, pascal and c references. rust lean4 pascal model sl-agpl3-001 covenant">
<div class="card-top"><span class="badge new">New</span><span class="badge kind">model</span><span class="badge lic">SL-AGPL3-001</span></div>
<h3><a href="https://huggingface.co/Snapkitty/sparse-router-formal">sparse-router-formal</a></h3>
<p>Formally verified locality-aware work-stealing scheduler: Rust with Kani proofs, Lean 4, Pascal and C references.</p>
<div class="card-foot"><div class="tags"><span class="tag">rust</span><span class="tag">lean4</span><span class="tag">pascal</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/sparse-router-formal">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/sparse-router-formal">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="true" data-search="unlambda-idris-spark handwritten unlambda derivations with checked proof terms in idris 2, ats and spark ada. unlambda idris ada model proprietary">
<div class="card-top"><span class="badge new">New</span><span class="badge kind">model</span><span class="badge lic">Proprietary</span></div>
<h3><a href="https://huggingface.co/Snapkitty/unlambda-idris-spark">unlambda-idris-spark</a></h3>
<p>Handwritten Unlambda derivations with checked proof terms in Idris 2, ATS and SPARK Ada.</p>
<div class="card-foot"><div class="tags"><span class="tag">unlambda</span><span class="tag">idris</span><span class="tag">ada</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/unlambda-idris-spark">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/unlambda-idris-spark">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="false" data-search="aes-verification-suite formal verification of aes implementation correctness. exhaustive test vectors, proof certificates. lean4 python model tri-license">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Tri-License</span></div>
<h3><a href="https://huggingface.co/Snapkitty/aes-verification-suite">aes-verification-suite</a></h3>
<p>Formal verification of AES implementation correctness. Exhaustive test vectors, proof certificates.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">python</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/aes-verification-suite">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/aes-verification-suite">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="false" data-search="ahmad-foundations mathematical foundations in lean 4. nlbhe, e7 lattice, black hole gravity, f4 algebra. 30+ zero-sorry theorems. lean4 model tri-license">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Tri-License</span></div>
<h3><a href="https://huggingface.co/Snapkitty/ahmad-foundations">ahmad-foundations</a></h3>
<p>Mathematical foundations in Lean 4. NLBHE, E7 lattice, black hole gravity, F4 algebra. 30+ zero-sorry theorems.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/ahmad-foundations">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/ahmad-foundations">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="false" data-search="cosmic-invariant-sieve invariant extraction and verification sieve for algebraic structures. lean4 python model sovereign source">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Sovereign Source</span></div>
<h3><a href="https://huggingface.co/Snapkitty/cosmic-invariant-sieve">cosmic-invariant-sieve</a></h3>
<p>Invariant extraction and verification sieve for algebraic structures.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">python</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/cosmic-invariant-sieve">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/cosmic-invariant-sieve">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="false" data-search="forge-polyglot-verifier cross-language verification: proofs hold across lean 4, agda, haskell, and runtime implementations. lean4 agda haskell model sovereign source">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Sovereign Source</span></div>
<h3><a href="https://huggingface.co/Snapkitty/forge-polyglot-verifier">forge-polyglot-verifier</a></h3>
<p>Cross-language verification: proofs hold across Lean 4, Agda, Haskell, and runtime implementations.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">agda</span><span class="tag">haskell</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/forge-polyglot-verifier">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/forge-polyglot-verifier">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="false" data-search="hyperkitty-constraint-dsl constraint dsl for hyperkitty pipeline with wasm compilation and formal barrier proofs. rust wasm model bsl-1.1">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">BSL-1.1</span></div>
<h3><a href="https://huggingface.co/Snapkitty/hyperkitty-constraint-dsl">hyperkitty-constraint-dsl</a></h3>
<p>Constraint DSL for HyperKitty pipeline with WASM compilation and formal barrier proofs.</p>
<div class="card-foot"><div class="tags"><span class="tag">rust</span><span class="tag">wasm</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/hyperkitty-constraint-dsl">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/hyperkitty-constraint-dsl">GitHub</a></div></div>
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<article class="card" data-kind="model" data-new="false" data-search="integrity-constraint-governance mumps+asp integrity constraint dag with 10 invariants. nothing executes without passing the graph. mumps asp model tri-license">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Tri-License</span></div>
<h3><a href="https://huggingface.co/Snapkitty/integrity-constraint-governance">integrity-constraint-governance</a></h3>
<p>MUMPS+ASP integrity constraint DAG with 10 invariants. Nothing executes without passing the graph.</p>
<div class="card-foot"><div class="tags"><span class="tag">mumps</span><span class="tag">asp</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/integrity-constraint-governance">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/integrity-constraint-governance">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="j-matrix-twin jacobian matrix formalization with interactive playground. 79 theorems, sovmonster proof suite. lean4 javascript model bsl-1.1">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">BSL-1.1</span></div>
<h3><a href="https://huggingface.co/Snapkitty/j-matrix-twin">j-matrix-twin</a></h3>
<p>Jacobian matrix formalization with interactive playground. 79 theorems, SovMonster proof suite.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">javascript</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/j-matrix-twin">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/j-matrix-twin">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="pure-validity pure validity checking framework with formal proof obligations and deterministic verification. lean4 model agpl-3.0">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">AGPL-3.0</span></div>
<h3><a href="https://huggingface.co/Snapkitty/pure-validity">pure-validity</a></h3>
<p>Pure validity checking framework with formal proof obligations and deterministic verification.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/pure-validity">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/pure-validity">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="quantabeta-core core mathematical engine for quantized algebraic beta reduction with formal proof obligations. lean4 haskell model sovereign source">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Sovereign Source</span></div>
