Kaydedildi:
| Yazar: | |
|---|---|
| Materyal Türü: | Recurso digital |
| Dil: | İngilizce |
| Baskı/Yayın Bilgisi: |
Zenodo
2026
|
| Konular: | |
| Online Erişim: | https://doi.org/10.5281/zenodo.20173678 |
| Etiketler: |
Etiketle
Etiket eklenmemiş, İlk siz ekleyin!
|
| _version_ | 1866901756709961728 |
|---|---|
| author | papanokechi, papanokechi |
| author_facet | papanokechi, papanokechi |
| contents | <p>We test whether simple low-dimensional integer relations occur among coordinates<br>derived from the empirical Khinchin-signature statistic S_n, evaluated on the<br>continued-fraction partial quotients of π. Using agreement across 256-, 512-, and<br>1024-bit runs, we isolate the maximal certified segment n=1,…,91 and perform PSLQ<br>searches on six fixed 3D/4D templates at 300-digit working precision with 600-digit<br>confirmation. Under the conservative bound maxcoeff=10^3 and residual threshold<br>10^{-20}, all 546 template-specific attempts are unsupported. A wide-cap diagnostic<br>rerun with maxcoeff=10^6 yields only high-coefficient fits, concentrated almost<br>entirely in the 4-dimensional template, and these disappear completely when the<br>conservative cap is restored. The outcome is therefore a reproducible,<br>precision-controlled null result for the tested coordinate family rather than<br>evidence of hidden arithmetic dependence. Open directions include coordinate<br>families involving nonlinear functions of the index, algebraic combinations with<br>additional constants, and longer certified prefixes obtainable only through still<br>higher-precision stabilization. A replication on e produces a consistent null<br>outcome, supporting the generality of the methodology.<br><br><br></p> <p>Companion archival deposit for a manuscript submitted to a peer-reviewed venue; the deposited file is the anonymized form per the venue's blinding policy. For citation use the concept DOI <a href="https://doi.org/10.5281/zenodo.20173677">10.5281/zenodo.20173677</a>, which always resolves to the latest version; see related-identifier entries for the SIARC-umbrella isPartOf links and the PCF-1 / PCF-2 citation graph.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20173678 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Precision-Controlled Null Result for a Khinchin-Signature PSLQ Family papanokechi, papanokechi PSLQ Khinchin constant continued fractions null result precision-controlled experiment experimental mathematics integer relation detection <p>We test whether simple low-dimensional integer relations occur among coordinates<br>derived from the empirical Khinchin-signature statistic S_n, evaluated on the<br>continued-fraction partial quotients of π. Using agreement across 256-, 512-, and<br>1024-bit runs, we isolate the maximal certified segment n=1,…,91 and perform PSLQ<br>searches on six fixed 3D/4D templates at 300-digit working precision with 600-digit<br>confirmation. Under the conservative bound maxcoeff=10^3 and residual threshold<br>10^{-20}, all 546 template-specific attempts are unsupported. A wide-cap diagnostic<br>rerun with maxcoeff=10^6 yields only high-coefficient fits, concentrated almost<br>entirely in the 4-dimensional template, and these disappear completely when the<br>conservative cap is restored. The outcome is therefore a reproducible,<br>precision-controlled null result for the tested coordinate family rather than<br>evidence of hidden arithmetic dependence. Open directions include coordinate<br>families involving nonlinear functions of the index, algebraic combinations with<br>additional constants, and longer certified prefixes obtainable only through still<br>higher-precision stabilization. A replication on e produces a consistent null<br>outcome, supporting the generality of the methodology.<br><br><br></p> <p>Companion archival deposit for a manuscript submitted to a peer-reviewed venue; the deposited file is the anonymized form per the venue's blinding policy. For citation use the concept DOI <a href="https://doi.org/10.5281/zenodo.20173677">10.5281/zenodo.20173677</a>, which always resolves to the latest version; see related-identifier entries for the SIARC-umbrella isPartOf links and the PCF-1 / PCF-2 citation graph.</p> |
| title | A Precision-Controlled Null Result for a Khinchin-Signature PSLQ Family |
| topic | PSLQ Khinchin constant continued fractions null result precision-controlled experiment experimental mathematics integer relation detection |
| url | https://doi.org/10.5281/zenodo.20173678 |