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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.20255281 |
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| _version_ | 1866901989196038144 |
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| author | The Clankers |
| author_facet | The Clankers |
| contents | <p>This preprint proves a universal affine noncoincidence theorem for multiplicative functions, classifies the exact prime and prime-power extremizers in Goldbach-type correlations of completely multiplicative {±1}-valued functions, establishes bounded-conductor twist obstructions and averaged scarcity results for powers of high-order characters, derives rigidity consequences from approximate quadratic Gauss-sum dilation symmetry including Liouville lower bounds and finite-image comparator theorems, and proves abundance results for additive-gap examples satisfying universal affine noncoincidence.</p><p>The arguments use published results of A. P. Mangerel and collaborators together with nearby source literature. Every theorem in the main text is proved from cited results, and finite computations are confined to supplementary verification files.</p><p>For provenance: the initial search for statements of the kind proved here was carried out by asking ChatGPT 5.4 Pro mode, across three successive runs, and later Codex, to examine the cited source papers and look for further theorem-level consequences. The manuscript includes only statements proved from cited literature.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20255281 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Universal Affine Noncoincidence, Exact Prime-Power Goldbach Extremizers, and Finite-Image Rigidity for Character Sums The Clankers <p>This preprint proves a universal affine noncoincidence theorem for multiplicative functions, classifies the exact prime and prime-power extremizers in Goldbach-type correlations of completely multiplicative {±1}-valued functions, establishes bounded-conductor twist obstructions and averaged scarcity results for powers of high-order characters, derives rigidity consequences from approximate quadratic Gauss-sum dilation symmetry including Liouville lower bounds and finite-image comparator theorems, and proves abundance results for additive-gap examples satisfying universal affine noncoincidence.</p><p>The arguments use published results of A. P. Mangerel and collaborators together with nearby source literature. Every theorem in the main text is proved from cited results, and finite computations are confined to supplementary verification files.</p><p>For provenance: the initial search for statements of the kind proved here was carried out by asking ChatGPT 5.4 Pro mode, across three successive runs, and later Codex, to examine the cited source papers and look for further theorem-level consequences. The manuscript includes only statements proved from cited literature.</p> |
| title | Universal Affine Noncoincidence, Exact Prime-Power Goldbach Extremizers, and Finite-Image Rigidity for Character Sums |
| url | https://doi.org/10.5281/zenodo.20255281 |