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| Hlavní autor: | |
|---|---|
| Médium: | Recurso digital |
| Jazyk: | angličtina |
| Vydáno: |
Zenodo
2026
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| Témata: | |
| On-line přístup: | https://doi.org/10.5281/zenodo.20173678 |
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- <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>