<h3><a href="https://huggingface.co/Snapkitty/quantabeta-core">quantabeta-core</a></h3>
<p>Core mathematical engine for quantized algebraic beta reduction with formal proof obligations.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">haskell</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/quantabeta-core">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/quantabeta-core">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="snapkitty-open-source formally specified integrity dag that gates every claim, proof, decision and execution in an ai pipeline. lean4 python model agpl-3.0">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">AGPL-3.0</span></div>
<h3><a href="https://huggingface.co/Snapkitty/snapkitty-open-source">snapkitty-open-source</a></h3>
<p>Formally specified integrity DAG that gates every claim, proof, decision and execution in an AI pipeline.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">python</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/snapkitty-open-source">Hugging Face</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="sov-kernel-monster sovereign method repository. public code, proofs, specs vs sovereign authority, state, execution boundary. lean4 fortran agda model sovereign source">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Sovereign Source</span></div>
<h3><a href="https://huggingface.co/Snapkitty/sov-kernel-monster">sov-kernel-monster</a></h3>
<p>Sovereign method repository. Public code, proofs, specs vs sovereign authority, state, execution boundary.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">fortran</span><span class="tag">agda</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/sov-kernel-monster">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/sov-kernel-monster">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="sovereign-array new array language with dependent types for shapes. broadcasting as pullbacks. verified softmax and nand attention. lean4 python model agpl-3.0">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">AGPL-3.0</span></div>
<h3><a href="https://huggingface.co/Snapkitty/sovereign-array">sovereign-array</a></h3>
<p>New array language with dependent types for shapes. Broadcasting as pullbacks. Verified softmax and NAND attention.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">python</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/sovereign-array">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/sovereign-array">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="sovereign-entropy-theorem hallucination elimination via discrete minimization (h &lt; 0.20 nats). lean 4, agda, python, cuda-q. lean4 agda python cuda model sovereign source">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Sovereign Source</span></div>
<h3><a href="https://huggingface.co/Snapkitty/sovereign-entropy-theorem">sovereign-entropy-theorem</a></h3>
<p>Hallucination elimination via discrete minimization (H &lt; 0.20 nats). Lean 4, Agda, Python, CUDA-Q.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">agda</span><span class="tag">python</span><span class="tag">cuda</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/sovereign-entropy-theorem">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/sovereign-entropy-theorem">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="sovereign-forge compact c99 verification kernel. linear-algebra witnesses with exact int64 arithmetic. lean 4 proofs. c lean4 model bsl-1.1">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">BSL-1.1</span></div>
<h3><a href="https://huggingface.co/Snapkitty/sovereign-forge">sovereign-forge</a></h3>
<p>Compact C99 verification kernel. Linear-algebra witnesses with exact int64 arithmetic. Lean 4 proofs.</p>
<div class="card-foot"><div class="tags"><span class="tag">c</span><span class="tag">lean4</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/sovereign-forge">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/sovereign-forge">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="sovereign-multiplicity c++20 multiplicity functor. rational exponentiation, overflow detection, nth-root binary search. c++ model agpl-3.0">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">AGPL-3.0</span></div>
<h3><a href="https://huggingface.co/Snapkitty/sovereign-multiplicity">sovereign-multiplicity</a></h3>
<p>C++20 multiplicity functor. Rational exponentiation, overflow detection, nth-root binary search.</p>
<div class="card-foot"><div class="tags"><span class="tag">c++</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/sovereign-multiplicity">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/sovereign-multiplicity">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="sovereign-trinity-kernel latex package: every cryptographic number proved by lean 4, verified by dex kernels, orchestrated by 6502 vm. lean4 latex 6502 asm model tri-license">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">Tri-License</span></div>
<h3><a href="https://huggingface.co/Snapkitty/sovereign-trinity-kernel">sovereign-trinity-kernel</a></h3>
<p>LaTeX package: every cryptographic number proved by Lean 4, verified by Dex kernels, orchestrated by 6502 VM.</p>
<div class="card-foot"><div class="tags"><span class="tag">lean4</span><span class="tag">latex</span><span class="tag">6502 asm</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/sovereign-trinity-kernel">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/sovereign-trinity-kernel">GitHub</a></div></div>
</article>
<article class="card" data-kind="model" data-new="false" data-search="xrex-invariants-formal formal verification of computational kernel behavior. agda proofs, scala runtime, starlark build gates. agda scala haskell model snapkitty">
<div class="card-top"><span class="badge kind">model</span><span class="badge lic">SnapKitty</span></div>
<h3><a href="https://huggingface.co/Snapkitty/xrex-invariants-formal">xrex-invariants-formal</a></h3>
<p>Formal verification of computational kernel behavior. Agda proofs, Scala runtime, Starlark build gates.</p>
<div class="card-foot"><div class="tags"><span class="tag">agda</span><span class="tag">scala</span><span class="tag">haskell</span></div><div class="links"><a class="link" href="https://huggingface.co/Snapkitty/xrex-invariants-formal">Hugging Face</a><a class="link" href="https://github.com/SNAPKITTYWEST/xrex-invariants-formal">GitHub</a></div></div>
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<h2>Commercial license</h2>
<p>SnapKitty code is free and open under AGPL-3.0 for open-source use. Building a commercial product or service? A proprietary commercial license from Snapkitty Collective LLC lets you ship SnapKitty code without the AGPL's source-sharing and network-use obligations.</p>
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<a class="btn" href="mailto:A.parr@belespritdaccord.uk?subject=SnapKitty%20commercial%20license">Get a commercial license</a>
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