Carry Mixing and Spectral Gap Analysis of the Collatz Conjecture: 202 Lean4 Theorems and the Fibonacci Firewall
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2026
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| _version_ | 1866902019151757312 |
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| author | Fujimoto, Nobuki Claude, Anthropic AI Gemini, Google AI |
| author_facet | Fujimoto, Nobuki Claude, Anthropic AI Gemini, Google AI |
| contents | A structural proof chain for the Collatz conjecture: 202 Lean4 theorems (zero sorry). Introduces Carry Mixing mechanism (firewall at consecutive zero-bits), Fibonacci Firewall (F(k+2)/2^k exponential decay), spectral gap analysis (gap >= 0.345), and Perelman-Collatz structural correspondence. Reduces Collatz to Carry Mixing Conjecture (CMC), strictly weaker than full equidistribution. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19495462 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Carry Mixing and Spectral Gap Analysis of the Collatz Conjecture: 202 Lean4 Theorems and the Fibonacci Firewall Fujimoto, Nobuki Claude, Anthropic AI Gemini, Google AI Collatz conjecture carry propagation spectral gap Fibonacci Lean4 formal verification Perelman correspondence A structural proof chain for the Collatz conjecture: 202 Lean4 theorems (zero sorry). Introduces Carry Mixing mechanism (firewall at consecutive zero-bits), Fibonacci Firewall (F(k+2)/2^k exponential decay), spectral gap analysis (gap >= 0.345), and Perelman-Collatz structural correspondence. Reduces Collatz to Carry Mixing Conjecture (CMC), strictly weaker than full equidistribution. |
| title | Carry Mixing and Spectral Gap Analysis of the Collatz Conjecture: 202 Lean4 Theorems and the Fibonacci Firewall |
| topic | Collatz conjecture carry propagation spectral gap Fibonacci Lean4 formal verification Perelman correspondence |
| url | https://doi.org/10.5281/zenodo.19495462 |