A Complete Conditional Proof that P ≠ NP via the Fractal Geometry of 3‑SAT Solution Spaces
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| Natura: | Recurso digital |
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2026
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| _version_ | 1866901775266611200 |
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| author | Derscariu, Radu-Daniel |
| author_facet | Derscariu, Radu-Daniel |
| contents | <p>We present a complete conditional proof that P ≠ NP, reducing the problem to the single standard hypothesis #P ≠ FP. The proof integrates the topological barrier (Alasli 2025), the #P‑hardness of the second Betti number (Schmidhuber–Lloyd 2023, Derscariu 2026), the collapse theorem (Alasli 2026), the Overlap Gap Property (Gamarnik 2021), the Franz–Parisi/SQ equivalence (Chen et al. 2025), and Recovery Reductions (Nareddy–Mishra 2025). Extensive experimental validation – annihilation of canonical barriers, direct Betti measurements, confirmation of the Valiant reduction on 20 graphs – provides overwhelming empirical support. The only remaining hypothesis is the widely believed assumption #P ≠ FP.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20217928 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Complete Conditional Proof that P ≠ NP via the Fractal Geometry of 3‑SAT Solution Spaces Derscariu, Radu-Daniel P vs NP topological barrier Betti numbers #P-hardness Overlap Gap Property Franz–Parisi Recovery Reductions fractal geometry <p>We present a complete conditional proof that P ≠ NP, reducing the problem to the single standard hypothesis #P ≠ FP. The proof integrates the topological barrier (Alasli 2025), the #P‑hardness of the second Betti number (Schmidhuber–Lloyd 2023, Derscariu 2026), the collapse theorem (Alasli 2026), the Overlap Gap Property (Gamarnik 2021), the Franz–Parisi/SQ equivalence (Chen et al. 2025), and Recovery Reductions (Nareddy–Mishra 2025). Extensive experimental validation – annihilation of canonical barriers, direct Betti measurements, confirmation of the Valiant reduction on 20 graphs – provides overwhelming empirical support. The only remaining hypothesis is the widely believed assumption #P ≠ FP.</p> |
| title | A Complete Conditional Proof that P ≠ NP via the Fractal Geometry of 3‑SAT Solution Spaces |
| topic | P vs NP topological barrier Betti numbers #P-hardness Overlap Gap Property Franz–Parisi Recovery Reductions fractal geometry |
| url | https://doi.org/10.5281/zenodo.20217928 |